1. A 2-kg pellet travels with velocity 100 m/s to the right when it collides wit

Question

1. A 2-kg pellet travels with velocity 100 m/s to the right when it collides with a 38-kg hanging mass which is initially at rest. After the collision, the pellet remains lodged in the hanging mass, i.e., it is a completely inelastic collision. The hanging mass (+pellet) then swings upward and reaches a maximum height hmax before swinging downward again. Assume that no external forces are present and therefore the momentum of the system is conserved.

a. What is the velocity vf (in m/s) of the hanging mass + pellet immediately after the collision?

b. What is the final kinetic energy Kf (in J) of the hanging mass + pellet immediately after the collision?

2. The displacement of an oscillating mass is given by x(t) = 20 cos( 2 t ). At time t = 1.5? s, what is the acceleration of the mass in m/s2?

Explanation / Answer

a) initital momentum = 2*100 = 200 kg m/sec

let the final velcocity be v

so.. (38+2)*v = 200

sp.. v = 5 m/sec

b) kinetic energy = 0.5*(38+2)*v^2 = 0.5 * 40*5^2 = 500 J

2) v(t) = dx / dt = - 40 * sin (2t )

a(t) = dv / dt = - 80 cos (2t)

so.. at t = 1.5 sec

acceleraiton a = 79.199399728 m/sec2

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