Problem 1 - A particle of mass m slides down a frictionless chute and enters a circular loop of diameter d. Find the minimum starting height h in order that the particle will make a complete circuit of the loop and exit normally without having lost contact with the loop.
Problem 2 - A skier descends the smooth slope above (right) starting from rest at point A. Her total mass is 52 kg. Determine the normal force she exerts on the ground the instant she arrives at B. What is her acceleration at this point?
Problem 3 - The block shown below is released from rest. What is the maximum velocity of the block, the maximum compression of the spring and the maximum distance from the spring after it rebounds up the plane?
Problem 4 - At the instant shown above (right) block B is 30 m below the level of Block A. At this time the velocity of each block is zero. Determine the velocities of A and B as they pass each other. The mass of A is 15 kg and the mass of B is 5 kg. The pulleys are light.
Problem 5 - A 10-kg block swings down and strikes an identical block. Assume that the 6-m rope breaks during impact and the coefficient of restitution is zero. How long will it be before m2 comes to rest? How far will it have traveled? What is the percentage of energy lost during the Impact? Compare the results to the case where e = 1.
Problem 6 - A cannonball is fired as shown above (right) with an initial speed of 1600 ft/sec. The cannon recoils and strikes a plate attached to a spring. Find the maximum spring deflection if the plane is smooth and the spring constant is 500 lb/ft.
Problem 7 - Weight W1 falls from rest through a distance H; it lands on another weight W2, which was in equilibrium atop a spring of modulus k. If the coefficient of restitution is zero, find the maximum compression of the spring.
Problem 8 - Two identical hockey pucks collide, coming into contact in the positions shown above (center). Their velocities before collision are given above. If e = 0.8, find the velocities of the pucks after collision and the impulse of the force on puck B.
Problem 9 - A man of mass m and a boat of mass M are at rest as shown above (right). If the man walks to the front of the boat, what is his distance from the pier at that instant?