An engine can pull 4 coaches at a maximum speed of 20 m s - 1 . Mass of the engine is twice the mass of every coach. Assuming resistive forces are proportional to the weight of train and velocity too,

Question

An engine can pull 4 coaches at a maximum speed of 20 m s - 1 . Mass of the engine is twice the mass of every coach. Assuming resistive forces are proportional to the weight of train and velocity too, approximate maximum speeds of the engine when it pulls 12 and 6 coaches are

TestHub · Accepted Answer

When 4 coaches (m each) are attached with engine (2m)
According to question, $P = K \cdot 6 m g v$ .......(1)

(constant power), (K being proportionally constant)

Since resistive force is proportional to weight

Now if 12 coaches are attached

$P = K \cdot 14 m g \cdot v_{1}$ ......(2)

So by equation (1) and (2)

$6 m g v = 14 m g v_{1} \Rightarrow v_{1} = \frac{6}{14} \times v$

$= \frac{6}{14} \times 20 = \frac{6 \times 10}{7} = \frac{60}{7} \Rightarrow v_{1} = 8.5 m s^{- 1}$

Similarly for 6 coaches, $K \cdot 6 m g v = K \cdot 8 m g v_{2}$

$\Rightarrow v_{2} = \frac{6}{8} \times 20 = \frac{3}{4} \times 20 = 15 m s^{- 1}$

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