
#1
Mar3008, 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? 



#2
Mar3008, 04:06 PM

P: 49

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



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