Question

1.A 500g ball rolling at 2.4m/s hits a stationary ball of mall 800g in a perfectly elastic collision. what are the velocities of the collisions?

2. A 14.0 block hangs by a light string that passes over a frictionless pulley of negligible mass the string is attached to a 6.0kg block on a table with Mu=0.20 The other side of the 6.0kg block is attached to a spring with k = 180 N/m. Find the speed of the 6.0 kg block when the 4kg block hits the ground?

Answer 1

Given

masses of the balls are

m1 = 0.5 kg, moving with initial velocity u1 = 2.4 m/s

m2 = 0.8 kg, moving with initial velocity u2 = 0 m/s (rest)

the collision is perfect elastic collision and head on collision

from the concept of conservation of momentum and kinetic energy we have the final velocities of the masses are

of first mass   v1 = (m1-m2)u1/(m1+m2) +2m2*u2/(m1+m2)

of second mass   v2 = (m2-m1)u2/(m1+m2) +2m1*u1/(m1+m2)

substituting the values

   v1 = ((0.5-0.8)(2.4))/(0.5+0.8) + (2*0.8*0)/(0.5+0.8) m/s

   v1 = -0.554 m/s

for mass2

   v2 = ((0.8-0.5)(0))/(0.5+0.8) + (2*0.5*2.4)/(0.5+0.8) m/s

   v2 = 1.85 m/s