A short train (an engine plus four cars) is accelerating at 1.10 . The mass of each car is 38000 , and each car has negligible frictional forces acting on it. In solving this problem, note the importance of selecting the correct set of cars to isolate as your object.

a.What is the force of the engine on the first car?
b.What is the force of the first car on the second car?
c.What is the force of the second car on the third car?
d. And what is the force of the third car on the fourth car?

A. The engine is pulling all four cars at the specified acceleration. Then

Force = 4 x 38,000 x 1.10 = 167 200 N

B. Now the first car is pulling the other three cars.
Force = 3 x 38,000 x 1.10 = 125 400 N

And similarly C. Force = 2 x 38,000 x 1.10 = 83 600 N; D. 41 800 N

To solve this problem, we need to consider the forces acting on each car in the train.

a. Force of the engine on the first car:
The force of the engine on the first car is equal to the mass of the first car multiplied by the acceleration of the train. We can use Newton's second law, F=ma, to determine this force.

F(engine on first car) = mass of first car × acceleration

F(engine on first car) = 38000 × 1.10

b. Force of the first car on the second car:
Since the first car is pushing the second car, the force that the first car exerts on the second car will be equal in magnitude but opposite in direction to the force of the engine on the first car.

F(first car on second car) = -F(engine on first car) = -38000 × 1.10

c. Force of the second car on the third car:
The force that the second car exerts on the third car is equal in magnitude and direction to the force that the first car exerts on the second car.

F(second car on third car) = F(first car on second car) = -38000 × 1.10

d. Force of the third car on the fourth car:
Similarly, the force that the third car exerts on the fourth car is equal in magnitude and direction to the force that the second car exerts on the third car.

F(third car on fourth car) = F(second car on third car) = -38000 × 1.10

So, the answers to the given questions are:
a. The force of the engine on the first car is 41800 N.
b. The force of the first car on the second car is -41800 N.
c. The force of the second car on the third car is -41800 N.
d. The force of the third car on the fourth car is -41800 N.

To find the forces in this scenario, we'll need to apply Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.

a. Force of the engine on the first car:
To find the force of the engine (F_engine) on the first car, we can use Newton's second law. The mass of the first car is given as 38,000 kg, and the acceleration of the train is given as 1.10 m/s^2. So, the force of the engine on the first car is calculated as:
F_engine = mass_first_car * acceleration
F_engine = 38,000 kg * 1.10 m/s^2

b. Force of the first car on the second car:
The force between two connected objects in a system is an internal force. In this case, the first car is pulling the second car, so the force of the first car on the second car (F1-2) is equal in magnitude but opposite in direction to the force of the second car on the first car. Therefore, F1-2 is also equal to the force of the engine on the first car.

c. Force of the second car on the third car:
Similarly, the force of the second car on the third car (F2-3) is equal in magnitude but opposite in direction to the force of the third car on the second car. Considering that each car has negligible frictional forces acting on it, the force between the second and third cars (F2-3) is equal to the force of the engine on the first car.

d. Force of the third car on the fourth car:
Again, we can apply the same logic. Since each car has negligible frictional forces acting on it, the force between the third and fourth cars (F3-4) is equal in magnitude but opposite in direction to the force of the fourth car on the third car. Thus, F3-4 is also equal to the force of the engine on the first car.

To summarize:
a. Force of the engine on the first car = 38,000 kg * 1.10 m/s^2
b. Force of the first car on the second car = Force of the engine on the first car
c. Force of the second car on the third car = Force of the engine on the first car
d. Force of the third car on the fourth car = Force of the engine on the first car

We will be happy to critique your thinking. Wouldn't it be wonderful if trains could have negligible friction.