Question

A 5 kg block of wood connected to a horizontal spring (constant 130 N/m) is at rest on a frictionless plane. Bullet (50 mg) is fired at block and horizontal velocity is 25 m/s and bullet is stuck in it. The block goes through simple harmonic oscillation.

What is the amplitude of resulting oscillation?

What is the total mechanical energy of the block with the bullet inside?

What is the magnitude of velocity of the block with the bullet when its half way between equilibrium position and the point of maximum displacement?

Answer 1

Let initial speed of bullet = v1 = 25 m/s

Let speed of block + bullet just after bullet hit = v2

Using momentum conservation

Now let amplitude = x

Using energy Conservation

(b) Total Mechanical energy E

(c) Let speed at halfway = v3

and compression in spring = x3

putting the value and solving we get

===========================================

mention in the comment box if you have any doubt