Bullet and a Block: Solve the Problem

[directdelta]

http://blog.360.yahoo.com/blog-rkirjZg1crSQi6eQnmqL4njg_w--?cq=1

Please try to solve this problem. Thanks.

 

[OlderDan]

http://blog.360.yahoo.com/blog-rkirjZg1crSQi6eQnmqL4njg_w--?cq=1

Please try to solve this problem. Thanks.

Please show us your attempt at solving this problem. Then we will help you work your way through it.

 

[directdelta]

Okay... i equated .5kx^2 and .5mv^2 for the block, and got the velocity, v. Then i used mv=MV (conservation of momentum) to find the final velocity of the bullet as it emerges out of the block. But that is not the correct answer.
Help me.

 

[OlderDan]

Okay... i equated .5kx^2 and .5mv^2 for the block, and got the velocity, v. Then i used mv=MV (conservation of momentum) to find the final velocity of the bullet as it emerges out of the block. But that is not the correct answer.
Help me.

Let's be clear on M vs m and V vs v. Your energy calculation involves the spring and the block, so i assume m is mass of block and v is its velocity when the spring starts to compress. The momentum conservation problem can be assumed complete before the spring compreses.

Look at the momentum problem again. You have a bullet moving with known velocity toward a stationary block. After the collision you know the velocity (from the energy calculation) of the block and you need the final velocity of the bullet. Your momentum equation does not correspond to this situation. See if you can fix it.

 

[Andrew Mason]

http://blog.360.yahoo.com/blog-rkirjZg1crSQi6eQnmqL4njg_w--?cq=1

Please try to solve this problem. Thanks.

Interesting problem.

Since the bullet is traveling at 500 m/sec, it passes through the block before the block really begins to move. So we can treat this as if the block acquires an instantaneous kinetic energy which is then transferred into the spring. We know what the energy transferred to the block is $E = kx^2/2$ where v₀ is the speed of the block after collision. So you can work out the speed of the block after the bullet passes through. I think that is what you have done.

Since momentum has to be conserved,

$$mv_{f-bullet} + Mv_{block} = mv_{i-bullet}$$

That may be where you are having some difficulty.

AM

 

[directdelta]

Thank You. I finally solved it. siggghhhh