10) Suppose a 5,000 kg train car is costing along a straight, flat track at a co

Question

10) Suppose a 5,000 kg train car is costing along a straight, flat track at a constant speed of 20 m/s If as it passes underneath a cliff a boulder of mass 4000 kg falls straight down, landing on top of the train car and sticking to it, how much work must the train's engine do in order to get the train car and boulder back up to a speed of 20 m/s? If the train does so in 400 s, what is the power output of the train's engine? (Hint: ignore everything happening in the middle. Find the initial total energy of the train car and boulder, then find the total final energy once they're both up to speed, the difference between these two energies is the work which must be done!)

Explanation / Answer

here,

mass of train car , m1 = 5000 kg

mass of boulder , m2 = 4000 kg

constant speed , v = 20 m/s

a)

the work done required by the engine, W = change in kinetic energy

W = 0.5 * v^2 * ( (m1 + m2) - m1 )

W = 0.5 * 20^2 * 4000 J

W = 8 * 10^5 J

b)

time taken , t = 400 s

the average power output , P = W/t

P = 8 * 10^5 /400 = 2 * 10^3 W

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