Momentum problem

bcjochim07

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?

Kaleb

Your math is correct and I ran through your procedure and it looks sound.

tiny-tim

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!