Question

A freight train consists of two 8.00x10⁴ kg engines and 45 cars with average masses of 5.50x10⁴ kg. What force must each engine exert backward on the track to accelerate the train at a rate of 5.00x10⁻² m/s² if the force of friction is 7.50x10⁵ N, assuming the engines exert identical forces?

Group of answer choices
a. 882 kN
b. 441 kN
c. 221 kN
d. 110 kN

Answer 1

The force that each engine must exert backward on the track to accelerate the train at the given rate, considering the force of friction, is 441 kN.

option b is the correct

Step-by-step explanation:

To determine the force that each engine must exert backward on the track, we have to consider both the mass of the train and the external force of friction. First, we calculate the total mass of the train by adding the masses of the engines and cars:

Total mass = (2 × 8.00 × 104 kg) + (45 × 5.50 × 104 kg).

Now, according to Newton's second law, the net force (Fnet) is equal to the total mass (m) times the acceleration (a):

Fnet = m × a.

Since we need to overcome the force of friction, we add the force of friction to the net force needed:

Total force needed = Fnet + Friction force.

Then we divide this total force by 2 to find the force exerted by each engine:

Force per engine = Total force needed / 2.

After computing the values, the force that each engine must exert is found to be 441 kN, which corresponds to option b.