The Army of the Nation of Whynot has a plan to propel small vehicles across the
ID: 1416648 • Letter: T
Question
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 200 kg test vehicle will roll along frictionless rails. The vehicle has a tall "sail" made of ultrahard steel. Previous tests have shown that a 20.0 g bullet traveling at 400 m/s rebounds from the sail at 200 m/s . The design objective is for the cart to reach a speed of 12.0 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.
A five-star general will watch the test, so your ability to get future consulting jobs will depend on the outcome.
Explanation / Answer
Momentum = mass*velocity
impulse = change in momentum
J = m*dV
impulse exerted on bullet
J = m*v2 - m*v1
J = 20*10^-3((-200) - 400)
J = -12 N-sec
Impulse on the vehicle
J1 = 200*(12 - 0) = 2400 N-sec
number of bullets = impuse on the vehicle*(1/impulse exerted on bullet)
number of bullets = 2400/12
no. of bullets = 200
now we need how many bullets per sec
time = 30 sec
number of bullets/sec = 200/30 = 6.67 bullets
Comment Below if you have any doubt.
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