Energy Conservation in Oscillatory Motion

[kaka2007]

A 2.25-g bullet embeds itself in a 1.50-kg block, which is attached to a spring of force constant 785 N/m. If the maximum compression of the spring is 5.88cm find (a) the initial speed of the bullet and (b) the tie for the bullet-block system to come to rest

I used:

E = K + U = .5(.00225)v^2 + 0

E=Umax = .5(785)(.0588)^2

and then solved for v but it's not right. btw the real answer is 897 m/s

 

[Gear300]

The bullet was embedded in the block, which means that some of the kinetic energy of the bullet was transferred to internal energy of the system. Instead of using energy conservation, use momentum conservation. You know that for the spring to to compress a certain amount, the bullet-block system had a certain initial velocity (kinetic energy). Use that velocity for the conservation equation.

 

[Dick]

Use conservation of momentum first to get an expression for the velocity of the block with the bullet embedded in terms of the velocity of the bullet. The equate initial kinetic energy of the block+bullet to the spring energy.