TIME OF COMPLETION DEPARTMENT OF NATURAL SCIENCES. PHYS 1111, Exam 2 Section 1 Version 1 October 30, 2002 Total Weight: 100 points

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1 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 are a total of ten (10) problems on eight (8) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 80 minutes to complete the examination. 4. The total weight of the examination is 100 points. 5. There are six (6) multiple choice and four (4) calculation problems. Work all problems. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 6:00 p.m. Stop: 7:20 p.m PROBLEM POINTS CREDIT TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN

2 MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. A a. 27,491 furlongs/fortnight. (5.00 yards/second)(1.00 furlong/220 yards)(14 x 24 x 3600 seconds/1.00 fortnight) = (5) b. 13,674 furlongs/fortnight. c. 6,221 furlongs/fortnight. d. 2,749 furlongs/fortnight. 27,491furlong/fortnight 2. On the Moon, the acceleration due to gravity is only about 1/6 of that on Earth. An astronaut whose weight on Earth is 600 N travels to the lunar surface. His mass as measured on the Moon will be: a. 600 kg. (5) b. 100 kg. W = m g m = W/g m = (600 N)/(9.80 m/s 2 ) = 61.2 kg c kg. d kg. 3. When we subtract a displacement vector from a velocity vector, the result is: a. A velocity. (5) b. An acceleration. c. Another displacement. d. Result doesn t have physical meaning. 4. Which of the following is an example of the type of force which acts at a distance? a. Gravitational.

3 (5) b. Magnetic. c. Electrical. d. All of the above. 5. Imagine a book sitting on a horizontal table. One of the forces acting on a book is a normal force exerted by the table (let s call it action). What force does form the Newton s 3 rd law pair (reaction)? e. Weight of the book. (5) f. Weight of the table. g. Normal force exerted on the table by the book. h. Friction. 6. Take a look at the graph representing one-dimensional motion of a body. Is the instantaneous velocity of the body at point A: (5) a. Positive. b. Negative. c. Zero. d. Cannot be determined from the graph. 7. Coasting due west on your bicycle at 8.00 m/s, you encounter a sandy patch of road 7.20 m across. When you leave the sandy patch your speed has been reduced to 6.50 m/s. (15) a. Assuming the bicycle slows with constant acceleration, what was its acceleration in the sandy patch? Give both magnitude and direction.

4 V 2 = V a ( x- x 0 ) a = (V 2 - V 2 0 )/ 2( x- x 0 ) V 0 = 8.00 m/s; V = 6.50 m/s; x 0 = 0 m; x = 7.20 m a = {(6.50 m/s) 2 - (8.00 m/s) 2 }/{2 x (7.50 m)} = m/s 2 west or 1.51 m/s 2 east b. What time did it take you to cross the patch? V = V 0 + a t t = (V - V 0 )/a t = (6.50 m/s 8.00 m/s) / (-1.51 m/s 2 ) = s c. What was your average velocity on the sand? V average = (x - x 0 )/(t - t 0 ) = (7.20 m)/(0.993 s) = 7.25 m/s 8. Deep inside an ancient physics text you discover two vectors: A: 45.0 o B: o Not content with these hoary relics, you are asked to find a new vector R = A - B. Find the magnitude and direction of vector R (15) A: o B: o Ax = A cos( A) = 45.0m cos(150 o ) = m Ay = A sin( A) = 45.0m sin(150 o ) = 22.5 m Bx = B cos( B) = 30.0m cos(-15.0 o ) = 29.0 m By = B sin( B) = 30.0m sin(-15.0 o ) = m Rx = Ax - Bx = m = m Ry = Ay - By = 22.5 m m = 30.3 m 2 R = (Rx 2 + Ry ) 1/2 = ( (-68.0 m) 2 + (30.3 m) 2 ) 1/2 = 74.4 m

5 R = tan -1 (Ry /Rx) = tan -1 (30.3 m /-68.0 m) = o o = 156 o (Rx < 0) 9. A soccer ball is kicked with a speed of 9.50 m/s at an angle of 40.0 o above the horizontal direction. Some time later the ball lands at the same level from which it was kicked. a. Find the components of the ball s initial velocity. Vi: o Vx0 = V0 cos( 0) = 9.50m/s cos(40.0 o ) = 7.28 m/s Vy0 = V0 sin( 0) = 9.50m/s sin(40.0 o ) = 6.11 m/s (20)

6 b. What are the components of the ball s velocity at the top of the trajectory? Vx = 7.28 m/s Vy = 0 m/s c. How long does it take the ball to reach the top of the trajectory? Vy = Vy0 - gt (Vy0 - Vy) /g = t t = (6.11 m/s 0 m/s)/9.80 m/s 2 = s d. How far does the ball go in the horizontal direction? x = x0 + Vx0 ( t) = 0 m + (7.28 m/s) (1.25 s) = 9.07 m 10. During your winter break, you enter a dogsled race in which students replace the dogs. Wearing cleats for traction, you begin the race by pulling on a rope attached to the sled with a force of 150 N at 25 o with the horizontal. The mass of the sled is 80.0 kg and there is negligible friction between the sled and ice. a. Draw a free-body diagram. (20) b. Find the acceleration of the sled.

7 Ax = A cos( ) = (150 N) cos( ) = 136 N Ay = A sin( ) = (150 N) sin( ) = 63.4 N nx = n cos(9 ) = 0 ny = n sin(9 ) = n wx = w cos(270 ) = 0 wy = w sin(270 ) = (80.0 kg) (9.80 m/s 2 ) = -784 N Fx = m ax Ax = m ax ax = Ax /m = (136.0 N)/(80.0 kg) = 1.70 m/s 2 c. Find the normal force exerted by the surface on the sled. Fy = m ay ay = 0 ny + wy + Ay = 0 n 784 N 63.4 N = 0 n = 721 N Problem 5

8

9 TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 2 October 4, 2005 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of ten (10) problems on seven (7) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 75 minutes to complete the examination. 4. The total weight of the examination is 100 points. 5. There are six (6) multiple choice and four (4) calculation problems. Work all problems. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 10:30 a.m. Stop: 11:45 a.m PROBLEM POINTS CREDIT TOTAL 100 PERCENTAGE

10 CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. Which of the following operations will not change a vector? a. Translate it parallel to itself. (5) b. Rotate it. c. Multiply it by a constant factor. d. Add a constant vector to it. 2. Suppose that an object travels from one point in space to another. Make a comparison between the displacement and the distance traveled. a. The displacement is either greater than or equal to the distance traveled. (5) b. The displacement is always equal to the distance traveled. c. The displacement is either less than or equal to the distance traveled. d. The displacement can be either greater than, smaller than, or equal to the distance traveled. 3. The position, x, of an object is given by the equation x = A + Bt +Ct 2, where t refers to time. What are the dimensions of A, B, and C? a. Distance, distance, distance. (5) b. Distance, time, time 2. c. Distance, distance/time, distance/ time 2. d. Distance/time, distance/ time 2, distance/ time 3.

11 4. In the diagram shown, the unknown vector is a. (5) b. c. d. Cannot be determined from the diagram. 5. Which of Newton's laws best explains why motorists should buckle-up? a. The first law. (5) b. The second law. c. The third law. d. The law of gravitation. 6. A net force F accelerates a mass m with an acceleration a. If the same net force is applied to mass 3m, then the acceleration will be a. 3a. (5) b. 2a. c. a/2. d. a/3.

12 7. A projectile is fired with an initial speed of 40.2 m/s at an angle of 35.0 o above the horizontal on a long flat firing range. Determine a. The components of the projectile s initial velocity. V i : o V x0 = V 0 cos( 0 ) = (40.2 m/s) cos(35.0 o ) = 32.9 m/s V y0 = V 0 sin( 0 ) = (40.2 m/s) sin(35.0 o ) = 23.1 m/s b. The maximum height reached by the projectile. V 2 y = V 2 y0 - g (y y 0 ) (y y 0 ) = (V 2 y - V 2 y0 )/(-g) (y 0) = (0 2 (23.1 m/s) 2 )/(-9.81 m/s 2 ) y = 54.4 m c. The time it takes to reach the maximum height. V y = V y0 - gt (V y0 - V y ) /g = t t = (23.1 m/s 0 m/s)/(9.81 m/s 2 ) = 2.35 s d. The projectile s range. x = x 0 + V x0 (2t) = 0 m + (32.9 m/s) (4.70 s) = 155 m Bonus (5 extra points): Find velocity of the projectile 1.00 s after firing. V x = V x0 = 32.9 m/s V y = V y0 gt = (23.1 m/s) (9.81 m/s 2 )(1.00 s) = 13.3 m/s V = (V 2 x + V 2 y ) 1/2 = ( (32.9 m/s) 2 + (13.3 m/s) 2 ) 1/2 = 35.5 m/s = tan -1 (V y /V x ) = tan -1 ((13.3 m/s) /(32.9 m/s)) = 22.0 o

13 8. A stone is thrown vertically upward with a speed of 18.0 m/s. a. How fast is it moving when it reaches a height of 7.00 m? V 2 y = V 2 y0 - g (y y 0 ) V 2 y = (18.0 m/s) 2 - (9.81 m/s 2 )((7.00 m) 0) V y = +/ m/s b. How long is required to reach this height? V y = V y0 - gt (V y0 - V y ) /g = t t 1 = (18.0 m/s 16.0 m/s)/(9.81 m/s 2 ) = s t 2 = (18.0 m/s m/s)/(9.81 m/s 2 ) = 3.47 s c. Why are there two answers to (b)? Because the stone reaches this point twice: on its way up and on its way down. 9. A student decides to move a box of books into her dormitory room by pushing on the box. She pushes with a force of 100 N at an angle of 15.0 o with the horizontal. The box has a mass of 25.0 kg, and we are going to neglect friction between the box and the floor for simplicity. a. Draw a free body diagram.

14 b. Find the acceleration of the box. A x = A cos(-15.0 o ) = (100 N) cos(-15.0 o ) = 96.6 N A y = A sin(-15.0 o ) = (100 N) sin(-15.0 o ) = N n x = n cos(90.0 o ) = 0 n y = n sin(90.0 o ) = n w x = w cos(-90.0 o ) = 0 w y = w sin(-90.0 o ) = (25.0 kg) (9.81 m/s 2 ) = -245 N F x = m a x A x = m a x a x = A x /m a x = (96.6 N)/(25.0 kg) = 3.86 m/s 2 c. Find the normal force the box exerts on the floor. F y = m a y a y = 0 n y + w y + A y = 0

15 n 245 N 25.9 N = 0 n = 271 N Note: this is the normal force that the FLOOR exerts on the BOX, but the third Newton s Law states that this force is equal in magnitude and opposite in direction to the force that the BOX exerts on the FLOOR. 10. Vector A has a magnitude of m/s and points in a direction 20.0 o below the x axis. A second vector, B, has a magnitude of 80.0 m/s and points in a direction 95.0 o above the x axis. Find a new vector R = A + B. Find the magnitude and direction of vector R. A: o B: o A x = A cos( A ) = (127 m/s) cos(-20.0 o ) = 119 m/s A y = A sin( A ) = (127 m/s) sin(-20.0 o ) = m/s B x = B cos( B ) = (80.0 m/s) cos(95.0 o ) = m/s B y = B sin( B ) = (80.0 m/s) sin(95.0 o ) = 79.7 m/s R x = A x + B x = 119 m/s + (-6.97 m/s) = 112 m/s R y = A y + B y = m/s m/s = 36.3 m/s R = (R x 2 + R y 2 ) 1/2 = ( (112 m/s) 2 + (36.3 m/s) 2 ) 1/2 = 118 m/s q R = tan -1 (R y /R x ) = tan -1 ((36.3 m/s) /(112 m/s)) = 18.0 o TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 1 October 2, 2006 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of ten (10)

16 problems on seven (7) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 75 minutes to complete the examination. 4. The total weight of the examination is 100 points. 5. There are six (6) multiple choice and four (4) calculation problems. Work all calculation problems and 5 (five) multiple choice. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 6:00 p.m. Stop: 7:15 p.m PROBLEM POINTS CREDIT TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. The metric prefix for one one-hundredth is a. Milli. b. Centi.

17 (4) c. Kilo. d. Mega. 2. An object moving in the +x axis experiences an acceleration of 2.0 m/s 2. This means the object is a. Traveling at 2.0 m in every second. (4) b. Traveling at 2.0 m/s in every second. c. Changing its velocity by 2.0 m/s. d. Increasing its velocity by 2.0 m/s in every second. 3. When an object is released from rest and falls in the absence of friction, which of the following is true concerning its motion? a. The speed of the falling object is proportional to its mass. (4) b. The speed of the falling object is proportional to its weight. c. The speed of the falling object is inversely proportional to its surface area. d. None of the above is true. 4. Ignoring air resistance, the horizontal component of a projectile's velocity a. Is zero. (4) b. Remains constant. c. Continuously increases. d. Continuously decreases.

18 5. When a football in a field goal attempt reaches its maximum height, how does its speed compare to its initial speed? a. It is zero. (4) b. It is less than its initial speed. c. It is equal to its initial speed. d. It is greater than its initial speed. 6. If you exert a force F on an object, the force which the object exerts on you will a. Depend on whether or not the object is moving. (4) b. Depend on whether or not you are moving. c. Depend on the relative masses of you and the object. d. Always be F. 7. Vector V 1 is 6.6 units long and points along the negative x axis. Vector V 2 points at 45º to the positive x axis. a. What are the x and y components of each vector? V 1x = V 1 cos( 1 ) = (6.60) cos(180 o ) = V 1y = V 1 sin( 1 ) = (6.60) sin(180 o ) = 0 V 2x = V 2 cos( 2 ) = (8.50) cos(45.0 o ) = 6.01 is 8.5 units long and

19 V 2y = V 2 sin( 2 ) = (8.50) sin( 45.0 o ) = 6.01 b. Determine the sum V 1 V 2 (magnitude and angle). R x = V 1x + V 2x = (- 6.60) + (6.01) = R y = V 1y + V 2y = (0) + (6.01) = R = ( R x + R 2 y ) 1/2 = ( (0.59) 2 + (6.01) 2 ) 1/2 = 6.04 R = tan -1 (R y /R x ) = tan -1 ((6.01)/(-0.59)) = o o = 95.6 o 8. A projectile is shot from the edge of a cliff with an initial speed of 65.0 m s at an angle of 37.0º with the horizontal. a. Determine the components of the initial velocity of the projectile. V 0x = V 0 cos( 0 ) = (65.0 m/s) cos(37.0 o ) = 51.9 m/s V 0y = V 0 sin( 0 ) = (65.0) sin( 37.0 o ) = 39.1 m/s b. If it takes 10.5 s for the projectile to reach the base of the cliff, how high is the cliff? y = y 0 + V y0 t ½ g t 2 0 = y 0 + V y0 t ½ g t 2 y 0 = - V y0 t + ½ g t 2 = - (39.1 m/s) (10.5 s) + ½ (9.81 m/s 2 ) (10.5 s) 2 y 0 = 130 m c. Determine the range X of the projectile as measured from the base of the cliff. x = x 0 + V x0 t x = (0 m) + (51.9 m/s) (10.5 s) =545 m Bonus (5 points): Find the maximum height above the cliff top reached by the projectile.

20 2 V y = V 2 y0-2 g (y-y 0 ) 0 = V 2 y0-2 g (y-y 0 ) (y-y 0 ) = V 2 y0 /(2 g) = 77.9 m y = 208 m 9.The driver of a truck slams on the brakes when he sees tree blocking the road. The truck slows down uniformly with an acceleration of m/s 2 for 4.20 s. If the truck was moving at 27.0 m/s the moment the driver sees the tree, a. With what speed does the truck hit the tree? V = V 0 + a t V = (27.0 m/s) + (-5.60 m/s 2 )(4.20 s) = 3.48 m/s b. How long are the skid marks? x = x 0 + V 0 t + ½ a t 2 x = 0 + (27.0 m) (4.20 s) + ½ (-5.60 m/s 2 ) (4.20 s) 2 x = 64.0 m c. What is the average velocity of the truck over these 4.20 s? V av = (x - x 0 )/(t - t 0 ) = (64.0 m)/(4.20 s) = 15.2 m/s 10. At the instant a race began, a 65-kg sprinter exerted a force of 720 N on the starting block at a 22º angle with respect to the ground. a. Draw a free body diagram for the sprinter.

21 b. What was the horizontal acceleration of the sprinter? A x = A cos(22.0 o ) = (720 N) cos(22.0 o ) = 668 N A y = A sin(22.0 o ) = (720 N) sin(22.0 o ) = 270 N n x = n cos(90.0 o ) = 0 n y = n sin(90.0 o ) = n w x = w cos(-90.0 o ) = 0 w y = w sin(-90.0 o ) = (65.0 kg) (9.81 m/s 2 ) = -638 N F x = m a x A x = m a x a x = A x /m a x = (668 N)/(65.0 kg) = 10.3 m/s 2

22 c. If the force was exerted for 0.32 s, with what speed did the sprinter leave the starting block? V = V 0 + a t V = (0 m/s) + (10.3 m/s 2 )(0.32 s) = 3.30 m/s TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 1 October 1, 2007 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of ten (10) problems on seven (7) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 75 minutes to complete the examination.

23 4. The total weight of the examination is 100 points. 5. There are six (6) multiple choice and four (4) calculation problems. Work all calculation problems and 5 (five) multiple choice. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 6:00 p.m. Stop: 7:15 p.m PROBLEM POINTS CREDIT TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. The velocity, V, of an object is given by the equation V = A + Bt, where t refers to time. What are the dimensions of A, and B? A) distance/time, distance/time 2. (4) B) distance/time, distance 2 /time 2. C) distance, distance/ time 2 D) distance/time 2, distance/ time 3

24 2. Can an object's velocity change direction when its acceleration is constant? Support your answer with an example. A) No, this is not possible because it is always speeding up. (4) B) No, this is not possible because it is always speeding up or always slowing down, but it can never turn around. C) Yes, this is possible, and a rock thrown straight up is an example. D) Yes, this is possible, and a car that starts from rest, speeds up, slows to a stop, and then backs up is an example. 3. A ball is thrown straight up, reaches a maximum height, then falls to its initial height. Make a statement about the direction of the velocity and acceleration as the ball is coming down. A) Both its velocity and its acceleration point upward. (4) B) Its velocity points upward and its acceleration points downward. C) Its velocity points downward and its acceleration points upward. D) Both its velocity and its acceleration point downward. 4. An object is moving with constant non-zero acceleration in the +x axis. The position versus time graph of this object is A) a horizontal straight line. (4) B) a vertical straight line. C) a straight line making an angle with the time axis. D) a parabolic curve. 5. Ignoring air resistance, the horizontal component of a projectile's acceleration A) is zero. B) remains a non-zero constant.

25 (4) C) continuously increases. D) continuously decreases. 6. A child's toy is suspended from the ceiling by means of a string. The Earth pulls downward on the toy with its weight force of 8.0 N. If this is the "action force," what is the "reaction force"? A) The string pulling upward on the toy with an 8.0-N force. (4) B) The ceiling pulling upward on the string with an 8.0-N force. C) The string pulling downward on the ceiling with an 8.0-N force. D) The toy pulling upward on the Earth with an 8.0-N force. 7. Vector V 1 is 20.7 m long and points at 55.0 o to the positive x axis. Vector V 2 points at o to the positive x axis. a. What are the x and y components of each vector? V 1x = V 1 cos( 1 ) = (20.7 m) cos(55.0 o ) = 11.9 m V 1y = V 1 sin( 1 ) = (20.7 m) sin(55.0 o ) = 17.0 m V 2x = V 2 cos( 2 ) = (15.0 m) cos(-15.0 o ) = 14.5 m V 2y = V 2 sin( 2 ) = (15.0 m) sin( o ) = m b. Determine the vector V 1 V 2 (magnitude and angle). is 15.0 m long and R x = V 1x - V 2x = (11.9 m) - (14.5 m) = m

26 R y = V 1y - V 2y = (17.0 m) - (-3.88 m) = 20.9 m R = ( R x 2 + R y 2 ) 1/2 = ( (-2.60 m) 2 + (20.9 m) 2 ) 1/2 = 21.0 m R = tan -1 (R y /R x ) = tan -1 ((20.9 m)/(-2.60 m)) = o o = 97.1 o 8. A diver running 1.8 m s dives out from the edge of a vertical cliff at an angle of 25.0 o with the horizontal. He hits the water 5.00 m away from the base of the cliff. a. What are the components of the initial velocity? V x0 = V 0 cos( 0 ) = (1.80 m/s) cos(25.0 o ) = 1.63 m/s V y0 = V 0 sin( 0 ) = (1.80 m/s) sin( 25.0 o ) = m/s x = x 0 + V x0 t b. How long was the diver in the air? t = (x - x 0 )/V x0 t = (5.00 m)/(1.63 m/s) = 3.07 s c. How high was the cliff? y = y 0 + V y0 t ½ gt 2 y 0 = y - V y0 t + ½ gt 2 y 0 = 0 (0.761 m/s) (3.07 s) + ½ (9.81 m/s 2 )(3.07 s) 2 = 43.9 m Bonus (5 points): How high above the edge of the cliff did the diver rise? 2 V y = V 2 y0-2 g (y-y 0 ) 0 = V 2 y0-2 g (y-y 0 ) (y-y 0 ) = V 2 y0 /(2 g)

27 (y m) = (0.761 m/s) 2 /(2 g) y = m (from the ground) or m from the edge of the cliff 9. A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5 m s ) in the first 15.0 m of the race. V 2 = V a (x-x 0 ) a. What is the average acceleration of this sprinter? a = (V 2 - V 0 2 )/(2(x-x 0 )) a = ((11.5 m/s) 2 0)/(2(15.0 m)) = 4.41 m/s 2 V = V 0 + at b. How long does it take her to reach that speed? t =(V - V 0 )/a = ((11.5 m/s) 0)/( 4.41 m/s 2 ) = 2.61 s c. What is her average velocity during this time? V av = x/ t = (15.0 m)/(2.61 s) = 5.75 m/s 10. A box sits at rest on a rough 30º inclined plane. Mass of the box is 10.0 kg. a. Draw a free body diagram including all the forces acting on the box.

28 b. Find the magnitude of the normal force exerted on the box by the incline. f x = f cos(0 o ) = f f y = f sin(0 o ) = 0 n x = n cos(90.0 o ) = 0 n y = n sin(90.0 o ) = n w x = w cos(-120 o ) = (10.0 kg) (9.81 m/s 2 ) cos(-120 o ) = N w y = w sin(-120 o ) = (10.0 kg) (9.81 m/s 2 ) sin(-120 o ) = N F y = m a y f y + n y + w y = 0 n N = 0 n = 85.0 N c. Find the magnitude of the friction force acting on the box. F x = m a x f x + n x + w x = 0 f N = 0

29 f = 13.8 N TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 1 February 16, 2005 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of ten (10) problems on eight (8) pages.

30 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 75 minutes to complete the examination. 4. The total weight of the examination is 100 points. 5. There are six (6) multiple choice and four (4) calculation problems. Work all problems. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 6:00 p.m. Stop: 7:15 p.m PROBLEM POINTS CREDIT TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 2. A furlong is a distance of 220 yards. A fortnight is a time period of 2 weeks. A race horse is running at a speed of 5 yards per second. What is its speed in furlongs per fortnight? e. 13,674 furlongs/fortnight. f. 6,221 furlongs/fortnight.

31 (5) g. 2,749 furlongs/fortnight. h. 27,491 furlongs/fortnight 2. On the Moon, the acceleration due to gravity is only about 1/6 of that on Earth. An astronaut whose weight on Earth is 600 N travels to the lunar surface. His mass as measured on the Moon will be: e. 600 kg. (5) f. 100 kg. g kg. h kg. 3. When we subtract a displacement vector from a velocity vector, the result is: a. A velocity. (5) b. An acceleration. c. Another displacement. d. Result doesn t have physical meaning. 4. Which of the following is an example of the type of force which acts at a distance? a. Gravitational. (5) b. Magnetic. c. Electrical. d. All of the above. 5. Imagine a book sitting on a horizontal table. One of the forces acting on a book is a normal force exerted by the table (let s call it action). What force does form the Newton s 3 rd law pair (reaction)? e. Normal force exerted on the Earth by the table.

32 (5) f. Normal force exerted on the table by the Earth. g. Normal force exerted on the table by the book. h. Normal force exerted on the Earth by the book. 6. Take a look at the graph representing one-dimensional motion of a body. The instantaneous velocity of the body at point A is e. Positive. (5) f. Negative. g. Zero. h. Cannot be determined from the graph. 7. Coasting due west on your bicycle at 8.00 m/s, you encounter a sandy patch of road 7.20 m across. When you leave the sandy patch your speed has been reduced to 6.50 m/s. a. Assuming the bicycle slows with constant acceleration, what was its acceleration

33 in the sandy patch? Give both magnitude and direction. V 0 = 8.00 m/s V= 6.50 m/s x x 0 = 7.20 m V 2 = V a (x x 0 ) a = (V 2 - V 0 2 )/[2(x x 0 )] = m/s 2 (15) b. What time did it take you to cross the patch? V = V 0 + a t t = (V - V 0 )/a = s c. What was your average velocity as you were crossing the patch? V av = (x x 0 )/t = (7.20 m) / (0.993 s) = 7.25 m/s 8. Deep inside an ancient physics text you discover two vectors: A: 45.0 o B: o Not content with these hoary relics, you are asked to find a new vector R = A - B. Find the magnitude and direction of vector R A x = A cos( A ) = (45.0 m) cos(150.0 o ) = m A y = A sin( A ) = (45.0 m) sin(150.0 o ) = 22.5 m B x = B cos( B ) = (30.0 m/s) cos(-15.0 o ) = 30.0 m B y = B sin( B ) = (30.0 m/s) sin(-15.0 o ) = m R x = A x - B x = (-40.0 m) - (30.0 m) = m R y = A y - B y = (22.5 m) - (-7.76 m) = 30.3 m R = ( R x 2 + R y 2 ) 1/2 = ( (-70.0 m) 2 + (30.3 m) 2 ) 1/2 = 76.3 m

34 R = tan -1 (R y /R x ) = = tan -1 ((30.3 m)/(-70.0 m)) = o o = 157 o (15) 9. A soccer ball is kicked with a speed of 9.50 m/s at an angle of 40.0 o above the horizontal direction. Some time later the ball lands at the same level from which it was kicked. V 0 : o a. Find the components of the ball s initial velocity. V x0 = V 0 cos( 0 ) = (9.50 m/s) cos(40 o ) = 7.28 m/s V y0 = V 0 sin( 0 ) = (9.50 m/s) sin(40 o ) = 6.11 m/s (20) b. What are the components of the ball s velocity at the top of the trajectory? V x = V x0 = 7.28 m/s V y = 0 m/s c. How long does it take the ball to reach the top of the trajectory? V y = V y0 - gt t = - (V y - V y0 )/g = s x = x 0 + V x0 t d. How far does the ball go in the horizontal direction? x = (0 m) + (7.28 m/s) (2 x s) = 9.08 m 10. During your winter break, you enter a dogsled race in which students replace the dogs. Wearing cleats for traction, you begin the race by pulling on a rope attached to the sled with a force of 150 N at 25 o with the horizontal. The mass of the sled is 80.0 kg and there is negligible friction between the sled and ice. a. Draw a free-body diagram.

35 b. Find the acceleration of the sled. A x = A cos( A ) = (150 N) cos(25.0 o ) = 136 N A y = A sin( A ) = (150 N) sin(25.0 o ) = 63.4 N w x = w cos( w ) = (80.0 kg)(9.80 m/s 2 ) cos(-90.0 o ) = 0 N w y = w sin( w ) = (80.0 kg)(9.80 m/s 2 ) sin(-90.0 o ) = -784 N n x = n cos( n ) = n cos(90.0 o ) = 0 N n y = n sin( n ) = n sin(90.0 o ) = n F X = m a X 136 N = (80.0 kg) a X a X = 1.70 m/s 2 c. Find the normal force exerted by the surface on the sled.

36 F Y = m a Y = N -784 N + n = 0 n = 721 N TIME OF COMPLETION NAME_SOLUTION SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 1 February 20, 2006 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of nine (9) problems on seven (7) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 50 minutes to complete the examination. 4. The total weight of the examination is 100 points. 5. There are five (5) multiple choice and four (4) calculation problems. Work all multiple choice problems and 4 calculation problems. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 6:00 p.m. Stop: 7:15 p.m PROBLEM POINTS CREDIT

37 TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. If 1 inch = 2.54 cm, and 1 yd = 36 in., how many meters are in 7.00 yd? (4) a m. b m. c. 640 m. d m. (7.00 yd)(36 in/1 yd)( m/1 in) = 6.40 m 2. Suppose that an object travels from one point in space to another. Make a comparison between the displacement and the distance traveled. a. The displacement is either greater than or equal to the distance traveled. b. The displacement is always equal to the distance traveled. (4) c. The displacement is either less than or equal to the distance traveled. d. The displacement can be either greater than, smaller than, or equal to the distance traveled. 3. Ignoring air resistance, the horizontal component of a projectile's velocity

38 a. Is zero. (4) b. Remains constant. c. Continuously increasing. d. Continuously decreasing. 4. Ignore this problem. 5. Mass and weight a. Both measure the same thing. (4) b. Are exactly equal. c. Are two different quantities. d. Are both measured in kilograms. 6. A person pushes a 14.0-kg lawn mower at constant speed with a force of F 88.0 N directed along the handle, which is at an angle of 45.0º to the horizontal. Making a highly unrealistic assumption that there is no friction between the mower and the ground,. a. Draw the free-body diagram showing all forces acting on the mower.

39 b. Calculate the acceleration of the mower. A x = A cos(-45.0 o ) = (88.0 N) cos(-45.0 o ) = 62.2 N A y = A sin(-45.0 o ) = (88.0 N) sin(-45.0 o ) = N n x = n cos(90.0 o ) = 0 n y = n sin(90.0 o ) = n w x = w cos(-90.0 o ) = 0 w y = w sin(-90.0 o ) = (14.0 kg) (9.81 m/s 2 ) = -137 N F x = m a x A x = m a x a x = A x /m a x = (62.2 N)/(14.0 kg) = 4.44 m/s 2 c. Calculate the magnitude of the normal force that the ground exerts on the mower. F y = m a y

40 a y = 0 n y + w y + A y = 0 n + (-137 N) + (-62.2 N) = 0 n = 199 N 7. A projectile is shot from the edge of a cliff with an initial speed of 65.0 m s at an angle of 37.0º with the horizontal. The projectile lands on the ground 10.0 s later. a. What are the components of the initial velocity? V 0 : o V x0 = V 0 cos( 0 ) = (65.0 m/s) cos(37.0 o ) = 51.9 m/s V y0 = V 0 sin( 0 ) = (65.0 m/s) sin(37.0 o ) = 39.1 m/s b. How high is the cliff? y = y 0 + V y0 t ½ g t 2 0 = y 0 + V y0 t ½ g t 2 y 0 = ½ g t 2 - V y0 t y 0 = ½ (9.81 m/s 2 ) (10.0 s) 2 - (39.1 m/s) (10.0 s) = 99.5 m c. Determine the range of the projectile as measured from the base of the cliff. x = x 0 + V x0 (t) = 0 m + (51.9 m/s) (10.0 s) = 519 m d. At the instant just before the projectile hits the ground, find the magnitude of the velocity. V x = V x0 = 51.9 m/s V y = V y0 g t = (39.1 m/s) - (9.81 m/s 2 ) (10.0 s) = m/s V = (V x 2 + V y 2 ) 1/2 = 78.6 m/s Bonus (5 points): Find the maximum height above the cliff top reached by the projectile.

41 2 2 V y = V y0 2 g (y y 0 ) (y y 0 ) = (V 2 y - V 2 y0 )/(-2 g) (y 0) = (0 2 (39.1 m/s) 2 )/(-2 x 9.81 m/s 2 ) y = 77.9 m 8. A fugitive tries to hop on a freight train. The fugitive starts from rest and accelerates at 2 a 4.0 m s to his maximum speed of 8.0 m s. a. How long does it take him to reach the maximum speed? V = V 0 + a t V = 0 + a t t = V/a = (8.00 m/s)/(4.00 m/s 2 ) = 2.00 s b. What is the distance traveled to reach the maximum speed? x = x 0 + V 0 t + ½ a t 2 = ½ a t 2 x = ½ (4.00 m/s 2 )(2.00 s) 2 = 8.00 m c. What is the average velocity of the fugitive during this time interval? V av = x/ t = (8.00 m)/(2.00 s) = 4.00 m/s 9. A car is driven 215 km 25º north of west and then 85 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram. A: o B: o A x = A cos( A ) = (215 km) cos(155 o ) = -195 km A y = A sin( A ) = (215 km) sin(155 o ) = 90.9 km

42 B x = B cos( B ) = (85.0 km) cos(225 o ) = km B y = B sin( B ) = (85.0 km) sin(225 o ) = km R x = A x + B x = -195 km + (-60.1 km) = -255 km R y = A y + B y = 90.9 km + (-60.1 km) = 30.8 km R = (R x 2 + R y 2 ) 1/2 = ( (-255 km) 2 + (30.8 km) 2 ) 1/2 = 257 km q R = tan -1 (R y /R x ) = tan -1 ((30.8 km) /(-255 km)) = o +180 o = 173 o TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 1 February 19, 2007 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of ten (10) problems on seven (7) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 75 minutes to complete the examination. 4. The total weight of the examination is 100 points.

43 5. There are six (6) multiple choice and four (4) calculation problems. Work all calculation problems and 5 (five) multiple choice. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 6:00 p.m. Stop: 7:15 p.m PROBLEM POINTS CREDIT TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. If you are 5'10'' tall, what is your height in meters? (1 in = 2.54 cm.) a. 1.5 m. (4) b. 1.6 m. c. 1.7 m. d. 1.8 m. 2. Suppose that a car traveling to the West (-x direction) begins to slow down as it approaches a

44 traffic light. Make a statement concerning its acceleration. a. The car s acceleration is positive. (4) b. The car s acceleration is negative. c. The acceleration is zero. d. A statement cannot be made using the information given. 3. A ball is thrown with a velocity of 20.0 m/s at an angle of 60.0 above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory? a m/s. (4) b m/s. c m/s. d. Zero. 4. The acceleration of an object is inversely proportional to a. The net force acting on it. (4) b. Its position. c. Its velocity. d. Its mass. 5. Action-reaction forces a. Sometimes act on the same object. (4) b. Always act on the same object. c. May be at right angles.

45 d. Always act on different objects. 6. The acceleration due to gravity is lower on the Moon than on Earth. Which of the following is true about the mass and weight of an astronaut on the Moon's surface, compared to Earth? a. Mass is less, weight is same. (4) b. Mass is same, weight is less. c. Both mass and weight are less. d. Both mass and weight are the same. 7. Vector V 1 is 9.60 units long and points along the positive x axis. Vector V 2 points at 75.0 o to the positive x axis. a. What are the x and y components of each vector? V 1 : o V 2 : o V 1x = V 1 cos( 1 ) = (9.60 units) cos(0 o ) = 9.60 units V 1y = V 1 sin( 1 ) = (9.60 units) sin(0 o ) = 0 V 2x = V 2 cos( 2 ) = (7.55 units) cos(75.0 o ) = 1.95 units V 2y = V 2 sin( 2 ) = (7.55 units) sin(75.0 o ) = 7.29 units is 7.55 units long and b. Determine the sum V 1 V 2 (magnitude and angle). R x = V 1x + V 2x = 9.60 units units = 11.6 units R y = V 1y + V 2y = units = 7.29 units R = (R x 2 + R y 2 ) 1/2 = ( (11.6 units) 2 + (7.29 units) 2 ) 1/2 = 13.7 units R = tan -1 (R y /R x ) = tan -1 ((7.29) /(11.6)) = 32.1 o 8. A football is kicked at ground level with a speed of 18.0 m s at an angle of 35.0º to the

46 horizontal. a. What are the components of the initial velocity? V 0 : o V x0 = V 0 cos( 0 ) = (18.0 m/s) cos(35.0 o ) = 14.7 m/s V y0 = V 0 sin( 0 ) = (18.0 m/s) sin(35.0 o ) = 10.3 m/s b. How much later does it hit the ground? y = y 0 + V y0 t ½ g t 2 0 = 0 + V y0 t ½ g t 2 0 = V y0 ½ g t 2 V y0 /g = t t = 2.10 s c. How far does it travel in the horizontal direction? x = x 0 + V x0 (t) = 0 m + (14.7 m/s) (2.10 s) = 30.9 m 9. A helicopter is ascending vertically with a speed of 5.20 m s. At a height of 125 m above the Earth, a package is dropped from a window. a. How much time does it take for the package to reach the ground? [Hint: The package s initial speed equals the helicopter s.] y = y 0 + V y0 t ½ g t 2 0 = (125 m) + (5.20 m/s) t ½ g t 2 t = 5.61 s b. How fast does the package move just before it hits the ground? V = V 0 g t = (5.20 m/s) - (9.81 m/s 2 ) (5.61 s) = m/s

47 c. What is the acceleration of the package just before it heats the ground? Acceleration due to gravity, 9.81 m/s 2 downward 10. During your winter break, you enter a dogsled race in which students replace the dogs. Wearing cleats for traction, you begin the race by pulling on a rope attached to the sled with a force of 100 N at 15 o with the horizontal. The mass of the sled is 60.0 kg and there is negligible friction between the sled and ice. a. Draw a free body diagram for the sled. (20) b.find the acceleration of the sled.

48 c. Find the normal force exerted by the surface on the sled. TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 1 February 20, 2008 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of ten (10) problems on seven (7) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 75 minutes to complete the examination. 4. The total weight of the examination is 100 points. 5. There are six (6) multiple choice and four (4) calculation problems. Work all calculation problems and 5 (five) multiple choice. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 6:00 p.m. Stop: 7:15 p.m PROBLEM POINTS CREDIT

49 TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. Which of the following is a scalar quantity? A) Velocity. (4) B) Force. C) Speed. D) Acceleration. 2. The density of a solid object is defined as the ratio of the mass of the object to its volume. The dimension of density is A) [M]/[L]. (4) B) [L] 3 /[M]. C) [M]/[L] 3. D) [M][L] A ball is thrown straight up. When it reaches its highest point, A) Its velocity is zero. (4) B) Its acceleration is zero. C) Both its velocity and acceleration are zero. D) Neither is zero.

50 4. Vector A is along the x-axis and vector B is along the y-axis. Which one of the following statements is correct? A) The x-component of vector A is equal to the x-component of vector B. (4) B) The y-component of vector A is equal to the y-component of vector B. C) The x-component of vector A is equal and opposite to the x-component of vector B. D) Vector A has a zero y-component and vector B has a zero x-component. 5. Under which of the following conditions would a car have a westward acceleration? A) The car going eastward and its speed is increasing. (4) B) The car going eastward and its speed is decreasing. C) The car going westward and its speed is constant. D) The car going eastward and its speed is constant. 6. When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) The parachutist s acceleration is equal to g. (4) B) The force of air resistance is equal to zero. C) The effect of gravity has died down. D) The force of air resistance is equal to the weight of the parachutist.

51 7. You are a player on a reality TV show. You and two other contestants are brought to the center of a large, flat field. Each is given a meter stick, a compass, a calculator, a shovel, and following two displacements: 72.4 m 32.0 o east of north, 57.3 m 36.0 o south of west. These two displacements lead to the point where the keys to a new Porsche are buried. Two players start measuring immediately, but you (knowledge is power!) first calculate where to go and reach the point first. How far do you go and in what direction? A x = A cos( A ) = (72.4 m) cos(58.0 o ) = 38.4 m A y = A sin( A ) = (72.4 m) sin(58.0 o ) = 61.4 m B x = B cos( B ) = (57.3 m) cos(216 o ) = m B y = B sin( B ) = (57.3 m) sin(216 o ) = m R x = A x + B x = (38.4 m) + (-46.4 m) = m R y = A y + B y = (61.4 m) + (-33.7 m) = 27.7 m 2 R = ( R x + R 2 y ) 1/2 = ( (-8.00 m) 2 + (27.7 m) 2 ) 1/2 = 28.8 m R = tan -1 (R y /R x ) = tan -1 ((27.7 m)/(-8.00 m)) = o +180 =106 o 11. A rock is tossed off a cliff at a speed of 20.0 m/s at an angle of 60.0 o to the horizontal. The rock lands at the base of the cliff 4.03 s later. a. What are the components of the initial velocity? V 0 : o V x0 = V 0 cos( 0 ) = (20.0 m/s) cos(60.0 o ) = 10.0 m/s

52 V y0 = V 0 sin( 0 ) = (20.0 m/s) sin(60.0 o ) = 17.3 m/s b. How high is the cliff? y = y 0 + V y0 t ½ gt 2 0 = y 0 + V y0 t ½ gt 2 y 0 = - V y0 t + ½ gt 2 y 0 = - (17.3 m/s)(4.03 s) ½ (9.80 m/s 2 )(4.03 s) 2 = 9.94 m V x = V x0 = 10.0 m V y = V y0 - gt c. What is the angle of impact? V y = (17.3 m/s) (9.80 m/s 2 )(4.03 s) = s = tan -1 (V y /V x ) = tan -1 ((-22.2 m/s)/(10.0 m/s)) = o Bonus (5 points): How high above the base of the cliff does the rock rise? V 2 y = V 2 y0-2 g (y y 0 ) (y y 0 ) = (V 2 y - V 2 y0 )/(- 2 g) V y = 0 m/s (y y 0 ) = (V 2 y0 )/(2 g) = 15.3 m 12. A student throws a water balloon vertically downward from the top of the building. The ballooh leaves the thrower s hand with a speed of 6.00 m/s. Air resistance may be ignored, so the water balloon is in free fall after it leaves the trower s hand.

53 a.what is its speed after falling for 2.00 s? (20) b. How far does it fall in 2.00 s? c. What is its velocity after falling 10.0 m? 13. A stockroom worker pushes a box with mass 11.2 kg on a horizontal surface with a constant speed of 3.50 m/s. The worker s force makes an angle of 30.0 o with the horizontal. There is a constant friction force acting on the box with a magnitude of 22.0 N.

54 d. Draw a free body diagram including all the forces acting on the box. (20) e. What is the magnitude of the force the worker must apply to maintain the motion?. f. Find the magnitude of the normal force the floor exerts on the box. TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 1 June 10, 2004 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of ten (10) problems on seven (7) pages.

55 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 80 minutes to complete the examination. 4. The total weight of the examination is 100 points. 5. There are six (6) multiple choice and four (4) calculation problems. Work all calculation problems multiple choice problems. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 10:15 a.m. Stop: 11:35 a.m PROBLEM POINTS CREDIT TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. If L stands for length, T for time, and M for mass, the dimensions of acceleration are? (5) i. ML 2. j. ML/T. k. L/T 2.

56 l. L/M. 2. Which one of the following statements is NOT true in case of 2-dimentional motion? a. If the acceleration is zero, the speed must be constant. (5) b. If the speed is constant, the acceleration must be zero. c. If the acceleration is zero, the direction of motion must be constant. d. If the speed and direction of the motion are constant, the acceleration must be zero. 3. Figure below represents the parabolic trajectory of a projectile going from point A to point C. What is the direction of the projectile s acceleration at point B? (5) i. Up and to the right. j. Down and to the left. k. Straight up. l. Straight down. 4. You have two vectors, A (6.00; -3.00) and B (-3.00; 4.00). Which one of the following vectors is A + B? a. (9.00; -7.00). (5) b. (3.00; 1.00). c. (-18.0; -12.0). d. (3.00; -7.00). 5.Imagine a physics textbook laying on a horizontal table. One of the forces acting on a textbook is a

57 normal force exerted by the table (let s call it action). What force does form the Newton s 3 rd law pair (reaction)? a. Gravitational force exerted on the textbook by the Earth. (5) b. Gravitational force exerted on the table by the textbook. c. Normal force exerted on the table by the textbook. d. Normal force exerted by the Earth on the table. 6. Take a look at the graph representing one-dimensional motion of a body. Is the instantaneous velocity of the body at point A: (5) i. Positive. j. Negative. k. Zero. l. Cannot be determined from the graph. 7. A joyful physics student throws his cap into the air with an initial velocity of 24.5 m/s at 36.9 o from the horizontal. Another physics student catches the cap at the same height it was thrown. a. What are the components of the cap s initial velocity? V0: o V0x = V0 cos( 0) = 24.5 m/s cos(36.9 o ) = 19.6 m/s V0y = V0 sin( 0) = 24.5 m/s sin(36.9 o ) = 14.7 m/s b. How long is the cap in the air?

58 y = y 0 + V 0y t ½ g t 2 0 = 0 + V 0y t ½ g t 2 0 = (V 0y ½ g t) t (V 0y ½ g t) = 0 t = 2 V 0y /g = 2 (14.7 m/s)/ (9.80 m/s 2 ) = 3.00 s c. What is the maximum height of the cap s trajectory? y = y 0 + V 0y t ½ g t 2 y = (0 m) + (14.7 m/s)(1.50 s) ½ (9.80 m/s 2 ) (1.50) 2 = 11.0 m d. How far does the cap travel in horizontal direction? x = x0 + V0x (t) = 0 m + (19.6 m/s) (3.00 s) = 58.8 m 8. A bullet traveling at 350 m/s strikes a telephone pole and penetrates a distance of 12.0 cm before stopping. a. Assuming that acceleration is constant, find the acceleration of the bullet inside the pole. V 2 = V a ( x- x 0 ) V = 0 m/s; V 0 = 350 m/s; x- x 0 = m a = (V 2 - V 2 0 )/ (2 ( x- x 0 )) a = -510,417 m/s 2 b. How long does it take for the bullet to stop? V = V 0 + a t t = (V - V 0 )/a t = (0 m/s 350 m/s) / (-510,417 m/s 2 ) = 6.84 x 10-4 s c. What is the average velocity of the bullet inside the pole?

59 V average = (x - x 0 )/(t - t 0 ) = (0.120 m)/(6.84 x 10-4 s) = 175 m/s 9. Two cats pull horizontally on the ropes attached to a toy mouse. Cat A exerts a force of 130 N at 20 O north of east and cat B exerts a force of 90 N due west. Find the magnitude of the resultant force on the toy and its direction. A: o B: o Ax = A cos( A) = (130 N) cos(20 o ) = 122 N Ay = A sin( A) = (130 N) sin(20 o ) = 44.5 N Bx = B cos( B) = (90.0 N) cos(180 o ) = N By = B sin( B) = (90.0 N) sin(180 o ) = 0 N Rx = Ax - Bx = 122 N 90.0 N = 32.0 N Ry = Ay - By = 44.5 N 0 N = 44.5 N 2 2 R = (Rx + Ry ) 1/2 = ( (32.0 N) 2 + (44.5 N) 2 ) 1/2 = 54.8 N R = tan -1 (Ry /Rx) = tan -1 (44.5 N /32.0 N) = 54.3 o 10. A 30.0 kg sled is coasting with constant velocity of 5.00 m/s over perfectly smooth, level ice. It enters a rough stretch of ice 20.0 m long in which the force of friction exerted by the ice on the sled is 12.0 N. a.draw a free body diagram indicating all forces acting on the sled while on rough stretch. b. Calculate the magnitude of the normal force the ice exerts on the sled. nx = n cos(9 ) = 0 ny = n sin(9 ) = n fx = f cos(180 ) = -f = N fy = f sin(180 ) = 0 wx = w cos(270 ) = 0 wy = w sin(270 ) = (30.0 kg) (9.80 m/s 2 ) = -294 N Fy = m ay = N + n = 0 n = 294 N

60 c. Calculate the acceleration of the sled while on rough stretch. Fx = m ax N = (30.0 kg) a x a x = m/s 2 Bonus (Worth 5 points): What is the coefficient of kinetic friction between ice and the sled? f = n = f/n = (12.0 N)/ (294 N) = TIME OF COMPLETION NAME SOLUTION

61 DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 1 June 20, 2005 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of ten (10) problems on seven (7) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 75 minutes to complete the examination. 4. The total weight of the examination is 100 points. 5. There are six (6) multiple choice and four (4) calculation problems. Work all problems. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 11:25 a.m. Stop: 12:50 p.m PROBLEM POINTS CREDIT TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR

62 PARTIAL CREDIT. 3. If a is acceleration, v is velocity, x is position, and t is time, then which equation is NOT dimensionally correct? m. t = x/v. (5) n. a = v 2 /x. o. v = a/t. p. t 2 = 2x /a 2. Which of the following expresses a principle initially stated by Galileo and later incorporated into Newton s laws of motion? i. An object s acceleration is inversely proportional to its mass. (5) j. For every action is an equal but opposite reaction. k. The natural condition for a moving object is to remain in motion. l. The natural condition for a moving object is to come to rest.. 3. A 7.00 kg bowling ball experiences a net force of 5.00 N. What is its acceleration? m m/s 2. n m/s 2. (5) a = F/m = (5.00 N)/(7.00 kg) o m/s 2. p m/s Which of the following is an example of the type of force which acts at a distance? a. Strong nuclear. b. Weak nuclear.

63 (5) c. Electromagnetic. d. All of the above. 5. Imagine a box sitting on a horizontal table. One of the forces acting on a box is a normal force exerted by the table (let s call it action). What force does form the Newton s 3 rd law pair (reaction)? q. Normal force exerted on the Earth by the table. (5) r. Normal force exerted on the table by the Earth. s. Normal force exerted on the table by the box. t. Normal force exerted on the Earth by the box. 6. Vector A points north and vector B points east. If C = B A, then vector C points: m. North of east. (5) n. South of east. o. North of west. p. South of west. 7. A projectile is fired with an initial speed of 51.2 m/s at an angle of 44.5 o above the horizontal on a long flat firing range. Determine a. The components of the projectile s initial velocity. V 0 : o V x0 = V 0 cos( 0 ) = (51.2 m/s) cos(44.5 o ) = 36.5 m/s

64 V y0 = V 0 sin( 0 ) = (51.2 m/s) sin(44.5 o ) = 35.9 m/s b. The maximum height reached by the projectile. V 2 y = V 2 y0-2 g (y y 0 ) (y y 0 ) = (V 2 y - V 2 y0 )/(- 2 g) V y = 0 m/s (y y 0 ) = (V 2 y0 )/(2 g) = 65.8 m Time to reach the top: c. The total time in the air. V y = V y0 gt 1/2 t 1/2 = V y0 /g = 3.66 s Total time: t = 2 t ½ t = 7.33 s d. The projectile s range. x = x 0 + V x0 t x = (0 m) + (36.5 m/s) (7.33 s) = 267 m Bonus (5 extra points): Find velocity of the projectile 1.50 s after firing. V x = V x0 = 36.5 m/s V y = V y0 gt = (35.9 m/s)- (9.80 m/s 2 )(1.50 s) = 21.2 m/s V =((36.5 m/s) 2 + (21.2 m/s) 2 ) 1/2 = 42.2 m/s = tan -1 (V y /V x ) = = tan -1 ((21.2 m/s)/(36.5 m/s)) = 30.0 o 9. A stone is thrown vertically upward with a speed of 10.0 m/s from the edge of the cliff

65 5.0 m high. a. How much later does it reach the bottom of the cliff? y = y 0 + V y0 t ½ gt 2 y = 5.00 m y 0 = 0 m V y0 = m/s 0 = t 4.9 t t 2-10 t - 5 = 0 t = 2.46 s V y = V y0 - gt b. What is its speed just before hitting? V y = (10.0 m/s) (9.80 m/s 2 )(2.46 s) = s V y = 14.1 s To the top: c. What total distance did it travel? V y 2 = V y0 2-2 g (y y 0 ) (y y 0 ) = (V y 2 - V y0 2 )/(- 2 g) V y = 0 m/s y - y 0 = (V y0 2 )/(2 g) = 5.10 m Total distance traveled: 5.10 m m m = 15.2 m 10. Jets at JFK International airport accelerate from rest at one end of a runaway, and must attain takeoff speed before reaching the other end of the runaway. A plane has acceleration of 11.0 m/s 2 and takeoff velocity of 90.0 m/s.

66 V 0 = 0 m/s V= 90.0 m/s a = 11.0 m/s2 a. What is the minimum runaway required for this airplane? V 2 = V a (x x 0 ) (x x 0 ) = (V 2 - V 0 2 )/(2 a) (x x 0 ) = 368 m V = V 0 + a t b. How long time does it take the plane to attain the takeoff speed? t = (V - V 0 )/a = 8.18 s c. What is the average velocity of the plane in the process? V av = (x x 0 )/t = (368 m) / (8.18 s) = 45.0 m/s 10. Vector A has a magnitude of 50.0 m and points in a direction 20.0 o below the x axis. A second vector, B, has a magnitude of 70.0 m and points in a direction 50.0 o above the x axis. Find a new vector R = A + B. Find the magnitude and direction of vector R. A x = A cos( A ) = (50.0 m) cos(-20.0 o ) = 47.0 m A y = A sin( A ) = (50.0 m) sin(-20.0 o ) = m B x = B cos( B ) = (70.0 m) cos(50.0 o ) = 45.0 m B y = B sin( B ) = (70.0 m) sin( 50.0 o ) = 53.6 m R x = A x + B x = (47.0 m) + (45.0 m) = 92.0 m R y = A y + B y = (-17.1 m) + (53.6 m) = 36.5 m R = ( R x 2 + R y 2 ) 1/2 = ( (92.0 m) 2 + (36.5 m) 2 ) 1/2 = 99.0 m

67 R = tan -1 (R y /R x ) = tan -1 ((36.5 m)/(92.0 m)) = 21.6 o TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 1 Version 1 June 20, 2007 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of ten (10) problems on seven (7) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 75 minutes to complete the examination.

68 4. The total weight of the examination is 150 points. 5. There are six (6) multiple choice and four (4) calculation problems. Work all calculation problems and 5 (five) multiple choice. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 1:30 p.m. Stop: 2:45 p.m PROBLEM POINTS CREDIT TOTAL 150 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. Which of the following is a vector quantity? a. Time (6) b. Mass. c. Displacement. d. Speed.

69 2. Suppose that a car traveling to the East (+ x direction) begins to slow down as it approaches a traffic light. Make a statement concerning its acceleration. a. The car s acceleration is positive. (6) b. The car s acceleration is negative. c. The acceleration is zero. d. A statement cannot be made using the information given. 3. If the position versus time graph of an object is a horizontal line, the object is a. Moving with constant non-zero velocity. (6) b. Moving with constant non-zero acceleration. c. At rest. d. Moving with infinite velocity. 4. The acceleration of an object is linearly proportional to a. The net force acting on it. (6) b. Its position. c. Its velocity. d. Its mass. 5. A ball is thrown straight up. When it reaches its highest point, PHYS 1111 Exam 1, Version 1 Fall

70 a. Both its velocity and its acceleration are zero. (6) b. Its velocity is zero and its acceleration is not zero. c. Its velocity is not zero and its acceleration is zero. d. Neither its velocity nor acceleration is zero. 6. A ball is thrown straight into the air. Ignore air resistance. At the highest point of its trajectory, the net force acting on it is a. Equal to its weight. (6) b. Greater than its weight. c. Less than its weight. d. Zero. 7. Vector V 1 is 12.5 units long and points along the negative x axis. Vector V 2 (30) points at 25.0 o to the positive x axis. a. What are the x and y components of each vector? is 4.35 units long and V 1x = V 1 cos( 1 ) = (12.5) cos(180 o ) = V 1y = V 1 sin( 1 ) = (12.5) sin(180 o ) = 0 V 2x = V 2 cos( 2 ) = (4.35) cos(25.0 o ) = 3.94 V 2y = V 2 sin( 2 ) = (4.35) sin( 25.0 o ) = 1.84 PHYS 1111 Exam 1, Version 1 Fall

71 b. Determine the sum V 1 V 2 (magnitude and angle). R x = V 1x + V 2x = (- 12.5) + (3.94) = R y = V 1y + V 2y = (0) + (1.84) = R = ( R x + R 2 y ) 1/2 = ( (-8.56) 2 + (1.84) 2 ) 1/2 = 8.76 R = tan -1 (R y /R x ) = tan -1 ((1.84)/(-8.56)) = o o = 168 o 14. A ball is thrown from the top of a 100-m building with an initial speed of 15.0 m/s at an angle of 40.0º to the horizontal. The ball hits the ground 5.60 s later. a. What are the components of the initial velocity? V x0 = V 0 cos( 0 ) = (15.0 m/s) cos(40.0 o ) = 11.5 m/s V y0 = V 0 sin( 0 ) = (15.0 m/s) sin( 40.0 o ) = 9.64 m/s x = x 0 + V x0 t b. How far from the base of the building does the ball land? x = (0 m) + (11.5 m/s) (5.60 s) =64.4 m c. What is the maximum height that the ball reaches? 2 V y = V 2 y0-2 g (y-y 0 ) 0 = V 2 y0-2 g (y-y 0 ) (y-y 0 ) = V 2 y0 /(2 g) (y- 100 m) = (9.64 m/s) 2 /(2 g) y = 105 m (from the ground) or 4.74 m from the top of the building PHYS 1111 Exam 1, Version 1 Fall

72 Bonus (8 points): Find the angle of the impact. V x = V x0 = 11.5 m/s V y = V y0 - gt = (9.64 m/s) (9.81 m/s 2 )(5.60 s) = m/s = tan -1 (V y /V x ) = tan -1 ((-45.3 m/s)/(11.5 m/s)) = o 15. A bullet traveling at 350 m/s strikes a telephone pole and penetrates a distance of 12.0 cm before stopping. a. What is the acceleration of the bullet assuming it is constant? V 2 = V a (x-x 0 ) a = (V 2 - V 2 0 )/(2(x-x 0 )) a = (0 2 (350 m/s) 2 )/(2(0.120 m)) = m/s 2 = x 10 5 m/s 2 V = V 0 + at b. How long did it take for the bullet to stop? t =(V - V 0 )/a = (0 (350 m/s))/( x 10 5 m/s 2 ) = 6.86 x 10-4 s 10. Dr. K is trying to move a box full of physics textbooks (total mass of 30 kg) up the incline by exerting a constant force of 200 N parallel to the surface of the incline. Luckily for her, the surface of the incline is frictionless. The surface is inclined to the horizontal at an angle of 35 o. g. Draw a free body diagram including all the forces acting on the box. PHYS 1111 Exam 1, Version 1 Fall

73 h. Find the magnitude of the normal force exerted on the box by the incline. A x = A cos(0 o ) = (200 N) cos(0 o ) = 200 N A y = A sin(0 o ) = (200 N) sin(0 o ) = 0 N n x = n cos(90.0 o ) = 0 n y = n sin(90.0 o ) = n w x = w cos( o ) = (30.0 kg) (9.81 m/s 2 ) cos( o ) = -169 N w y = w sin( o ) = (30.0 kg) (9.81 m/s 2 ) sin( o ) = -241 N F y = m a y A y + n y + w y = 0 n -241 N = 0 n = 241 N i. Find the acceleration of the box. PHYS 1111 Exam 1, Version 1 Fall

74 F x = m a x A x w x = m a x a x = (A x + w x )/m a x = (200 N 169 N)/(30.0 kg) = 1.03 m/s 2 TIME OF COMPLETION NAME SOLUTION DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 1 Section 2 PHYS 1111 Exam 1, Version 1 Fall

75 Version 2 February 22, 2010 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There are a total of nine (9) problems on six (6) pages. 2. Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet (provided by your instructor). 3. You will have 50 minutes to complete the examination. 4. The total weight of the examination is 100 points. 5. There are six (6) multiple choice and three (3) calculation problems. Work all calculation problems and 5 (five) multiple choice. Show all work; partial credit will be given for correct work shown. 6. If you have any questions during the examination, see your instructor who will be located in the classroom. 7. Start: 5:00 p.m. Stop: 6:15 p.m. PROBLEM POINTS CREDIT TOTAL 100 PERCENTAGE CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT. 1. A bird flies 3.00 km due west and then 2.00 km due north. What is the magnitude of the PHYS 1111 Exam 1, Version 1 Fall

76 bird s displacement? u km. (5) v km. w km. x km. 2. The gas pedal in a car is sometimes referred to as the accelerator. Which other controls on the vehicle can be used to produce acceleration? m. The breaks. (5) n. The steering wheel. o. The gear shift. p. All of the above. 3.Two vectors appear as in figure below. Which combination points directly to the left? (5) a. P Q b. P Q PHYS 1111 Exam 1, Version 1 Fall

77 c. Q P d. Q P 4. A ball fired from a canon at point 1 follows a trajectory shown below. Air resistance may be neglected. Four possible vectors are also shown in the figure. Which vector best represents the ball s velocity at point 2? a. A. (5) b. B. c. C. d. D. 5. A ball fired from a canon at point 1 follows a trajectory shown above. Air resistance may be neglected. Four possible vectors are also shown in the figure. Which vector best represents the ball s acceleration at point 4? a. A. (5) b. B. c. C. d. D. PHYS 1111 Exam 1, Version 1 Fall

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