(5%) Problem 21: There are N cannons on a railway car. The total mass of the car
ID: 2037088 • Letter: #
Question
(5%) Problem 21: There are N cannons on a railway car. The total mass of the car and the cannons is M. The cannons can fire cannon balls of mass m at a speed u with respect to the car regardless of the state of motion of the car. Initially the car is at rest. If cannons are fired horizontally in the direction of the back of the car, the car moves forward 33% Part (a) Write and expression for the final speed of the car v when all cannons are fired at the same time? Grade Summary Deductions Potential 0% 100% Submissions Attempts remaining:5 % per attempt) detailed view 0 Submit Hint I give up! Hints: 0% deduction per hint. Hint s remaining: 1 Feedback: 0% deduction per feedback. ? ? 33% Part (b) Write an expression for the speed of the car ) if cannons are fired one after another with one cannonball being fired per second? This problem is similar to a "rocket" problem, where the rocket equation for a constant "burn" rate ? is dv/dt = ??/(M-ut) 33% Part (c) Supposed there are 3 cannons on the railway car. The car has a mass of 166 kg. The cannon balls are fired with a speed 28 m/s and each have a mass or 7 kg. What is the final speed of the car if all of the cannons are fired at the same time?Explanation / Answer
When all canons are fired at the same time,(M-Nm)*v = Nm*u; so, final speed of the car v = Num/(M-Nm)
Expression for the speed of the car v(t) is d(v(t))/dt = u*m / (M-mt)
Final speed of the car when all the canons are fired at the same time is 3*28*7 / 166 = 3.54m/s
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