Momentum and Energy COnservation and Collisions

Question

A block of mass M, at rest on a frictionless horizontal table, is attached to a rigid wall by an ideal spring with spring constant k. A bullet of mass m and speed v strikes the block and becomes embedded in the block. The block + bullet system then executes simple harmonic motion.

Calculate the block + bullet system’s maximum speed.

Hello! this is the problem above. Can someone please explain to me why KE-max=PE max cannot be used here?

I tried to solve for the velocity this way. However, the answer says to use conservation of momentum. Can anyone explain why?

Answer 1

I'm not sure if this is what you meant but the max kinetic energy can never equal the max potential energy because potential energy and kinetic energy change in a system and the total mechanical energy has to stay the same. It is better to use momentum because the second that the bullet hits the block is when it will have it's maximum speed. This is because the kinetic energy will transform into potential energy when the spring compresses. First calculate the momentum of the bullet which is P=(M of Bullet)*(Velocity of Bullet). The momentum of the block is zero because it is at rest. This means that the combination of the block and bullet's momentum is equal to the momentum of the bullet.

(M of Bullet)*(V of Bullet)=(M of Bullet+Block)*(V of Bullet+Block).

Max velocity is equal to ((M of Bullet)*(V of Bullet))/(M of Bullet+Block)