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Momentum problem

by bcjochim07
Tags: momentum
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bcjochim07
#1
Mar30-08, 03:56 PM
P: 374
1. The problem statement, all variables and given/known data
The Army of the Nation of Whynot has a plan to propel small vehicles across the battlefield by shooting them, from behind, with a machine gun. They've hired you as a consultant to help with an upcoming test. A 100 kg test vehicle will roll along frictionless rails. The vehicle has a tall "sail" made of ultrahard steel. Previous tests have shown that a 20.0g bullet traveling at 400 m/s rebounds from the sail at 100 m/s. The design objective is for the cart to reach a speed of 19.0 m/s in 30.0 s . You need to tell them how many bullets to fire per second from the machine gun. Note that your answer should be a rate, which can be fractional, rather than a quantity, which must be an integer.


2. Relevant equations
p=mv J=change in momentum


3. The attempt at a solution
I found the impulse exerted on a bullet.
J=(.02kg)(-100m/s)-(.02kg)(400m/s)
J= -10 Ns

Then I set up an equation to find what impulse needs to be exerted on the cart to speed up to 19 m/s:

0kgm/s + J = (100kg)(19 m/s)
J=1900 Ns

Then I assumed the impulse exerted on a bullet is the same as the impulse exerted on the sail by a single bullet :

1900Ns* (1 bullet/10Ns) =190 bullets
I then divided that by 30 sec. & came up with 6.33 bullets/sec.

Is this correct?
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Kaleb
#2
Mar30-08, 04:06 PM
P: 49
Your math is correct and I ran through your procedure and it looks sound.
tiny-tim
#3
Mar30-08, 05:48 PM
Sci Advisor
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Thanks
tiny-tim's Avatar
P: 26,148
The Nation of Because regards your militaristic experiments as a threat to our beliefs!

The ancient Nation of Because will always defeat the Nation of Whynot!

Go to your room!


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