1. A 6000 lb pickup truck A moving at 40 ft/s collides with a 4000 lb car B moving at 30 ft/s. What is the velocity of their common center of mass after the impact? If the collision is perfectly plastic, how much kinetic energy is lost during the collision?
2. The 1 – lb block A is given an initial velocity v0 = 14 ft/s to the right when it is in position θ = 0, causing it to slide up the smooth circular surface. Determine the normal force exerted by the surface on the block when θ = 60⁰. What is the velocity of the block at this point?
3. The mass is released from rest with the springs unstretched. Its downward acceleration is a=32.2-50s ft/s2, where s is the position of the mass measured from the position in which it is released. How far does the mass fall and what is the maximum velocity that it attains as it falls?
4. Bar AB rotates at 10 rad/s in the counterclock-wise direction. Determine the velocity of point E.
5. The coefficient of kinetic friction between the 14 kg box and the inclined surface is μk = 0.1. The box is initially at rest when it is subjected to a constant horizontal force F = 20 N. What is the velocity of the box two seconds later?
6. The car increases its speed at a constant rate from 40 mph at point A to 60 mph at point B. Find the magnitude of its acceleration when it has traveled along the road a distance a) 120 ft from A and b) 160 ft from A.
7. Bar AC has an angular velocityof 2 rad/s in the counterclockwise direction that is decreasing at 4 rad/s2. The pin at C slides in the slot in bar BD. Determine the angular acceleration and angular velocity of bar BD. Determine the acceleration and velocity of pin C relative to the slot.
8. Determine the acceleration of the 8 kg collar A relative to the bar if the coefficient of kinetic friction between the collar and the bar is μk = 0.1.
9. The 4 kg collar is released from rest in position 1 on the smooth bar. Its velocity when it has fallen to position 2 is 4 m/s. The spring is unstretched when the collar is in position 2. What is the spring constant k?
10. The car is traveling 30 mph when the traffic light 295 feet ahead turns yellow. The driver takes 1 second to react before he applies the brakes. After applying the brakes, what constant rate of deceleration will cause the car to stop just as it reaches the light? How long does it take the car to travel the 295 ft to the light?
11. The 400 lb wrecker’s ball swings at the end of a 25 foot cable. The magnitude of the ball’s velocity at position 1 is 4 ft/s. Find the magnitude of the ball’s velocity just as it hits the wall at position 2. What is the maximum tension in the cable as the ball moves from position 1 to position 2?
12. Cliff divers must time their dives so that they enter the water at the crest of a wave. The crests of the waves are 1 meter above the mean water depth of h = 4 m. The horizontal velocity of the waves is equal to gh. The diver’s aiming point is 2 m out from the base of the cliff. Assuming that the diver’s initial velocity is horizontal, what is the magnitude of his velocity when enters the water? How far out from the aiming point must a crest be when he dives in order for him to enter the water at the crest?
13. If θ = 45⁰ and sleeve P is moving to the right at a constant velocity of 2 m/s, what are the angular velocities and angular accelerations of bars OQ and PQ?
14. The rocket, initially at rest, has a mass of 250 kg and its engine has a constant thrust of 45 kN. The length of the launching ramp is 10 m. If the magnitude of the rocket’s velocity when it reaches the end of the ramp is 52 m/s, how much work is done on the rocket by friction and aerodynamic drag?