A model steam engine of 1.00-kg mass pulls eight cars of 1.00-kg mass each. The cars start at rest and reach a velocity of 3.00 m/s in a time of 4.00 s while moving a distance of 5.00 m. During that time the engine takes in 134 J of heat. What is the change in the internal energy of the engine?
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Total mass of the train = 8+1kg = 9kg
The data is inconsistent with constant acceleration, which means the force developed by the engine and the acceleration are not constant.
So we can only work with the AVERAGE force developed, which we can calculate from
Impulse = change in momentum
F*dt = d(m*v)
av F = 9kg * 3m/s / 4s = 6.75N
(We can't use s = 0.5*a*t^2 or v^2 = 2a*s, but we could use v = a*t)
Hence work done by the train = av F * d = 6.75N * 5m = 33.75J
Neglecting friction etc, the change in internal energy of the train is therefore
134 - 33.75J = 100.25J
The data is inconsistent with constant acceleration, which means the force developed by the engine and the acceleration are not constant.
So we can only work with the AVERAGE force developed, which we can calculate from
Impulse = change in momentum
F*dt = d(m*v)
av F = 9kg * 3m/s / 4s = 6.75N
(We can't use s = 0.5*a*t^2 or v^2 = 2a*s, but we could use v = a*t)
Hence work done by the train = av F * d = 6.75N * 5m = 33.75J
Neglecting friction etc, the change in internal energy of the train is therefore
134 - 33.75J = 100.25J