Afreight train consists of two 8.00×104-kg engines and 45 cars with average masses of 5.50×104 kg . (a) what force must each engine exert backward on the track to accelerate the train at a rate of 5.00×10–2m/s2 if the force of friction is 7.50×105n, assuming the engines exert identical forces?

Explanation:

First of all, let's calculate the total mass of the train+the engines:

Then we can apply Newton's second law, which states that the resultant of the forces is equal to the product between mass (m) and acceleration (a):

(1)

In this case there are two forces:

- The pushing force exerted by the engines, F

- The frictional force, , in an opposite direction to the acceleration

So (1) becomes

Since the acceleration must be

We  can solve the formula to find F:

However, this is the force exerted by both engines. So the force exerted by each engine must be half this value: