How Far Does the Block Slide Before Coming to Rest?

In summary, the problem involves a bullet of mass m and initial velocity V0 colliding with a wooden block of mass M and coefficient of kinetic friction μ. The bullet comes to a stop in the block and the block slides along a horizontal surface. To find the distance the block slides before coming to rest, the work-energy theorem is used, with the initial kinetic energy equal to the work done by friction. Conservation of momentum can also be used to find the initial velocity of the block+bullet system. The approach of using both conservation of momentum and the work-energy theorem is correct.
  • #1
renaldocoetz
33
0

Homework Statement



Consider a bullet of mass m fired at a speed of V0 into a wooden block of mass M. The bullet instantaneously comes to rest in the block. The block with the embedded bullet slides along a horizontal surface with a coefficient of kinetic energy [tex]\mu[/tex].
How far does the block slide before it comes to rest? Express your answer in terms of m, M, [tex]\mu[/tex] and g.

Homework Equations



W = Fs

W = KEf - KE0

where s = displacement

The Attempt at a Solution



I started by saying W = Fs and thought the only net force working here is kinetic friction.
so W = FN [tex]\mu[/tex] s and since FN = mg i said...
W = (m +M)g [tex]\mu[/tex]s

then i said since W = KEf - KE0 ...
(m + M)g[tex]\mu[/tex]s = KEf - KE0

is this the right appoach?

I can't use conservation of momentum since the sum of external forces arent 0, I am assuming since they give the coefficient of kinetic friction.
 
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  • #2
Yes, you can use conservation of momentum. The problem says that the bullet stops instantly. This means that the collision is completed before the block starts moving, i.e. before the external force of friction with the table starts acting on the block. You need to conserve momentum to find the initial velocity of the block+bullet system.
 
  • #3
OK it seems i missread. It says "coefficient of kinetic energy", not "coefficient of kinetic friction".

Either way I am really clueless as to how to proceed :( Especially how to eventually get to distance. How do i know when to use conservation of momentum and when to use conserv of Kinetical Energy?
 
  • #4
It should be coefficient of kinetic friction. It is safe to say that you conserve momentum when you have a collision, when two objects come together or push each other apart. As far as energy conservation is concerned, one usually talks about conservation of mechanical energy, which the sum of kinetic and potential energy. You conserve that when there are no dissipative forces such as friction or air resistance. If there are such things present (there is usually wording in the problem to indicate one way or the other), you have to use the work-energy theorem that says that the change in kinetic energy is equal to the net work (work done by the net force).

In answer to your question, yes your approach is correct. All you need to do is find KE0. You do that by conserving momentum for the part of the motion where the bullet embeds itself in the block.
 

1. What happens when a bullet hits a block of wood?

When a bullet hits a block of wood, it creates a high amount of pressure and heat. The bullet's kinetic energy is transferred to the wood, causing it to compress and heat up. This compression and heat can cause the wood to crack, splinter, or even catch fire depending on the type of bullet and wood.

2. Can a bullet completely penetrate a block of wood?

It is possible for a bullet to completely penetrate a block of wood, but it depends on the type of bullet and the density of the wood. A high velocity, armor-piercing bullet may be able to penetrate a thick block of wood, while a slower, softer bullet may not have enough force to do so.

3. How does the angle of impact affect the wood when a bullet hits it?

The angle of impact can greatly affect the damage done to the wood when a bullet hits it. A perpendicular impact will transfer the most energy and result in the most damage, while a glancing impact may cause the bullet to ricochet off the surface of the wood.

4. What factors determine the amount of damage done to the block of wood?

The amount of damage done to the block of wood by a bullet depends on several factors, including the type and velocity of the bullet, the density and thickness of the wood, and the angle of impact. Additionally, the condition and composition of the wood can also affect the damage done.

5. Can a bullet change direction when it hits a block of wood?

Yes, a bullet can change direction when it hits a block of wood. This is known as bullet deflection and can occur when the bullet hits a knot or other imperfection in the wood, causing it to redirect its path. The angle of impact and the surface of the wood can also contribute to bullet deflection.

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