Problem 15.1 In Active Example 15.1, what is the velocity of the container when it has reached the position s = 2m?


 Chad Morton
 2 years ago
 Views:
Transcription
1 Problem 5. In Active Example 5., what is the velocity of the container when it has reached the position s = m? A s The 8kg container A starts from rest at s =. The horizontal force (in newtons) is F = 7 5s. The coefficient of kinetic friction is µ k =.6. U = T T (7 5s.6[8(9.8)])ds = (8 kg)v 7() (5)() (.6[8(9.8)][]) = 9v v =.4 m/s. Problem 5. The mass of the Sikorsky UH6A helicopter is 93 kg. It takes off vertically with its rotor exerting a constant upward thrust of kn. Use the principle of work and energy to determine how far it has risen when its velocity is 6 m/s. Strategy: Be sure to draw the freebody diagram of the helicopter. U = T T [( 93[9.8])N]h = (93 kg)(6 m/s) h = 8.6 m. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 79
2 Problem 5.3 The N box is at rest on the horizontal surface when the constant force F = 5 N is applied. The coefficient of kinetic friction between the box and the surface is µ k =.. Determine how fast the box is moving when it has moved m from its initial position by applying Newton s second law; by applying the principle of work and energy. F The equations of motion can be used to find the acceleration F x : F f = W g a, F y : N W =, f = µ k N Solving we have ( ) ) F 5N a = g W µ k = ( )( N. 9.8m/s =.49 m/s Now we integrate to find the velocity at the new position a = v dv v m ds vdv = ads v = a( m) = (.49 m/s )( m) v =. 4 m/s Using the principle of work and energy we have (recognizing that N = W ) U = T T (F µ k N)d = ( ) W v g ( ) ) F 5N v = g W µ k d = ( 9.8 m/s )( N. ( m) v =.4 m/s Problem 5.4 At the instant shown, the 3N box is moving up the smooth inclined surface at m/s. The constant force F = 5 N. How fast will the box be moving when it has moved m up the surface from its present position? F U = T T = Solving we find [(5 N) cos (3 N) sin ]( m) ( ) 3 N v ( ) 3 N ( m/s) 9.8 m/s 9.8 m/s v =.55 m/s. 8 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
3 Problem 5.5 The.45kg soccer ball is m above the ground when it is kicked straight upward at m/s. By using the principle of work and energy, determine: how high above the ground the ball goes, the magnitude of the ball s velocity when it falls back to a height of m above the ground, (c) the magnitude of the ball s velocity immediately before it hits the ground. m/s m Find the height above the ground mg( m h) = mv, h = v g + m= ( m/s) (9.8 m/s + m= 6. m ) When the ball returns to the same level, the velocity must be equal to the initial velocity (but now it is moving downward) because the net work is zero v = m/s (c) The velocity just before it hits the ground mg( m) = mv mv v = v + g( m) = ( m/s) + (9.8 m/s )( m) v =.9 m/s. h = 6. m, v =. m/s, (c) v =.9 m/s. Problem 5.6 Assume that the soccer ball in Problem 5.5 is stationary the instant before it is kicked upward at m/s. The duration of the kick is. s. What average power is transferred to the ball during the kick? U = (.45 kg)( m/s) = 3.4 Nm Power = U t = 3.4 Nm. s =.6 kw c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 8
4 Problem 5.7 The N drag racer starts from rest and travels a quarterkilometre course. It completes the cours in 4.54 seconds and crosses the finish line traveling at km/h. How much work is done on the car as it travels the course? Assume that the horizontal force exerted on the car is constant and use the principle of work and energy to determine it. e The work is equal to the change in kinetic energy. U = mv = ( )[ ( N )] (35.77 km/h) 9.8 m/s 36 U = Nm The work is equal to the force times the distance U = Fd F = U d = Nm 4 ( ) = 3339 N m F = 3339 N Problem 5.8 The N drag racer starts from rest and travels a quarterkilometre course. It completes the course in 4.54 seconds and crosses the finish line traveling at km/h. Assume that the horizontal force exerted on the car is constant. Determine the maximum power and the average power transferred to the car as it travels the quarterkilometre course. From problem 5.7 we know that the force is The maximum power occurs when the car has reached its maximum velocity ( ) P = Fv= ( 3339 N)(35.77 km/h) = 3. 5 N m/s. 36 The average power is equal to the change in kinetic energy divided by the time. ( )[ ( )] N (35.77 km/h) P ave = mv 9.8 m/s 36 = t 4.54 s 5 =. 845 Nm/s Nm/s, Nm/s. 8 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
5 Problem 5.9 As the 3,N airplane takes off, the tangential component of force exerted on it by its engines is F t = 45, N. Neglecting other forces on the airplane, use the principle of work and energy to determine how much runway is required for its velocity to reach km/h. U = mv Fd = mv d = mv F ( )[ ( 3, N )] ( km/h) 9.8 m/s 36 d = = m. (45, N) d = m Problem 5. As the 3,N airplane takes off, the tangential component of force exerted on it by its engines is F t = 45, N. Neglecting other forces on the airplane, determine the maximum power and the average power transferred to the airplane as its velocity increases from zero to km/h. The maximum power occurs when the velocity is a maximum [ ] P = Fv = (45, N) km/h =.5 6 N m/s. 36 To find the average power we need to know the time that it takes to reach full speed a = F m = ( 45, N ) = 3.8 m/s 3, N 9.8 m/s v = at t = v km/h a = 36 = 4.3 s. 3.8 m/s Now, the average power is the change in kinetic energy divided by the time ( )( ) 3, N P ave = mv km/h 9.8 m/s 36 6 = =.5 Nm/s. t 4.3 s.5 6 Nm/s,.5 6 Nm/s. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 83
6 Problem 5. The 3,N airplane takes off from rest in the position s =. The total tangential force exerted on it by its engines and aerodynamic drag (in Newtons) is given as a function of its position s by F t = 45, 5.s. Use the principle of work and energy to determine how fast the airplane is traveling when its position is s = 95 m. 95 U = (45, 5.s)ds = (45, )(95) (5.)(95) = Nm U = mv = ( ) 3, N v 9.8 m/s Solving, we find v = 57.4 m/s. Problem 5. The spring (k = N/m) is unstretched when s =. The 5kg cart is moved to the position s = m and released from rest. What is the magnitude of its velocity when it is in the position s =? k s First we calculate the work done by the spring and by gravity U = ( ks + mg sin ) ds m = k( m) + mg sin (m) = ( N/m)( m) + (5 kg)(9.8 m/s ) sin (m) = 6.8 Nm. Now using work and energy U = mv v = U m = (6.8 Nm) = 3.7 m/s. 5kg v = 3.7 m/s. 84 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
7 Problem 5.3 The spring (k = N/m) is unstretched when s =. The 5kg cart is moved to the position s = m and released from rest. What maximum distance down the sloped surface does the cart move relative to its initial position? k s The cart starts from a position of rest, and when it reaches the maximum position, it is again at rest. Therefore, the total work must be zero. s U = ( ks + mg sin ) ds m = k(s [ m] ) + mg sin (s [ m]) = ( N/m)(s [ m] ) + (5 kg)(9.8 m/s ) sin (s [ m]) = This is a quadratic equation that has the two solutions s = m,s =.68 m. The distance relative to the initial is s = s + m. s = 3.68 m. Problem 5.4 The force exerted on a car by a prototype crash barrier as the barrier crushes is F = (s + 4s 3 ) N, where s is the distance in metre from the initial contact. The effective length of the barrier is 8 m. How fast can a 5N car be moving and be brought to rest within the effective length of the barrier? s The barrier can provide a maximum amount of work given by 8 U = (s + 4s 3 ) ds = ()(8) 4 (4)(8)4 =.7 6 Nm. Using work and energy, we have U = mv.7 6 m = ( ) 5 N N v 9.8 m/s Solving for the velocity, we find v = 64.8 m/s. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 85
8 Problem 5.5 A 5N car hits the crash barrier at 8 km/h and is brought to rest in. seconds. What average power is transferred from the car during the impact? s The average power is equal to the change in kinetic energy divided by the time ( )( ) 5 N 8 km/h P = mv 9.8 m/s 36 = =.4 6 N m/s. t. s P =.4 6 Nm/s. Problem 5.6 A group of engineering students constructs a sunpowered car and tests it on a circular track with a m radius. The car, with a weight of 46 N including its occupant, starts from rest. The total tangential component of force on the car is F t = 3.s N, where s is the distance (in ft) the car travels along the track from the position where it starts. Determine the work done on the car when it has gone a distance s = m. Determine the magnitude of the total horizontal force exerted on the car s tires by the road when it is at the position s = m. m U = [3. s] Nds = 6 Nm 6 Nm = ( ) 46 N v 9.8 m/s v = 9.6 m/s F t = [3.()] = 6N ( ) F n = m v 46 N ( ) ρ = 9.6 m/s 9.8 m/s m = 4.3 N F = F t + F n = (6N) + (4.3 N) = 7.39 N 86 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
9 Problem 5.7 At the instant shown, the 6N vaulter s center of mass is 8.5 m above the ground, and the vertical component of his velocity is 4 m/s. As his pole straightens, it exerts a vertical force on the vaulter of magnitude 8 +.8y N, where y is the vertical position of his center of mass relative to its position at the instant shown. This force is exerted on him from y = toy = 4 m, when he releases the pole. What is the maximum height above the ground reached by the vaulter s center of mass? The work done on him by the pole is 4 U pole = (8 +.8 y )dy = 8(4) +.8 (4)3 3 = 78 N m. Let y max be his maximum height above the ground. The work done by his weight from the instant shown to the maximum height is 6(y max 8.5) = U weight,oru weight + U pole = mv / mv / 78 6(y max 8.5) = ( ) 6 (4). 9.8 Solving, y max = 4. m Problem 5.8 The springs (k = 5 N/ cm) are unstretched when s =. The 5N weight is released from rest in the position s =. When the weight has fallen cm, how much work has been done on it by each spring? What is the magnitude of the velocity of the weight when it has fallen cm? k k s The work done by each spring cm U = ksds = (5 N/cm)(cm) =.5 Ncm. The velocity is found from the workenergy equation. The total work includes the work done by both springs and by gravity U = (5 N)( cm) (.5 Ncm) = 5 Ncm. U = mv = ( ) 5 N v 9.8 m/s Solving for the velocity we find v =.3 m/s..5 Ncm,.3 m/s. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 87
10 Problem 5.9 The coefficients of friction between the 6kg crate and the ramp are µ s =.3 and µ k =.8. What tension T must the winch exert to start the crate moving up the ramp? If the tension remains at the value T after the crate starts sliding, what total work is done on the crate as it slides a distance s = 3 m up the ramp, and what is the resulting velocity of the crate? 8 s The tension is T = W sin θ + µ s N, from which T = mg(sin θ + µ s cos θ) = 93.9 N. The work done on the crate by (nonfriction) external forces is mg µ s N N T T mg N µ k N 3 3 U weight = T ds (mg sin θ)ds = 93.9(3) 455. = Nm. The work done on the crate by friction is 3 U f = ( µ k N)ds = 3µ k mg cos θ = 53.9 Nm. From the principle of work and energy is U weight + U f = mv, from which 6(T mg(sin θ + µ k cos θ)) v = m v =.6 m/s Problem 5. In Problem 5.9, if the winch exerts a tension T = T ( +.s) after the crate starts sliding, what total work is done on the crate as it slides a distance s = 3 m up the ramp, and what is the resulting velocity of the crate? The work done on the crate is From the principle of work and energy, U = mv, from which U = Tds (mg sin θ)ds µ k (mg cos θ)ds, from which v = U m =.5 m/s U = T [( s +.5s )] 3 (mg sin θ)(3) µ k(mg cos θ)(3). From the solution to Problem 5.9, T = 93.9 Nm, from which the total work done is U = = Nm. 88 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
11 Problem 5. The mmdiameter gas gun is evacuated on the right of the 8kg projectile. On the left of the projectile, the tube contains gas with pressure p = 5 Pa (N/m ). The force F is slowly increased, moving the projectile.5 m to the left from the position shown. The force is then removed and the projectile accelerates to the right. If you neglect friction and assume that the pressure of the gas is related to its volume by pv = constant, what is the velocity of the projectile when it has returned to its original position? m Gas Projectile F The constant is K = pv = 5 ()(.) π = 34.6 Nm. The force is F = pa. The volume is V = As, from which the pressure varies as the inverse distance: p = K, from which As F = K s. From the principle of work and energy, the work done by the gas is equal to the gain in kinetic energy: K ln() = mv, and v = K m ln(), The work done by the gas is K U = Fds= ds = [K ln(s)] x = K ln(). v = K m ln() = 3.33 m/s Note: The argument of ln() is dimensionless, since it is ratio of two distances. Problem 5. In Problem 5., if you assume that the pressure of the gas is related to its volume by pv = constant while it is compressed (an isothermal process) and by pv.4 = constant while it is expanding (an isentropic process), what is the velocity of the projectile when it has returned to its original position? The isothermal constant is K = 34.6 Nm from the solution to Problem 5.. The pressure at the leftmost position is p = K A(.5) = 5 N/m. The isentropic expansion constant is K e = pv.4 = ( 5 )(A.4 )(.5.4 ) = Nm The pressure during expansion is From the principle of work and energy, the work done is equal to the gain in kinetic energy, Fds=.5 mv, from which the velocity is (9.8) v = =.8 m/s. m p = K e (As).4 = K e A.4 s.4. The force is F = pa = K e A.4 s.4. The work done by the gas during expansion is.. [ s U = Fds= K e A.4 s.4 ds = K e A.4.4 ] = 9.8 Nm. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 89
12 Problem 5.3 In Example 5., suppose that the angle between the inclined surface and the horizontal is increased from to 3. What is the magnitude of the velocity of the crates when they have moved 4 mm? v A Doing work energy for the system B.4 (m A g sin 3 µ k m A g cos 3 + m B g)ds = (m A + m B )v v [4 sin 3 (.5)(4) cos 3 + 3](9.8)(.4) = (7)v Solving for the velocity we find v =.4 m/s. Problem 5.4 The system is released from rest. The 4kg mass slides on the smooth horizontal surface. By using the principle of work and energy, determine the magnitude of the velocity of the masses when the kg mass has fallen m. 4 kg kg Write workenergy for system U = ( kg)(9.8 m/s )( m) = (4 kg)v v = 4.4 m/s Problem 5.5 Solve Problem 5.4 if the coefficient of kinetic friction between the 4kg mass and the horizontal surface is µ k =.4. (4 kg)(9.8 m/s ) Fy : N (4 kg)(9.8 m/s ) = N = 39.4 N Write workenergy for system U = [( kg)(9.8 m/s ).4(39.4 N)]( m) = 8.5 Nm.4 N T 8.5 Nm = (4 kg)v v = 3.88 m/s N 9 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
13 Problem 5.6 Each box weighs 5 N and the inclined surfaces are smooth. The system is released from rest. Determine the magnitude of the velocities of the boxes when they have moved m Write workenergy for the system U = (5 N sin 45 )( m) (5 N sin 3 )( m) =.36 Nm.36 Nm = ( ) N v v =.43 m/s 9.8 m/s Problem 5.7 Solve Problem 5.6 if the coefficient of kinetic friction between the boxes and the inclined surfaces is µ k =.5. 5 N 5 N F : N (5 N) sin 45 = F : N (5 N) cos 3 =.5 N N = 35.4 N, N = 43.3 N Workenergy for the system U = (5 N sin 45 )( m) (.5)(35.4 N)( m) N N.5 N (5 N sin 3)( m) (.5)(43.3 N)( m) = 6.4 Nm 6.4 Nm = ( ) N v v =. m/s 9.8 m/s c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 9
14 Problem 5.8 The masses of the three blocks are m A = 4 kg, m B = 6 kg, and m C = kg. Neglect the mass of the bar holding C in place. Friction is negligible. By applying the principle of work and energy to A and B individually, determine the magnitude of their velocity when they have moved 5 mm. B C A 45 Denote b =.5 m. Since the pulley is onetoone, denote v A = v B =v. The principle of work and energy for weight A is b (m A g sin θ T)ds = m Av, b and for weight B (T m B g sin θ)ds = m Bv. T m A g T m B g N AB N AB N BC Add the two equations: N A (m A m B )gb sin θ = (m A + m B )v. (ma m Solve: B )gb sin θ v A = v B = =.7 m/s (m A + m B ) Problem 5.9 Solve Problem 5.8 by applying the principle of work and energy to the system consisting of A, B, the cable connecting them, and the pulley. Choose a coordinate system with the origin at the pulley axis and the positive x axis parallel to the inclined surface. Since the pulley is onetoone, x A = x B. Differentiate to obtain v A = v B. Denote b =.5 m. From the principle of work and energy the work done by the external forces on the complete system is equal to the gain in kinetic energy, xa xb m A g sin θds+ m B g sin θds= m AvA + m BvB, m B g N BC from which m A g (m B m A )gb sin θ = (m A + m B )v A N A (ma m and B ) v A = v B = gb sin θ =.7 m/s. (m A + m B ) 9 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
15 Problem 5.3 The masses of the three blocks are m A = 4 kg, m B = 6 kg, and m C = kg. The coefficient of kinetic friction between all surfaces is µ k =.. Determine the magnitude of the velocity of blocks A and B when they have moved 5 mm. (See Example 5.3.) We will apply the principles of work energy to blocks A and B individually in order to properly account for the work done by internal friction forces. A B C b (m A g sin θ T µ k N A µ k N AB ) ds = m Av, 45 b (T m B g sin θ µ k N BC µ k N AB ) ds = m Bv. Adding the two equations, we get ([m A m B ]g sin θ µ k [N A + N AB + N BC ])b = (m A + m B )v The normal forces are N A = (m A + m B + m C )g cos θ, N AB = (m B + m C )g cos θ, N BC = (m C )g cos θ. Substitute and solve v =.4 m/s. Problem 5.3 In Example 5.5, suppose that the skier is moving at m/s when he is in position. Determine the horizontal component of his velocity when he reaches position, m below position. 3 U = mg(y y ) = mv mv Solving for v we find m(9.8)( ) = mv m() v = 8. m/s. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 93
16 Problem 5.3 Suppose that you stand at the edge of a 6 m cliff and throw rocks at 9. m/s in the three directions shown. Neglecting aerodynamic drag, use the principle of work and energy to determine the magnitude of the velocity of the rock just before it hits the ground in each case. 3 3 (c) 6 m U = m( 9.8 m/s )( 6 m) = mv m( 9. m/s) v = 35.7 m/s Note that the answer does not depend on the initial angle. Problem 5.33 The 3kg box is sliding down the smooth surface at m/s when it is in position. Determine the magnitude of the box s velocity at position in each case. m The work done by the weight is the same in both cases. U = m(9.8 m/s )( m) = mv m( m/s) 6 4 v = 6.34 m/s Problem 5.34 Solve Problem 5.33 if the coefficient of kinetic friction between the box and the inclined surface is µ k =.. The work done by the weight is the same, however, the work done by friction is different. U = m(9.8 m/s )( m) (.)[m(9.8 m/s ) cos 6 ] [ ] m sin 6 U = mv m( m/s) v = 5.98 m/s U = m(9.8 m/s )( m) (.)[m(9.8 m/s ) cos 4 ] [ ] m sin 4 U = mv m( m/s) v = 5.56 m/s Problem 5.35 In case, a 5N ball is released from rest at position and falls to position. In case, the ball is released from rest at position and swings to position. For each case, use the principle of work and energy to determine the magnitude of the ball s velocity at position. (In case, notice that the force exerted on the ball by the string is perpendicular to the ball s path.) m the same. The work is independent of the path, so both cases are U = m( 9.8m/s )( m) = mv v = 6.6 m/s 94 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
17 Problem 5.36 The kg ball is released from rest in position with the string horizontal. The length of the string is L = m. What is the magnitude of the ball s velocity when it is in position? 4 L kg L sin α U = mgj dsj U = mg( L sin α) = ()(9.8)() sin 4 α m L = m L SIN α U =.6 Nm U = mv mv v ()v =.6 v = 3.55 m/s Problem 5.37 The kg ball is released from rest in position with the string horizontal. The length of the string is L = m. What is the tension in the string when the ball is in position? Strategy: Draw the freebody diagram of the ball when it is in position and write Newton s second law in terms of normal and tangential components. m = kg Fr : T + mg cos 5 = mv /L 4 From Problem 5.36, T v = 3.55 m/s T = mg cos 5 + mv /L e r e θ T = 37.8 N 5 mg c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 95
18 Problem 5.38 The 4N wrecker s ball swings at the end of a 5m cable. If the magnitude of the ball s velocity at position is 4 m/s, what is the magnitude of its velocity just before it hits the wall at position? U = (4 N)( 5 m sin 95 [ 5 m sin 65 ]) U = ( ) 4 N (v [4 m/s] ) 9.8 m/s v = 7.75 m/s Problem 5.39 The 4N wrecker s ball swings at the end of a 5m cable. If the magnitude of the ball s velocity at position is 4 m/s, what is the maximum tension in the cable as the ball swings from position to position? From the solution to Problem 5.37, the tension in the cable is T = mg sin α + m v. From the solution to Problem 5.38, L v = gl[sin α sin 65 ](65 α 95 ), from which T = 3 mg sin α mg sin 65. The maximum tension occurs when sin α is a maximum in the interval (65 α 95 ), from which T = 3 mg sin 9 mg sin 65 = N. 96 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
19 Problem 5.4 A stunt driver wants to drive a car through the circular loop of radius R = 5 m. Determine the minimum velocity v at which the car can enter the loop and coast through without losing contact with the track. What is the car s velocity at the top of the loop? R First, let us find V T V TOP = V T Fn : N + mg = mv T /R For minimum velocity, N mg = mv T /R ds = dxi + dyj R V T = Rg = 7. m/s Now find V using workenergy V U T = mgj (dxi + dyj) N U T = mg dy = mgy e t U T = 98.m (Nm) Also, U T = mv T mv = 98.m (Nm) e n mg Solving for V (V T = 7. m/s) V = V T + (98.)() V = 5.68 m/s Problem 5.4 The kg collar starts from rest at position and slides down the smooth rigid wire. The yaxis points upward. What is the magnitude of the velocity of the collar when it reaches position? y (5, 5, ) m kg x z (3,, 3) m The work done by the weight is U weight = mgh, where h = y y = 5 ( ) = 6 m. From the principle of work and energy, mgh = mv, from which v = gh =.85 m/s c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 97
20 Problem 5.4 The 4N collar slides down the smooth rigid wire from position to position. When it reaches position, the magnitude of its velocity is 4 m/s. What was the magnitude of its velocity at position? (, 6, 4) m 4 N y x z (4nN,, 4) m U = (4 N)(6 [ ]) = ( ) 4N m /s ([4 m/s] v 9.8 m ) v =.9 m/s Problem 5.43 The forces acting on the 5 kn airplane are the thrust T and drag D, which are parallel to the airplane s path, the lift L, which is perpendicular to the path, and the weight W. The airplane climbs from an altitude of 94 m to an altitude of 348 m. During the climb, the magnitude of its velocity decreases from 44 m/s to 83 m/s. What work is done on the airplane by its lift during the climb? What work is done by the thrust and drag combined? D L W T The work due to the lift L is zero since it acts perpendicular to the motion. U = U L+D ( 5 N)( ) m U = ( ) 5 N ([83 m/s] [44 m/s] ) 9.8 m/s U L+D =.7 7 Nm 98 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
21 Problem 5.44 The.7 kn car is traveling 64.4 km/h at position. If the combined effect of the aerodynamic drag on the car and the tangential force exerted on its wheels by the road is that they exert no net tangential force on the car, what is the magnitude of the car s velocity at position? m 3.5 m 3 The initial velocity is v = km/h = 7. 9 m/s The change in elevation of the car is h = 36.6( cos 3 ) + 3.5( cos 3 ) = 67.( cos 3 ) = 8.98 m From the principle of work and energy the work done is equal to the gain in kinetic energy: U gravity = from which ( ) W v g ( ) W v g, g( ) v = =.96 m/ s W The initial kinetic energy is ( ) W v g = N The work done by gravity is h U gravity = ( W)ds = Wh = 7(h) = Nm. Problem 5.45 The.7 kn car is traveling 64.4 km/h at position. If the combined effect of aerodynamic drag on the car and the tangential force exerted on its wheels by the road is that they exert a con. stant.78 kn tangential force on the car in the direction of its motion, what is the magnitude of the car s velocity at position? From the solution to Problem 5.44, the work done by gravity is U gravity = ( Nm ) due to the change in elevation of W the car of h = m, and v g = Nm. The length of road between positions and is ( s = (3 π ) ( π ) 36.6 ) (3 ) 8 = 35. m. The work done by the tangential force is s U tgt = 78 ds = 78 ( 35. ) = N m. From the principle of work and energy U gravity + U tgt = from which ( ) W v g ( ) W v g, ( 9. 8 )( ) v = 4 = 6. m/s = 57.9 km/ h c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 99
22 Problem 5.46 The mass of the rocket is 5 kg. Its engine has a constant thrust of 45 kn. The length of the launching ramp is m. If the magnitude of the rocket s velocity when it reaches the end of the ramp is 5 m/s, how much work is done on the rocket by friction and aerodynamic drag? m U = U Fr+Dr + (45 kn)( m) (5 kg)(9.8 m/s )( m) U = (5 kg)(5 m/s) U Fr+Dr = 7 knm Problem 5.47 A bioengineer interested in energy requirements of sports determines from videotape that when the athlete begins his motion to throw the 7.5kg shot (Fig. a), the shot is stationary and.5 m above the ground. At the instant the athlete releases it (Fig. b), the shot is. m above the ground. The shot reaches a maximum height of 4.6 m above the ground and travels a horizontal distance of 8.66 m from the point where it was released. How much work does the athlete do on the shot from the beginning of his motion to the instant he releases it? Let v x and v y be the velocity components at the instant of release. Using the chain rule, a y = dv y dt = dv y dy dy dt = dv y dy v y = g, y and integrating, 4.6 v y dv y = g dy. v y.. m vy vx 4.6 m 8.66 m x v y = g(4.6.), wefind that v y = 7. m/s. The shot s x and y coordinates are given by x = v x t, y =. + v y t gt. Solving the first equation for t and substituting it into the second, ( ) x y =. + v y ( ) x v x g v x Setting x = 8.66 m, y = in this equation and solving for v x gives v x =. m/s. The magnitude of the shot s velocity at release is U = v x + v y = 3. m/s. Let U A be the work he does U A mg(y y ) = mv mv U A (7.5 kg)(9.8 m/s )(..5) = (7.5)(3.), or U A = 666 Nm c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
23 Problem 5.48 A small pellet of mass m =. kg starts from rest at position and slides down the smooth surface of the cylinder to position, where θ = 3. What work is done on the pellet as it slides from position to position? What is the magnitude of the pellet s velocity at position?.8 m u m v = R =.8 m U = mv mv R R cos 3 3 U = (.5)(.)v =.v The work is U = (.)(9.8)(.8.8 cos 3 ) =. Nm. U =. (Nm).v =. (Nm) v =.45 m/s Problem 5.49 In Active Example 5.4, suppose that you want to increase the value of the spring constant k so that the velocity of the hammer just before it strikes the workpiece is 4 m/s. what is the required value of k? Hammer The 4kg hammer is released from rest in position. The springs are unstretched when in position. Neglect friction. k k 4 mm U = mgh + kd = mv k = m d ( v gh k = ) ( 4 kg [4 m] ) (. m) [9.8m/s ][.4m] Workpiece 3 mm k = 48 N/m. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
24 Problem 5.5 Suppose that you want to design a bumper that will bring a 5 N. package moving at m/s to rest 5.4 mm from the point of contact with bumper. If friction is negligible, what is the necessary spring constant k? m/s k From the principle of work and energy, the work done on the spring must equal the change in kinetic energy of the package within the distance 5.4 m. ks = from which ( ) W v g k = ( W g ) ( v ) ( )( 5 = S ) = 6 N/m Problem 5.5 In Problem 5.5, what spring constant is necessary if the coefficient of kinetic friction between the package and the floor is µ k =.3 and the package contacts the bumper moving at m/s? The work done on the spring over the stopping dis tance is S S U S = Fds= ks ds = ks. The work done by friction over the stopping distance is S S U f = Fds= µ k Wds= µ k WS. From the principle of work and energy the work done must equal the kinetic energy of the package: ks + µ k WS = ( ) W v, g from which, for S =.5 m, k = ( ) W (v gµ k S) g S = 863 N/m c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
25 Problem 5.5 The 5N package starts from rest, slides down the smooth ramp, and is stopped by the spring. If you want the package to be brought to rest.5 m from the point of contact, what is the necessary spring constant k? What maximum deceleration is the package subjected to? 3 4 m k Find the spring constant N U = mgh kx = k = mgh x = (5 N)(4.5 m)sin 3 (.5m) k = 9 N/m The maximum deceleration occurs when the spring reaches the maximum compression (the force is then the largest). kx mg sin θ = ma a = k m x g sin θ (9 N/m) a = ( ) (.5 m) ( 9.8m/s ) sin 3 5 N 9. 8 m/s a = 83.4 m/s Problem 5.53 The 5N package starts from rest, slides down the smooth ramp, and is stopped by the spring. The coefficient of static friction between the package and the ramp is µ k =.. If you want the package to be brought to rest.5 m from the point of contact, what is the necessary spring constant k? 4 m k 3 Find the spring constant U = mgd sin θ µ k mg cos θ d kx = k = mgd x (sin θ µ k cos θ) (5 N)(4.5m) k = (.5 ) (sin 3. cos 3 ) m k = 73 N/ m. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 3
26 Problem 5.54 The system is released from rest with the spring unstretched. The spring constant k = N/m. Determine the magnitude of the velocity of the masses when the right mass has fallen m. 4 kg kg k When the larger mass falls m, the smaller mass rises m and the spring stretches m. For the system of two masses, springs, and the cable, U = ( ks)ds + ( m g) ds + m gds U = ks m gs + m gs U = k 4(9.8) + ()(9.8) U = Nm Also U = (m + m )V f m m 4 kg kg k Solving V f =.8 m/s Problem 5.55 The system is released from rest with the spring unstretched. The spring constant k = N/m. What maximum downward velocity does the right mass attain as it falls? From the solution to Problem 5.54, U = Ks + (m m )gs and U = (m + m )V For all s. Setting these equal, we get (m + m )V = (m m )gs Ks () Solve for dv ds and set dv ds to zero (m + m )v dv ds = (m m )g Ks = The extreme value for V occurs at S = (m m )g K =.785 m Substituting this back into () and solving, we get V =.7 m/s 4 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
27 Problem 5.56 The system is released from rest. The 4kg mass slides on the smooth horizontal surface. The spring constant is k = N/m, and the tension in the spring when the system is released is 5 N. By using the principle of work and energy, determine the magnitude of the velocity of the masses when the kg mass has fallen m. k 4 kg kg 5 N = ( N/m)x x =.5 m U = ( kg)(9.8 m/s )( m) ( N/m)([.5 m] [.5 m] ) U = (4 kg)(v ) v =.83 m/s Problem 5.57 Solve Problem 5.56 if the coefficient of kinetic friction between the 4kg mass and the horizontal surface is µ k =.4. 5 N = ( N/m)x x =.5 m U = ( kg)(9.8 m/s )( m) ( N/m)([.5 m] [.5 m] ) (.4)(4 kg)(9.8 m/s )( m) U = (4 kg)(v ) v =.59 m/s c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 5
28 Problem 5.58 The 4 N crate is released from rest on the smooth inclined surface with the spring unstretched. The spring constant is k = 8 N/ m. How far down the inclined surface does the crate slide before it stops? What maximum velocity does the crate attain on its way down? k 3 At an arbitrary distance s down the slope we have: U = (4 N)(s sin 3 ) (8 N/m)s = ( 4 N ) v 9.8 m/s When it stops, we set v = and solve for s = 5m Solving for v, we have v =.49(s 4s ) dv ds =.49( 8s) = s =.5 m Using s =.5 m v max = 3.5 m/s Problem 5.59 Solve Problem 5.58 if the coefficient of kinetic friction between the 4kg mass and the horizontal surface is µ k =.. At an arbitrary distance s down the slope we have: U = (4 N)(s sin 3 ) (8 N/m)s (.)(4 N cos 3 )s = ( 4 N ) v 9.8 m/s When it stops, we set v = and solve for s = 3.7 m Solving for v, we have v =.49(3.7s 4s ) dv =.49(3.7 8s) = ds s =.63 m Using s =.63 m v max =.9 m/s 6 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
29 Problem 5.6 The 4kg collar starts from rest in position with the spring unstretched. The spring constant is k = N/m. How far does the collar fall relative to position? k V = V f = Let position be the location where the collar comes to rest ks U = Ks + mgs k Also U = mv f mv = Thus = mgs Ks s(mg Ks) = Solving, s =.785 m. mg s c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 7
30 Problem 5.6 In position on the smooth bar, the 4kg collar has a downward velocity of m/s and the spring is unstretched. The spring constant is k = N/m. What maximum downward velocity does the collar attain as it falls? The work is U = Ks + mgs Also, k U = mv mv where m = 4 kg and V = m/s Thus, mv mv = Ks + mgs () Finding dv, and setting it to zero, ds mv dv ds = Ks + mg = s = mg/k =.39 m Solving () for V we get V =. m/s Problem 5.6 The 4kg collar starts from rest in position on the smooth bar. The tension in the spring in position is N. The spring constant is k = N/m. How far does the collar fall relative to position? For this problem, we need a new reference for the spring. If the tension in the spring is N T = kδ and K = N/m δ =. m. (the initial stretch) In this case, we have U = Ks s+. + mgs s+... Also V = V f = U = K(s +.) = + K(.) + mg(s +.) mg(.) Solving, we get s =.385 m 8 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
31 Problem 5.63 The 4kg collar is released from rest at position on the smooth bar. If the spring constant is k = 6 kn/m and the spring is unstretched in position, what is the velocity of the collar when it has fallen to position? Denote d = mm, h = 5 mm. The stretch of the spring in position is S = h + d d =. m and at S =. The work done by the spring on the collar is 5 mm k [ U spring = ( ks)ds = ]. ks = 43.3 Nm.. The work done by gravity is h U gravity = ( mg) ds = mgh = 9.8 Nm. From the principle of work and energy U spring + U gravity = mv, from which v = ( ) (U spring + U gravity ) = 5.5 m/s m mm Problem 5.64 The 4kg collar is released from rest in position on the smooth bar. The spring constant is k = 4 kn/m. The tension in the spring in position is 5 N. What is the velocity of the collar when it has fallen to position? Denote d = mm, h = 5 mm. The stretch of the spring at position is S = T k = 5 =.5 m. 4 The unstretched length of the spring is L = d S =..5 =.75 m. The stretch of the spring at position is S = h + d L =.45 m. The work done by the spring is U spring = S S ( ks)ds = k(s S ) = Nm. The work done by gravity is U gravity = mgh = 9.8 Nm. From the principle of work and energy is U spring + U gravity = mv, from which (Uspring + U gravity ) v = = 7.3 m/s m c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 9
32 Problem 5.65 The 4kg collar starts from rest in position on the smooth bar. Its velocity when it has fallen to position is 4 m/s. The spring is unstretched when the collar is in position. What is the spring constant k? The kinetic energy at position is mv = 3 Nm. From the solution to Problem 5.63, the stretch of the spring in position is S = h + d d =. m. The potential of the spring is U spring = ( ks)ds = S ks. The work done by gravity is U gravity = mgh = 9.8 Nm. From the principle of work of work and energy, U spring + U gravity = mv. Substitute and solve: k = ( ) mv U gravity S = 38 N/m Problem 5.66 The kg collar starts from rest at position and slides along the smooth bar. The yaxis points upward. The spring constant is k = N/m and the unstretched length of the spring is m. What is the velocity of the collar when it reaches position? y (4, 4, ) m (6,, ) m The stretch of the spring at position is (,, ) m S = (6 ) + ( ) + ( ) = 3. m. x The stretch of the spring at position is z S = (6 4) + ( 4) + ( ) = m. The work done by the spring is U spring = S S ( ks)ds = k(s S ) = 46.8 Nm. The work done by gravity is h U gravity = ( mg) ds = mgh = ()(9.8)(4 ) = 94.3 Nm. From the principle of work and energy: U spring + U gravity = mv, from which (Uspring + U gravity ) v = = 5.77 m/s m c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
33 Problem 5.67 A springpowered mortar is used to launch 44.5 N packages of fireworks into the air. The package starts from rest with the spring compressed to a length of 5. 4 mm. The unstretched length of the spring is 76 mm. If the spring constant is k =76 N/m, what is the magnitude of the velocity of the package as it leaves the mortar? 76 mm Equating the work done to the change in the kinetic energy, k(s S ) mg(y y ) = mv mv : 5.4 mm 6 ( 76 )[ (.6m ) ] ( 44.5)(.6sin 6 ft) = ( 44.5 / 9.8 )v. Solving, we obtain v = 39.3 m/s. Problem 5.68 Suppose that you want to design the mortar in Problem 5.67 to throw the package to a height of 45.7 m above its initial position. Neglecting friction and drag, determine the necessary spring constant. See the solution of Problem Let v be the velocity as the package leaves the barrel. To reach 45.7 m, mg( sin 6 ) = m(v sin 6 ). Solving, we obtain v = 34.4 m/s. Work and energy inside the barrel is k[ ( ).6m ] ( 44.5)(.6sin 6 m)= ( 44.5 / 9.8 )( 34.4 ), which gives k = 4549 N/m. Problem 5.69 Suppose an object has a string or cable with constant tension T attached as shown. The force exerted on the object can be expressed in terms of polar coordinates as F = T e r. Show that the work done on the object as it moves along an arbitrary plane path from a radial position r to a radial position r is U = T(r r ). r θ The work done on the object is U = r r F ds. T Suppose that the arbitrary path is defined by dr = (dre r + rdθe θ ), and the work done is r r U = F dr = T(e r e r )dr + r r r = Tdr= T(r r ) r since e r e s = bydefinition. r r T(re r e θ )rdθ c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
34 Problem 5.7 The kg collar is initially at rest at position. A constant N force is applied to the string, causing the collar to slide up the smooth vertical bar. What is the velocity of the collar when it reaches position? (See Problem 5.69.) mm The constant force on the end of the string acts through a distance s = =.3385 m. The work done by the constant force is U F = Fs = Nm. The work done by gravity on the collar is 5 mm N h U gravity = ( mg) ds = mgh = ()(9.8)(.5) = 9.8 Nm. From the principle of work and energy: U F + U gravity = mv, (UF + U gravity ) from which v = m = 4.9 m/s Problem 5.7 The kg collar starts from rest at position. The tension in the string is N, and the y axis points upward. If friction is negligible, what is the magnitude of the velocity of the collar when it reaches position? (See Problem 5.69.) y (,, ) m (4, 4, ) m N (6,, ) m The constant force moves a distance x s = (6 ) + ( ) + ( ) z (6 4) + ( 4) + ( ) =. m. The work done by the constant force is s U F = Fds= Fs = 439. Nm. The work done by gravity is h U gravity = ( mg) ds = mgh = ()(9.8)(3) = 94.3 Nm. From the principle of work and energy U F + U gravity = mv, from which (UF + U gravity ) v = = 5.38 m/s c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
35 Problem 5.7 As the F/A  8 lands at 64 m/s, the cable from A to B engages the airplane s arresting hook at C. The arresting mechanism maintains the tension in the cable at a constant value, bringing the 5.6 kn airplane to rest at a distance of m. What is the tension in the cable? (See Problem 5.69.) m U = T( ( m) + (. m). m) = ( ) 56 N ( [64 m/s] ) 9.8 m/s T = kn A C. m B Problem 5.73 If the airplane in Problem 5.7 lands at 73. m/s,what distance does it roll before the arresting system brings it to rest? U = ( 8585)( s + (. m). m) = ( ) 56 ( [64 m/s] ) 9.8 m/s Solving we find s = 6.6 m Problem 5.74 A spacecraft 3 km above the surface of the earth is moving at escape velocity v esc =,9 m/s. What is its distance from the center of the earth when its velocity is 5 percent of its initial value? The radius of the earth is 637 km. (See Example 5.6.) ( U = mgre ) = r r mv mv [ ] v r = v gre + r 3 km v esc [ (545 m/s) (,9 m/s) ] r = (9.8 m/s )(6,37, m) + 6,69, m r = 6,6 km. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 3
36 Problem 5.75 A piece of ejecta is thrown up by the impact of a meteor on the moon. When it is km above the moon s surface, the magnitude of its velocity (relative to a nonrotating reference frame with its origin at the center of the moon) is m/s. What is the magnitude of its velocity just before it strikes the moon s surface? The acceleration due to gravity at the surface of the moon is.6 m/s. The moon s radius is 738 km. km m/s The kinetic energy at h = km is [ m v] RM +h = 4 Nm. The work done on the ejecta as it falls from km is RM ( ) RM RM U ejecta = ( W ejecta )ds = mg M R M+h R M +h s ds = [ mg M R M s ] RM R M +h = mg M R M h R M + h, U ejecta =.8 m 6 Nm. From the principle of work and energy, at the Moon s surface: [ m [ m U ejecta = v] surface v] RM +h from which v surface = ( ) = 448 m/s 4 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
37 Problem 5.76 A satellite in a circular orbit of radius r around the earth has velocity v = gre /r, where R E = 637 km is the radius of the earth. Suppose you are designing a rocket to transfer a 9kg communication satellite from a circular parking orbit with 67km radius to a circular geosynchronous orbit with 4,km radius. How much work must the rocket do on the satellite? Denote the work to be done by the rocket by U rocket. Denote R park = 67 km, R geo = 4 km. The work done by the satellite s weight as it moves from the parking orbit to the geosynchronous orbit is Rgeo U transfer = Fds= R park = [ mg R E s ] Rgeo Rgeo R park ( R park = mgr E mg R E s ds ) ( ), R geo R park U transfer = Nm. From the principle of work and energy: [ ] [ ] U transfer + U rocket = mv geo mv. park from which [ ] [ ] U rocket = mv geo mv U transfer. park Noting [ ] mv = m geo ( gr E R geo ) = Nm, [ ] ( ) mv = m g R E =.67 Nm, park R park from which U rocket =.5 Nm Problem 5.77 The force exerted on a charged particle by a magnetic field is F = qv B, where q and v are the charge and velocity of the particle and B is the magnetic field vector. Suppose that other forces on the particle are negligible. Use the principle of work and energy to show that the magnitude of the particle s velocity is constant. The force vector F is given by a cross product involving v. This means that the force vector is ALWAYS perpendicular to the velocity vector. Hence, the force field does no work on the charged particle  it only changes the direction of its motion. Hence, if work is zero, the change in kinetic energy is also zero and the velocity of the charged particle is constant. c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 5
38 Problem 5.78 The N box is released from rest at position and slides down the smooth inclined surface to position. (c) If the datum is placed at the level of the floor as shown, what is the sum of the kinetic and potential energies of the box when it is in position? What is the sum of the kinetic and potential energies of the box when it is in position? Use conservation of energy to determine the magnitude of the box s velocity when it is in position. 3 m M5 m Datum T + V = + ( N)(5 m) = 5 Nm T + V = T + V = 5 Nm (c) 5  = ( ) N N m v + ( N)( m) v = 7.67 m/s 9.8 m/s Problem 5.79 The.45kg soccer ball is m above the ground when it is kicked upward at m/s. Use conservation of energy to determine the magnitude of the ball s velocity when it is 4 m above the ground. Obtain the answer by placing the datum at the level of the ball s initial position and at ground level. m/s m Datum m/s m Datum T = (.45 kg)( m/s), V = T = (.45 kg)v,v = (.45 kg)(9.8 m/s )(3 m) T + V = T + V v = 9.3 m/s T = (.45 kg)( m/s), V = (.45 kg)(9.8 m/s )( m) T = (.45 kg)v,v = (.45 kg)(9.8 m/s )(4 m) T + V = T + V v = 9.3 m/s 6 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
39 Problem 5.8 The Lunar Module (LM) used in the Apollo moon landings could make a safe landing if the magnitude of its vertical velocity at impact was no greater than 5 m/s. Use conservation of energy to determine the maximum height h at which the pilot could shut off the engine if the vertical velocity of the lander is m/s downward and m/s upward. The acceleration due to gravity at the moon s surface is.6 m/s. h Use conservation of energy Let state be at the max height and state at the surface. Datum is at the lunar surface., mv + mgh = mv + v = 5 m/s g =.6 m/s v =± m/s (m cancels from the equation.) h = g (v v ) (The sign of V does not matter since v is the only occurrence of v in the relationship). Solving h = 6.48 m Problem 5.8 The.4kg collar starts from rest at position and slides down the smooth rigid wire. The y axis points upward. Use conservation of energy to determine the magnitude of the velocity of the collar when it reaches point. y (5, 5, ) m.4 kg x z (3,,) m Assume gravity acts in the y direction and that y = is the datum. By conservation of energy, mv + V = constant where V = mgy. Thus, mv + mgy = mv + mgy m =.4 kg, g = 9.8 m/s, v =, y =, and y = 5 m. Thus y (5, 5, ) m.4 kg + (.4)(9.8)(5) = (.4)v + v = 9.9 m/s x z (3,, ) m c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior 7
40 Problem 5.8 At the instant shown, the kg mass is moving downward at.6 m/s. Let d be the downward displacement of the mass relative to its present position. Use conservation of energy to determine the magnitude of the velocity of the kg mass when d = m. m = 4kg m = kg 4 kg kg v =.6 m/s V g = 9.8 m/s d = m.6 m s.6 m/s A Energy for the system is conserved 4 kg A B kg d V ( m v + ) + ( m v + ) = m v + m v + m g(d) m g(d) (m + m )v = (m + m )v + (m m )gd Datum State () V A = V B = B State () d Substituting known values and solving v = 3.95 m/s Problem 5.83 The mass of the ball is m = kg and the string s length is L = m. The ball is released from rest in position and swings to position, where θ = 4. Use conservation of energy to determine the magnitude of the ball s velocity at position. Draw graphs of the kinetic energy, the potential energy, and the total energy for values of θ from zero to 8. m u L m = kg L = m Use conservation of energy State θ = ; State, <θ<8 Datum: θ =, v =, g = 9.8 m/s mv + mg() = mv + mg( L sin θ) KE = mv V = mgl sin θ for all θ. Total energy is always zero (datum value). KE, PE, and (PE + KE) Nm Kinetic and Potential Energy vs α KE positive, PE negative, (KE + PE) zero 5 KE PE 5 TOT Theta (degrees) Evaluating at θ = 4, v = 3.55 m/s 8 c 8 Pearson Education South Asia Pte Ltd. All rights reserved. This publication is protected by Copyright and permission should be obtained from the publisher prior
B) 286 m C) 325 m D) 367 m Answer: B
Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of
More informationB) 40.8 m C) 19.6 m D) None of the other choices is correct. Answer: B
Practice Test 1 1) Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.60 s and reaches the level of the top of the pole after a total elapsed time
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More information2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.
2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationAP Physics  Chapter 8 Practice Test
AP Physics  Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A single conservative force F x = (6.0x 12) N (x is in m) acts on
More informationwww.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x
Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity
More informationMidterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m
Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From
More informationF N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26
Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250N force is directed horizontally as shown to push a 29kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More informationPHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
More informationProblem Set #8 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01L: Physics I November 7, 2015 Prof. Alan Guth Problem Set #8 Solutions Due by 11:00 am on Friday, November 6 in the bins at the intersection
More informationPHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013
PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be
More informationWORK DONE BY A CONSTANT FORCE
WORK DONE BY A CONSTANT FORCE The definition of work, W, when a constant force (F) is in the direction of displacement (d) is W = Fd SI unit is the Newtonmeter (Nm) = Joule, J If you exert a force of
More informationPhysics 2101, First Exam, Fall 2007
Physics 2101, First Exam, Fall 2007 September 4, 2007 Please turn OFF your cell phone and MP3 player! Write down your name and section number in the scantron form. Make sure to mark your answers in the
More information8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential
8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential energy, e.g. a ball in your hand has more potential energy
More informationProblem Set 1. Ans: a = 1.74 m/s 2, t = 4.80 s
Problem Set 1 1.1 A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h. Determine her constant acceleration. How long does it take her to
More informationPHY231 Section 1, Form B March 22, 2012
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
More informationCh 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43
Ch 7 Kinetic Energy and Work Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Technical definition of energy a scalar quantity that is associated with that state of one or more objects The state
More informationChapter 6 Work and Energy
Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
More informationF f v 1 = c100(10 3 ) m h da 1h 3600 s b =
14 11. The 2Mg car has a velocity of v 1 = 100km>h when the v 1 100 km/h driver sees an obstacle in front of the car. It takes 0.75 s for him to react and lock the brakes, causing the car to skid. If
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion
Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckleup? A) the first law
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) A person on a sled coasts down a hill and then goes over a slight rise with speed 2.7 m/s.
More information1) 0.33 m/s 2. 2) 2 m/s 2. 3) 6 m/s 2. 4) 18 m/s 2 1) 120 J 2) 40 J 3) 30 J 4) 12 J. 1) unchanged. 2) halved. 3) doubled.
Base your answers to questions 1 through 5 on the diagram below which represents a 3.0kilogram mass being moved at a constant speed by a force of 6.0 Newtons. 4. If the surface were frictionless, the
More information5. Forces and MotionI. Force is an interaction that causes the acceleration of a body. A vector quantity.
5. Forces and MotionI 1 Force is an interaction that causes the acceleration of a body. A vector quantity. Newton's First Law: Consider a body on which no net force acts. If the body is at rest, it will
More informationNewton s Law of Motion
chapter 5 Newton s Law of Motion Static system 1. Hanging two identical masses Context in the textbook: Section 5.3, combination of forces, Example 4. Vertical motion without friction 2. Elevator: Decelerating
More informationChapter 9. particle is increased.
Chapter 9 9. Figure 936 shows a three particle system. What are (a) the x coordinate and (b) the y coordinate of the center of mass of the three particle system. (c) What happens to the center of mass
More informationExam 1 Review Questions PHY 2425  Exam 1
Exam 1 Review Questions PHY 2425  Exam 1 Exam 1H Rev Ques.doc  1  Section: 1 7 Topic: General Properties of Vectors Type: Conceptual 1 Given vector A, the vector 3 A A) has a magnitude 3 times that
More informationLecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014
Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014 Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7,
More informationKE =? v o. Page 1 of 12
Page 1 of 12 CTEnergy1. A mass m is at the end of light (massless) rod of length R, the other end of which has a frictionless pivot so the rod can swing in a vertical plane. The rod is initially horizontal
More informationcharge is detonated, causing the smaller glider with mass M, to move off to the right at 5 m/s. What is the
This test covers momentum, impulse, conservation of momentum, elastic collisions, inelastic collisions, perfectly inelastic collisions, 2D collisions, and centerofmass, with some problems requiring
More informationCh 6 Forces. Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79
Ch 6 Forces Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79 Friction When is friction present in ordinary life?  car brakes  driving around a turn  walking  rubbing your hands together
More informationPhysics 125 Practice Exam #3 Chapters 67 Professor Siegel
Physics 125 Practice Exam #3 Chapters 67 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the
More informationWork, Kinetic Energy and Potential Energy
Chapter 6 Work, Kinetic Energy and Potential Energy 6.1 The Important Stuff 6.1.1 Kinetic Energy For an object with mass m and speed v, the kinetic energy is defined as K = 1 2 mv2 (6.1) Kinetic energy
More informationCurso20122013 Física Básica Experimental I Cuestiones Tema IV. Trabajo y energía.
1. A body of mass m slides a distance d along a horizontal surface. How much work is done by gravity? A) mgd B) zero C) mgd D) One cannot tell from the given information. E) None of these is correct. 2.
More informationChapter 4 Dynamics: Newton s Laws of Motion
Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal
More informationPHYS 211 FINAL FALL 2004 Form A
1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each
More information7. Kinetic Energy and Work
Kinetic Energy: 7. Kinetic Energy and Work The kinetic energy of a moving object: k = 1 2 mv 2 Kinetic energy is proportional to the square of the velocity. If the velocity of an object doubles, the kinetic
More information1. Newton s Laws of Motion and their Applications Tutorial 1
1. Newton s Laws of Motion and their Applications Tutorial 1 1.1 On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 5.00 kg, and on this particular planet its weight is 40.0
More informationChapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.
Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular
More information10.1 Quantitative. Answer: A Var: 50+
Chapter 10 Energy and Work 10.1 Quantitative 1) A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 4.8 m above the ground. What is the mass
More informationWeight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N)
Gravitational Field A gravitational field as a region in which an object experiences a force due to gravitational attraction Gravitational Field Strength The gravitational field strength at a point in
More informationWork, Power, Energy Multiple Choice. PSI Physics. Multiple Choice Questions
Work, Power, Energy Multiple Choice PSI Physics Name Multiple Choice Questions 1. A block of mass m is pulled over a distance d by an applied force F which is directed in parallel to the displacement.
More informationMechanics 2. Revision Notes
Mechanics 2 Revision Notes November 2012 Contents 1 Kinematics 3 Constant acceleration in a vertical plane... 3 Variable acceleration... 5 Using vectors... 6 2 Centres of mass 8 Centre of mass of n particles...
More informationHomework 4. problems: 5.61, 5.67, 6.63, 13.21
Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find
More informationAP Physics C Fall Final Web Review
Name: Class: _ Date: _ AP Physics C Fall Final Web Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. On a position versus time graph, the slope of
More informationAP Physics Newton's Laws Practice Test
AP Physics Newton's Laws Practice Test Answers: A,D,C,D,C,E,D,B,A,B,C,C,A,A 15. (b) both are 2.8 m/s 2 (c) 22.4 N (d) 1 s, 2.8 m/s 16. (a) 12.5 N, 3.54 m/s 2 (b) 5.3 kg 1. Two blocks are pushed along a
More information9. The kinetic energy of the moving object is (1) 5 J (3) 15 J (2) 10 J (4) 50 J
1. If the kinetic energy of an object is 16 joules when its speed is 4.0 meters per second, then the mass of the objects is (1) 0.5 kg (3) 8.0 kg (2) 2.0 kg (4) 19.6 kg Base your answers to questions 9
More informationLecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.84.12, second half of section 4.7
Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.84.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal
More informationAt the skate park on the ramp
At the skate park on the ramp 1 On the ramp When a cart rolls down a ramp, it begins at rest, but starts moving downward upon release covers more distance each second When a cart rolls up a ramp, it rises
More informationAP Physics C. Oscillations/SHM Review Packet
AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete
More informationChapter 11. h = 5m. = mgh + 1 2 mv 2 + 1 2 Iω 2. E f. = E i. v = 4 3 g(h h) = 4 3 9.8m / s2 (8m 5m) = 6.26m / s. ω = v r = 6.
Chapter 11 11.7 A solid cylinder of radius 10cm and mass 1kg starts from rest and rolls without slipping a distance of 6m down a house roof that is inclined at 30 degrees (a) What is the angular speed
More informationKE = ½mv 2 PE = mgh W = Fdcosθ THINK ENERGY! (KE F + PE F ) = (KE 0 + PE 0 ) + W NC. Tues Oct 6 Assign 7 Fri Preclass Thursday
Tues Oct 6 Assign 7 Fri Preclass Thursday Conservation of Energy Work, KE, PE, Mech Energy Power To conserve total energy means that the total energy is constant or stays the same. With Work, we now have
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The following four forces act on a 4.00 kg object: 1) F 1 = 300 N east F 2 = 700 N north
More information3 Work, Power and Energy
3 Work, Power and Energy At the end of this section you should be able to: a. describe potential energy as energy due to position and derive potential energy as mgh b. describe kinetic energy as energy
More informationPhysics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE
1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object
More informationHW Set II page 1 of 9 PHYSICS 1401 (1) homework solutions
HW Set II page 1 of 9 450 When a large star becomes a supernova, its core may be compressed so tightly that it becomes a neutron star, with a radius of about 20 km (about the size of the San Francisco
More informationChapter 5 Newton s Laws of Motion
Chapter 5 Newton s Laws of Motion Sir Isaac Newton (1642 1727) Developed a picture of the universe as a subtle, elaborate clockwork slowly unwinding according to welldefined rules. The book Philosophiae
More informationVectors; 2D Motion. Part I. Multiple Choice. 1. v
This test covers vectors using both polar coordinates and ij notation, radial and tangential acceleration, and twodimensional motion including projectiles. Part I. Multiple Choice 1. v h x In a lab experiment,
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued Clicker Question 4.3 A mass at rest on a ramp. How does the friction between the mass and the table know how much force will EXACTLY balance the gravity
More informationWork Energy & Power. September 2000 Number 05. 1. Work If a force acts on a body and causes it to move, then the force is doing work.
PhysicsFactsheet September 2000 Number 05 Work Energy & Power 1. Work If a force acts on a body and causes it to move, then the force is doing work. W = Fs W = work done (J) F = force applied (N) s = distance
More information1. Mass, Force and Gravity
STE Physics Intro Name 1. Mass, Force and Gravity Before attempting to understand force, we need to look at mass and acceleration. a) What does mass measure? The quantity of matter(atoms) b) What is the
More informationIMPORTANT NOTE ABOUT WEBASSIGN:
Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationSteps to Solving Newtons Laws Problems.
Mathematical Analysis With Newtons Laws similar to projectiles (x y) isolation Steps to Solving Newtons Laws Problems. 1) FBD 2) Axis 3) Components 4) Fnet (x) (y) 5) Subs 1 Visual Samples F 4 1) F 3 F
More informationPHYSICS 218 EXAM 2 Thursday, October 22, 2009
PHYSICS 218 EXAM 2 Thursday, October 22, 2009 NAME: SECTION: 525 526 527 528 Note: 525 Recitation Wed 9:1010:00 526 Recitation Wed 11:3012:20 527 Recitation Wed 1:502:40 528 Recitation Mon 11:3012:20
More informationSupplemental Questions
Supplemental Questions The fastest of all fishes is the sailfish. If a sailfish accelerates at a rate of 14 (km/hr)/sec [fwd] for 4.7 s from its initial velocity of 42 km/h [fwd], what is its final velocity?
More informationProjectile motion simulator. http://www.walterfendt.de/ph11e/projectile.htm
More Chapter 3 Projectile motion simulator http://www.walterfendt.de/ph11e/projectile.htm The equations of motion for constant acceleration from chapter 2 are valid separately for both motion in the x
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting
More informationPhysics 1A Lecture 10C
Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. Oprah Winfrey Static Equilibrium
More informationMechanics 1: Conservation of Energy and Momentum
Mechanics : Conservation of Energy and Momentum If a certain quantity associated with a system does not change in time. We say that it is conserved, and the system possesses a conservation law. Conservation
More informationTIME OF COMPLETION DEPARTMENT OF NATURAL SCIENCES. PHYS 1111, Exam 2 Section 1 Version 1 October 30, 2002 Total Weight: 100 points
TIME OF COMPLETION NAME DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 2 Section 1 Version 1 October 30, 2002 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There
More informationPhysics Notes Class 11 CHAPTER 5 LAWS OF MOTION
1 P a g e Inertia Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line its own, is
More informationChapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc.
Chapter 4 Dynamics: Newton s Laws of Motion Force Units of Chapter 4 Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal
More informationRotational Dynamics. Luis Anchordoqui
Rotational Dynamics Angular Quantities In purely rotational motion, all points on the object move in circles around the axis of rotation ( O ). The radius of the circle is r. All points on a straight line
More informationKINEMATICS OF PARTICLES RELATIVE MOTION WITH RESPECT TO TRANSLATING AXES
KINEMTICS OF PRTICLES RELTIVE MOTION WITH RESPECT TO TRNSLTING XES In the previous articles, we have described particle motion using coordinates with respect to fixed reference axes. The displacements,
More informationWorkEnergy Bar Charts
Name: WorkEnergy Bar Charts Read from Lesson 2 of the Work, Energy and Power chapter at The Physics Classroom: http://www.physicsclassroom.com/class/energy/u5l2c.html MOP Connection: Work and Energy:
More informationWork, Energy & Momentum Homework Packet Worksheet 1: This is a lot of work!
Work, Energy & Momentum Homework Packet Worksheet 1: This is a lot of work! 1. A student holds her 1.5kg psychology textbook out of a second floor classroom window until her arm is tired; then she releases
More informationP211 Midterm 2 Spring 2004 Form D
1. An archer pulls his bow string back 0.4 m by exerting a force that increases uniformly from zero to 230 N. The equivalent spring constant of the bow is: A. 115 N/m B. 575 N/m C. 1150 N/m D. 287.5 N/m
More information= Ps cos 0 = (150 N)(7.0 m) = J F N. s cos 180 = µ k
Week 5 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions o these problems, various details have been changed, so that the answers will come out dierently. The method to ind the solution
More informationv v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )
Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationPROBLEM SET. Practice Problems for Exam #1. Math 2350, Fall 2004. Sept. 30, 2004 ANSWERS
PROBLEM SET Practice Problems for Exam #1 Math 350, Fall 004 Sept. 30, 004 ANSWERS i Problem 1. The position vector of a particle is given by Rt) = t, t, t 3 ). Find the velocity and acceleration vectors
More informationProblem Set 5 Work and Kinetic Energy Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department o Physics Physics 8.1 Fall 1 Problem Set 5 Work and Kinetic Energy Solutions Problem 1: Work Done by Forces a) Two people push in opposite directions on
More informationG U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M
G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M CONTENTS Foreword... 2 Forces... 3 Circular Orbits... 8 Energy... 10 Angular Momentum... 13 FOREWORD
More information8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight
1. What is the average speed of an object that travels 6.00 meters north in 2.00 seconds and then travels 3.00 meters east in 1.00 second? 9.00 m/s 3.00 m/s 0.333 m/s 4.24 m/s 2. What is the distance traveled
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Vector A has length 4 units and directed to the north. Vector B has length 9 units and is directed
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension
Physics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension Conceptual Questions 1) Suppose that an object travels from one point in space to another. Make
More informationTennessee State University
Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an Fgrade. Other instructions will be given in the Hall. MULTIPLE CHOICE.
More informationPOTENTIAL ENERGY AND CONSERVATION OF ENERGY
Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 1 A good eample of kinetic energy is provided by: A a wound clock spring B the raised weights of a grandfather's clock C a tornado D a gallon of gasoline
More informationPhysics 111: Lecture 4: Chapter 4  Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.
Physics 111: Lecture 4: Chapter 4  Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and noncontact forces. Whats a
More informationLecture Presentation Chapter 4 Forces and Newton s Laws of Motion
Lecture Presentation Chapter 4 Forces and Newton s Laws of Motion Suggested Videos for Chapter 4 Prelecture Videos Newton s Laws Forces Video Tutor Solutions Force and Newton s Laws of Motion Class Videos
More informationGravitational Potential Energy
Gravitational Potential Energy Consider a ball falling from a height of y 0 =h to the floor at height y=0. A net force of gravity has been acting on the ball as it drops. So the total work done on the
More informationF13HPhysQ5 Practice
Name: Class: Date: ID: A F13HPhysQ5 Practice Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A vector is a quantity that has a. time and direction.
More information1) The gure below shows the position of a particle (moving along a straight line) as a function of time. Which of the following statements is true?
Physics 2A, Sec C00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to ll your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationPractice Exam Three Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Practice Exam Three Solutions Problem 1a) (5 points) Collisions and Center of Mass Reference Frame In the lab frame,
More informationPhysics 590 Homework, Week 6 Week 6, Homework 1
Physics 590 Homework, Week 6 Week 6, Homework 1 Prob. 6.1.1 A descent vehicle landing on the moon has a vertical velocity toward the surface of the moon of 35 m/s. At the same time it has a horizontal
More informationEDUH 1017  SPORTS MECHANICS
4277(a) Semester 2, 2011 Page 1 of 9 THE UNIVERSITY OF SYDNEY EDUH 1017  SPORTS MECHANICS NOVEMBER 2011 Time allowed: TWO Hours Total marks: 90 MARKS INSTRUCTIONS All questions are to be answered. Use
More informationChapter 6. Work and Energy
Chapter 6 Work and Energy The concept of forces acting on a mass (one object) is intimately related to the concept of ENERGY production or storage. A mass accelerated to a nonzero speed carries energy
More information