Question

An eight thousand kilogram engine pulls a train of five wagons, each of the two thousand kilogram along a horizontal track. If the engine exerts a force of forty thousand Newton and the track offers a friction force of five thousand Newton, then calculate the net accelerating force and the acceleration of the train.

Answer 1

Hint: If we know an object's mass and the net force applying on it then we can calculate the acceleration of the object by dividing the net force by the mass.

Formula used: $\dfrac{{{\text{Net force}}}}{{{\text{Mass}}}}$.

Complete step-by-step solution -
Given that,
Engine exerts a force $ = 40000{\text{N}}$
Track offers a friction force $ = 5000{\text{N}}$
Therefore net force exerted $ = 40000 - 5000 = 35000{\text{N}}$
Also given that $8000{\text{kg}}$engine pulls a train of five wagons, each of the two thousand kilogram,
Therefore total weight $ = 8000 + (5 \times 2000) = 18000{\text{kg}}$
Then acceleration $ = \dfrac{{{\text{Net force}}}}{{{\text{Mass}}}}$$ = \dfrac{{35000}}{{18000}} = 1.944{\text{m/}}{{\text{s}}^2}$
Hence net accelerating force $ = 35000{\text{N}}$
and acceleration $ = 1.944{\text{m/}}{{\text{s}}^2}$

Note: In this question first we calculated the net force exerted by subtracting the frictional force from the force exerted by the engine which is found to be thirty five thousand Newton after that we applied the acceleration formula and got the required value of acceleration in terms of meter per second square.