An engine can pull 4 coaches at a maximum speed of 20 m/s. Mass of the engine is twice the mass of every coach. Assuming resistive forces to be proportional to the weight, approximate maximum speeds of the engine when it pulls 12 and 6 coaches are (power of engine remains constant):
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(8.5 m/s and 15 m/s respectively)
Sol. When 4 coaches (m each) are attached with engine (2m)
according to question P = K 6mgv..............(1)
(constant power), (K being proportionality constant)
Since resistive force is proportional to weight
Now if 12 coaches are attached
P = K.14mg.v 1 ............(2)
Since engine power is constant
So, by equation (1) and (2)
6Kmgv = 14Kmgv 1
v 1 = 
× v
= 
× 20 = 
= 
=v 1 = 8.5 m/sec
Similarly, for 6 coaches
K6mgv = K8mgv 2
v 2 = 
×20 = 
× 20 = 15 m/sec
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