A train consists of a diesel shunter of mass 100 tonnes pulling a truck of mass 25 tonnes along a level track. The engine is working at a rate of 125kW. The resistance to motion of the truck and shunter is 50N per tonne. (i)Calculate the constant speed of the train. While travelling at this constant speed, the truck becomes uncoupled. The shunter engine continues to produce the same power. (ii) Find the acceleration of the shunter immediately after this happens. (iii) Find the greatest speed the shunter can now reach.

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MathPhys MathPhys · Answer 1 · 2019-07-23T22:37:55+02:00

Answer:

(i) 20 m/s

(ii) 0.00625 m/s²

(iii) 25 m/s

Explanation:

(i) The train moves at constant speed when it has no acceleration, meaning when the sum of the forces is zero.

There are two forces acting on the train. The force of the engine pushing the train forward, and the resistance.

∑F = ma

F − R = 0

F = R

The resistance is:

50 N/tonne × (100 tonne + 25 tonne) = 6250 N

Therefore, the force of the engine is 6250 N. The power of the engine is 125 kW. Power is work per time, and work is force times distance, so:

P = W / t

P = Fd / t

P = Fv

125000 Nm/s = (6250 N) v

v = 20 m/s

(ii) The truck becomes uncoupled. The engine is still pushing with 6250 N of force, but the resistance has changed to:

50 N/ton × 100 tonne = 5000 N

∑F = ma

F − R = ma

6250 N − 5000 N = (100 tonne × 2000 kg/tonne) a

a = 0.00625 m/s²

(iii) When the force of the engine matches the new resistance force:

P = Fv

125000 Nm/s = (5000 N) v

v = 25 m/s