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


 Bartholomew Christopher McCormick
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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 = (2t1)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 50m 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 200kg 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 2kg 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 5kg 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 2kg ball is thrown at the suspended 20kg 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 80kg 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 2kg 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 50kg 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 20kg 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 20mm 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
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