Question

A wad of sticky clay of mass m and velocity vector v i is fired at a solid cylinder of mass M and radius R (see figure). The cylinder is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at a distance d < R from the center. (a) Find the angular speed of the system just after the clay strikes and sticks to the surface of the cylinder. (Use the following as necessary: m, M, R, d, and vi for the magnitude of vector v i.) ω = rad/s (b) Is the mechanical energy of the clay–cylinder system constant in this process? Yes No Correct: Your answer is correct. Explain your answer. This answer has not been graded yet. (c) Is the momentum of the clay–cylinder system constant in this process? Yes No Correct: Your answer is correct. Explain your answer.

Answer 1

a] by conservation of angular momentum,

initial angular momentum = final angular momentum

mvd = [0.5*MR^2 + mR^2]w

w = mvd/ [0.5*MR^2 + mR^2]

b] Mechanical energy is not conserved. Energy is lost in collision as it is inelastic collision.

c] No, External force acts as cylinder is fixed, so it will not be conserved.