Problem 1:
The mass m compresses the linear elastic spring, whose constant is k, a distance δ0. The mass is released from rest and it slides along the horizontal surface with negligible friction until it encounters the bottom of rod OB. The mass attaches to B via a slot in the mass, and the rod and mass begin swinging upward in the vertical plane. Neglecting the mass of the rod, determine the initial compression of the spring so that the rod and mass reach the opposite vertical position with zero tension or compression in the rod.
Problem 2:
The box B of mass mB is attached the cart C of mass mC via the linear elastic spring of constant k. The spring is compressed a amount δ when the system is released from rest. Determine the velocity of the box relative to the cart at the instant the spring becomes uncompressed. Use mB D 10 kg, mC D 25 kg, k D 150N=m, and δ D 0:5m. Neglect the mass of the spring and of the wheels.
Problem 3:
Disc B is moving at speed vB in the direction shown when it encounters disc A, which is at rest. If the coef?cient of restitution of the impact is e and the mass of A is twice that of B, determine the post-impact velocities of A and B. The discs lie in the horizontal plane. Express your answers in the given component system.
