A ball of mass m slides with velocity v on a frictionless horizontal surface and

Question

A ball of mass m slides with velocity v on a frictionless horizontal surface and hits a large wooden block of mass M which lies on the same frictionless surface. The block M is suspended like a pendulum and initially at rest. The ball has become embedded in the block after the collision.

a. What is conserved during the collision?

b. Why is that conserved? (provide a short explination)

c. What is the speed of the block just after the ball has become embedded in terms of m, M, and v?

As a result of the collision, the block and the ball swing up to a maximum height h.

d. What is conserved during the swing?

e. Why is that conserved? (provide a short explanation)

f. Determine the maximum height h in terms of m, M, and v.

Explanation / Answer

linear momentum is conserved because no net enternal force is acting on the system.

by conservation of linear momentum >

mv = (m+M)V

V = mv/(m+M)

Total mechanical energy of the system is conserved afterwards as kinetic evergy at the bottom most point will convert into potential energy for reaching maximum height for both masses as energy can only be transformed from 1 form to other

1/2(m+M)V^2 = (m+M)gh

h = V^2/29

h = {mv/(m+M}^2/2g

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