A locomotive pulls 12 identical freight cars. The force between the locomotive and the first car is 150.0 kN, and the acceleration of the train is 2 m/s2. There is no friction to consider.

Find the force between the eleventh and twelfth cars. (Express your answer to two significant figures.)

To find the force between the eleventh and twelfth cars, we can use 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.

In this case, the force acting between the locomotive and the first car is 150.0 kN, and the acceleration of the train is 2 m/s^2.

Since all the freight cars are identical, we can assume that the force between each car is the same.

To find the force between the eleventh and twelfth cars, we need to know the mass of each car and the total number of cars.

Let's assume the mass of each car is m, and there are n cars in total.

The force between the locomotive and the first car is given by:
Force_1 = m * a (1)

Since the force between each car is the same, we can express the force between the eleventh and twelfth cars as:
Force_11_12 = m * a (2)

Now, we can use the information given to find the mass of each car.

The force between the locomotive and the first car is 150.0 kN, which is equal to 150,000 N.
The acceleration of the train is 2 m/s^2.

Using equation (1), we can solve for the mass of each car:
150,000 N = m * 2 m/s^2

Dividing both sides by 2 m/s^2, we get:
m = 75,000 kg

Now that we know the mass of each car, we can use equation (2) to find the force between the eleventh and twelfth cars:
Force_11_12 = 75,000 kg * 2 m/s^2

Calculating the result, we get:
Force_11_12 = 150,000 N

Therefore, the force between the eleventh and twelfth cars is 150,000 N.

To find the force between the eleventh and twelfth cars, we need to consider the net force acting on the train.

Since there is no friction to consider, the only forces acting on the train are the force between the locomotive and the first car, and the force between the eleventh and twelfth cars. By Newton's third law, these forces are equal in magnitude but opposite in direction.

Given:
Force between the locomotive and the first car (F12) = 150.0 kN
Acceleration of the train (a) = 2 m/s^2

To find the force between the eleventh and twelfth cars (F11-12), we can calculate the net force acting on the train using Newton's second law:

Net force = m * a

Since all the freight cars are identical, the total mass of the train (m) is the sum of the masses of the locomotive and the freight cars. Let's assume the mass of each car is 'm_c' and the mass of the locomotive is 'm_l'. Since there are 12 cars, we have:

Total mass of the train (m) = (12 * m_c) + m_l

Now, we can calculate the net force using the formula:

Net force = (12 * m_c + m_l) * a

Since the force between the first car and the locomotive is equal to the force between the eleventh and twelfth cars, we have:

Net force = (F12 + F11-12) - F11-12

Simplifying this gives:

Net force = F12

Therefore, we have:

F12 = (12 * m_c + m_l) * a

We know the acceleration (a) is 2 m/s^2 and the force between the first car and the locomotive (F12) is 150.0 kN. We can rearrange the equation to solve for F11-12:

F11-12 = F12 / (12 * m_c + m_l) * a

Now, you need to find the mass of each car (m_c) and the mass of the locomotive (m_l). Without that information, we cannot calculate the force between the eleventh and twelfth cars.

150 kN to pull 12 cars

to pull one car ... 150/12 kN