Bullet shot into a block

  • Thread starter oadeyemi
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  • #1
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Homework Statement



A bullet of mass m is fired into a block of mass M initially at rest on a frictionless table of height h. The bullet remains m in the block, and after impact the block lands a distance d from the bottom of the table. Determine the initial speed of the bullet.

Homework Equations



I used (m +M)gh for the potential energy and set that equal to the kinetic energy ½(m + M)v₂² and found that v₂ = √(2gh).

And since it was a completely inelastic collision (right?) I used mv₁ = (m + M)v₂ → v₁ = (m + M)v₂ * 1/m

Is this right?


The Attempt at a Solution



initial velocity = √(2gh)*((m + M)/m)
 
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Answers and Replies

  • #2
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Do you have an attempt at the problem? If not, tell me your thought process for the problem.
 
  • #3
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Do you have an attempt at the problem? If not, tell me your thought process for the problem.
I used (m +M)gh for the potential energy and set that equal to the kinetic energy ½(m + M)v₂² and found that v₂ = √(2gh).

And since it was a completely inelastic collision (right?) I used mv₁ = (m + M)v₂ → v₁ = (m + M)v₂ * 1/m

Is this right?
 
  • #4
114
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I used mv₁ = (m + M)v₂ → v₁ = (m + M)v₂ * 1/m
Something about this chunk doesn't seem right to me for some reason. Everything else is correct, from my understanding. Is this a formula you received from your text, or is this something that you derived yourself?

Check out the Wiki article, I think I see where you're going with this, but I see a slight error in your formula: http://en.wikipedia.org/wiki/Inelastic_collision
 
  • #5
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Something about this chunk doesn't seem right to me for some reason. Everything else is correct, from my understanding. Is this a formula you received from your text, or is this something that you derived yourself?

Check out the Wiki article, I think I see where you're going with this, but I see a slight error in your formula: http://en.wikipedia.org/wiki/Inelastic_collision
It's from my textbook
 
  • #6
Borek
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I think the formula here is OK, wiki describes different situation (initial velocity of M not being zero) and uses different symbols, hence the confusion.

Problems are with the other part - v2 that you calculated from the energy conservation is a vertical component of the speed when block with a bullet hits the ground. That's not initial HORIZONTAL speed of the body.
 
  • #7
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I think the formula here is OK, wiki describes different situation (initial velocity of M not being zero) and uses different symbols, hence the confusion.

Problems are with the other part - v2 that you calculated from the energy conservation is a vertical component of the speed when block with a bullet hits the ground. That's not initial HORIZONTAL speed of the body.
Elaborate please
 
  • #8
Borek
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Once the bodies (m+M) left the table they behave just like something thrown norizontally - they maintain horizontal speed, but they start to fall down, till they hit the ground at distance d from the table border.
 

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