Calculating Change in Internal Energy: A Steam Engine's Performance

[jmb07]

A steam engine of 1kg pulls 8 cars of 1kg each. The velocity of the engine is 0m/s initially then gets up to 4m/s in a time of 4 s while moving a distance of 5.3 meters. During that time, the engine takes in 134J of heat. What is the change in internal energy?


Ok so i know that:
internal energy= Q + W
and, W=Fd
and, F=ma

so, (8x1kg)(4m/s/4s) = 8 N = F
also, W= (8N)(5.3m) = 42.4
so, internal energy = 134 J + (-42.4) = 91.6

However, the correct answer is about 62, what am i doing wrong?? It seems like the steps would make sense to get the correct answer.

 

[cepheid]

The total mass of the system is more than 8 kg.

 

[jmb07]

oops! so it would be 9 kg?? Even then, the answer would still be incorrect...

 

[jmb07]

i realized i have to use the work/kinetic energy theorem...i got it! thanks!

 

[cepheid]

If I use the change in kinetic energy of the train to calculate the work done, I get the right answer. Doing so bypasses using the average acceleration to calculate the force.

The hint that you should not do the latter thing comes from the fact that the distance covered during the 4 s is NOT consistent with constant acceleration at 1 m/s^2 suggesting that a is not constant and that calculating force using a_average won't be good enough.