Final answer:
To calculate the force needed by each train engine to accelerate the train, sum the force of friction and the product of the total mass and desired acceleration, then divide by the number of engines.
Step-by-step explanation:
Calculating Force on a Train's Engines
The question is related to calculating the force that must be exerted by the train's engines to achieve a certain acceleration, taking into account the force of friction. The total mass of the train is the sum of the mass of the engines and the mass of the cars. With the given masses, the total mass (M) of the train is:
M = 2(8.00 × 10⁵ kg) + 45(5.50 × 10⁵ kg)
To find the force required to accelerate this mass at 5.00 × 10⁻² m/s², we use Newton's second law of motion (F = ma). The force (F) needed to overcome friction and accelerate the train is the sum of the force of friction plus the product of the total mass and the acceleration:
F = (Total Mass) × (Acceleration) + (Frictional Force)
Since there are two engines exerting equal forces, the force exerted by each engine is half of the total force calculated above.
The second part of the question involves the force in the coupling between two specific cars. Assuming that all cars and both engines contribute equally to friction, we distribute the frictional force equally. Then, the force in the coupling is the force required to accelerate one car at the given rate.