Question

A locomotive draws a train of mass 400 tones, including its own mass, on a level ground, with a uniform acceleration, until it acquires a velocity of 54 kph in 5 minutes If the frictional resistance is 40 Newtons per tone of mass and the air resistance varies with the square of the velocity, fine the power of the engine. Take air resistance as 500 Newtons at 18 kph.

Answer 1

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Answer 2

Given:

Mass of the train+ locomotive = 400 tonne

final velocity = 54 kph

time = 5 min

frictional force = 40 N/tonne

Air resistance = 500 N at 18 kph

Air resistance ∝ v²

To find:

Power (P) of the engine.

Formula Used:

P = F x v

Calculations:

Frictional resistance:

$f=40 \frac{N}{tonne}\times 400 tonne =16000 N$

Air resistance:

$R=Cv^2$

First calculate the constant

$500=C(18\times \frac{5}{18} m/s)^2\\C = 20 N/m.s^2\\R = 20 (54\times \frac{5}{18})^2 = 4500 N$

Force exerted by locomotive:

F = m a

$F = \frac{400 \times 1000 kg}{5 \times 60 s} \times {54 \times\frac{5}{18} = 20,000 N$

Total force:

$f+R+F = 16000 N+4500 N+20000 N = 40500 N$

Power, $P = 40500 \times 15 =607500 W$

Learn more about: Force and Power

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