Problem Set 1. Ans: a = 1.74 m/s 2, t = 4.80 s

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1 Problem Set 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 reach 30 km/hr? Ans: a = 1.74 m/s 2, t = 4.80 s 1.2 Traveling with an initial speed of 70 km/hr, a car accelerates at 6000 km/hr 2 along a straight road. How long will it take to reach a speed of 120 km/h? Through what distance does the car travel during this time? Ans: t = 30 s, s = 792 m 1.3 The acceleration of a particle as it moves along a straight line is given by a = (2t-1)m/s 2, where t is in seconds. If s = 1m and v = 2 m/s when t = 0, determine the particle s velocity and position when t = 6 s. Also, determine the total distance the particle travels during this time period. Ans: v = 32 m/s, s = 67 m, d = 66 m Problem Set A garden hose discharges water at the rate of 15 m/s. If the nozzle is held at ground level and directed θ = 30 from the ground, determine the maximum height reached by the water and the horizontal distance from the nozzle to where the water strikes the ground. Ans: h = 2.87 m, s x = 19.9 m 2.2 Starting from rest, the motorboat travels around a circular path, ρ = 50 m, at a speed of v = (0.8t)m/s, where t is in seconds. Determine the magnitudes of the boat s velocity and acceleration when it has traveled 20 m. Ans: v = 5.66 m/s, a = 1.02 m/s The motion of a particle is defined by the equations x = (2t + t 2 )m and y = t 2 m, where t is in seconds. Determine the normal and tangential components of the particle s velocity and acceleration when t = 2s Ans: v n = 0, v t = 7.21 m/s, a n = m/s 2, a t = 2.77 m/s 2

2 Problem Set For the system of Problem 10.1, determine the time needed for the load at B to reach a speed of 8 m/s, starting from rest, if the cable as drawn into the motor with an acceleration of 0.2 m/s 2. Ans: t = 160 s 3.2 If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed and direction of block B. Ans: v B = 0.5 m/s 3.3 A man can row a boat at 5 m/s in still water. He wishes to cross a 50-m wide river to point B, 50 m downstream. If the river flows with a velocity of 2 m/s, determine the speed of the boat and the time needed to make the crossing. Ans: v b = 6.21 m/s, t = 11.4 s 3.4 A passenger in an automobile observes that raindrops make an angle of 30 with the horizontal as the auto travels forward with a speed of 60 km/h. Compute the (constant) terminal speed of the rain if it is assumed to fall vertically. Ans: v r = 34.6 km/hr

3 Problem Set The baggage truck A has a mass of 800 kg and is used to pull two cars, each with a mass of 300 kg. If the tractive force F on the truck is F = 480 N, determine the initial acceleration of the truck. What is the acceleration of the truck if the coupling at C suddenly fails? The car wheels are free to roll; neglect the mass of the wheels. Ans: a = m/s 2, a = m/s Each of the two blocks has the same mass m. The coefficient of kinetic friction, μ, is the same at all surfaces of contact. If a horizontal force P moves the bottom block, determine the acceleration of the bottom block in each case. Ans: a A = (P/2m) 2μg 4.3 Determine the tension developed in the cords attached to each block and the accelerations of the blocks. Neglect the mass of the pulleys and cords. Ans: a A = 1.51 m/s 2, T A = 90.6 N, a B = 6.04 m/s 2, T B = 22.6 N, 4.4 The sports car, having a mass of 1700 kg, is traveling horizontally along a 20 banked circular track with a radius of curvature of 100 m. If μ s = 0.2, determine the maximum constant speed at which the car can travel without sliding up the slope. Ans: v max = 24.4 m/s

4 Problem Set Determine the velocity of the 20- kg block A after it is released from rest and moves 2 m down the plane. Block B has a mass of 10 kg and the coefficient of kinetic friction between the plane and A is μ k = 0.2. Also, what is the tension in the cord? Ans: v = 2.64 m/s, T = 115 N 5.2 Determine the height h to the top of the incline D to which the 200-kg roller coaster car will reach, if it is launched at B with a speed just sufficient for it to round the top of the loop at C without leaving the track. The radius of curvature at C is ρ C = 25 m Ans: h = 47.5 m 5.3 The 2-kg ball of negligible size is fired from point A with an initial velocity of 10 m/s up the smooth slope. Determine the distance from point C to where it hits the horizontal surface at D. Also, what is its velocity when it strikes the surface? Ans: d = 8.53 m, v D = 10 m/s

5 Problem Set Blocks A and B have mass of 3 kg and 5 kg, respectively. If the system is released from rest, determine the velocity of block B in 6 s. Neglect the mass of the pulleys and cord. Ans: v B = 35.8 m/s ; T = 19.2 N 6.2 The 5-kg package is released from rest at A. It slides down the smooth plane which is inclined at 30 onto the the rough horizontal surface (μ k = 0.2). Determine the total time of travel before the package stops sliding. Ans: t = 5.47 s 6.3 The 2-kg ball is thrown at the suspended 20-kg block with a velocity of 4 m/s. If e = 0.8, determine the maximum height h to which the block will swing before it momentarily stops. Ans: h = 21.8 mm

6 Problem Set Starting from rest when s = 0, pulley A is given a constant angular acceleration a C = 6 rad/s 2. Determine the speed of block B when it has risen s = 6 m. The pulley has an inner hub D which is fixed to C and turns with it. Ans: v B = 1.34 m/s 7.2 The operation of reverse for a 3- speed transmission is illustrated. If the crack shaft G is turning with an angular speed of 60 rad/s, determine the angular speed of the driveshaft H. Each of the gears rotates about a fixed axis. Note that gears A and B, C and D, E and F are in mesh. Ans: ω H = 126 rad/s 7.3 The crankshaft AB is rotating about a fixed axis passing through A. Determine the speed of the piston P at the instant it is the position shown. Ans: v C = 50 m/s

7 Problem Set The sports car has a mass of 1.5 Mg and a center of gravity at G. Determine the shortest time it takes for it to reach a speed of 80 km/hr, starting from rest, if the engine drives only the rear wheels. μ s = 0.2. Neglect the mass of the wheels. If power can be supplied to all wheels, what would be the shortest time for the car to reach 80 km/hr? Ans: rear wheels: t = 17.5 s 4 wheels: t = 11.3 s. 8.2 The 80-kg disk is supported by a pin at A. If it is released from rest from the position shown, determine the initial horizontal and vertical reactions at the pin. Ans: A x = 0, A y = 262 N 8.3 The disk has a mass M and a radius R. If a block of mass m is attached to the cord, determine the angular acceleration of the disk when the block is released from rest. Also, what is the velocity of the block after it falls a distance of 2R starting from rest? Ans: α = 2mg/[R(M + 2m)] v 2 = 8mgR/(M + 2m) 8.4 The 2-kg slender bar is supported by cord BC and then released from rest at A. Determine the initial angular acceleration of the bar and the tension in the cord. Ans: α = 28.0 rad/s 2, T = 5.61 N

8 Problem Set The hand winch is used to lift the 50-kg load. Determine the work required to rotate the handle five revolutions. The gear at A has a radius of 20 mm. Ans: U = 237 J 9.2 The pendulum of the Charpy impact machine has a mass of 50 kg and a radius of gyration k A = 1.75 m. If it is released from rest when θ = 0, determine its angular velocity just before it strikes the specimen S, θ = 90. Ans: ω = 2.83 rad/s 9.3 The spool has a mass of 50 kg and a radius of gyration k O = m. If the 20-kg block A is released from rest, determine the distance the block must fall in order for the spool to have an angular velocity ω = 5 rad/s. Also, what is the tension in the cable while the block is in motion? Neglect the mass of the cord. Ans: s = m, T = 163 N

9 Problem Set The drum has a mass of 70 kg, a radius of 300 mm and radius of gyration k O = 125 mm. If μ s = 0.4 and μ k = 0.3, determine the drum s angular velocity 2 s after it is released from rest. Take θ = 30. Ans: ω = 27.9 rad/s 10.2 The crate has a mass m c. Determine the constant speed v o it acquires as it moves down the conveyor. Treat the rollers as thin rings with have mass m, radius r and spaced d apart. Note that friction causes each roller to rotate when the crate comes in contact with it. Ans: v 0 2 = (2gdm c /m) sinθ 10.3 A thin ring having a mass of 15 kg strikes the 20-mm high step. Determine the minimum angular velocity ω 1 the ring can have so that it will just roll over the step at A when it strikes it. Ans: ω 1 = rad/s