The Army of the Nation of Whynot has a plan to propel small vehicles across the
ID: 1696851 • 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 300 m/s rebounds from the sail at 100 m/s. The design objective is for the cart to reach a speed of 14.0 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.Explanation / Answer
Required acceleration of testvehicle = a = (vf- vi)/t = (14.0 - 0.0)/30.0 = 0.466 m/s2 Forcerequired F = m *a = 200 *0.466 = 93.2 N Also F = rate of change of linear momentum F = n* (p2 - p1)/ t Forbullet p = m *v p1 = m* v1 = 20.0 *10-3 * ( - 300) = -6.00 kg-m/s p2 = m* v2 = 20.0 *10-3 *100 = 2.00 kg-m/s => F = 93.2 = n* {2.00 - ( -6.00)} / t no. of bullets fired per second = (n/t) = 93.2/8.0 = 11.65 bullets/second ( I have taken v1 as negativebecause it is opposite in direction to v2) Forcerequired F = m *a = 200 *0.466 = 93.2 N Also F = rate of change of linear momentum F = n* (p2 - p1)/ t Forbullet p = m *v p1 = m* v1 = 20.0 *10-3 * ( - 300) = -6.00 kg-m/s p2 = m* v2 = 20.0 *10-3 *100 = 2.00 kg-m/s => F = 93.2 = n* {2.00 - ( -6.00)} / t no. of bullets fired per second = (n/t) = 93.2/8.0 = 11.65 bullets/second ( I have taken v1 as negativebecause it is opposite in direction to v2)Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.