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Muzzle Speed

Date: 03/21/2002 at 22:27:11
From: Jaime
Subject: Physics

A 15-gram bullet strikes and becomes embedded in a 1.10 kg block of 
wood placed on a horizontal surface just in front of the gun. If the 
coefficient of friction between the block and the surface is .25 and 
the impact drives the block 9.5 meters before it comes to rest, what 
was the muzzle speed of the bullet?

Date: 03/22/2002 at 09:28:12
From: Doctor Ian
Subject: Re: Physics

Hi Jaime,

There are two things going on here. The first is that the bullet 
transfers its momentum to the block. That is, 

  momentum of bullet before = momentum of bullet and block after

Now, this doesn't help you unless you know one of the speeds involved.  
Fortunately, you know that the block starts sliding with some initial 
velocity, v0; and there is a force acting to slow it down; and it 
comes to a rest after some point. 

This is exactly the same situation you get when you throw a ball into 
the air, and gravity slows it down until it pauses for a moment at the 
top of its trajectory, except you have a frictional force instead of a 
gravitational force, and the direction is horizontal instead of 

Think about how you would solve the problem for the ball (i.e., if it 
reaches a certain height before stopping, what was the initial upward 
velocity), and use that same approach to find the initial velocity of 
the block. 

Once you have the initial velocity of the block, you can use 
conservation of momentum to deduce the velocity of the bullet when it 
hit the block. 

Does this help? 

- Doctor Ian, The Math Forum   
Associated Topics:
High School Physics/Chemistry

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