Final answer:
The question involves calculating the forces exerted by train engines to accelerate the train and the force in the coupling between two cars. Newton's second law is used to determine engine force, while the coupling force is calculated based on the mass and acceleration of the following cars.
Step-by-step explanation:
Calculating Force Exerted by Train Engines and Coupling Between Cars
The question asks for a calculation of the forces involved in a freight train system consisting of two engines and multiple cars. We aim to determine the force exerted backward on the track by each engine to accelerate the train and the force in the coupling between two specific cars.
Engine Force Calculation
To calculate the force that each engine must exert, we start by using Newton's second law of motion, F=ma, where F is the force, m is the mass, and a is the acceleration. To accommodate the forces, we must consider the total mass of the train (engines + cars) and the force of friction opposing the motion.
The total mass of the train (M) is calculated by adding the mass of the two engines to the mass of the 45 cars:
M = 2 × 8.00 × 105 kg + 45 × 5.50 × 105 kg;
Next, we calculate the total force needed to accelerate the train (Ftotal):
Ftotal = M × a + friction force,
where 'a' is the given acceleration rate, and the friction force is given. Since both engines exert identical forces, the force each engine must exert (Fengine) is:
Fengine = Ftotal / 2.
Coupling Force Calculation
To determine the force in the coupling between the 37th and 38th cars, assume that all cars have the same mass and that the force of friction is evenly distributed. The force in the coupling is a result of the components of the train that follow the coupling being accelerated, and it can be calculated using the mass of those following cars multiplied by the acceleration (minus their portion of frictional force).