# A greater force? (A train engine pulling two identical cars)

• BurpHa
In summary, the engine pulls on car 1, so car 1 is having a force acting on it, which pulls car 1 forward. Likewise, the same amount of force is applied on car 2 by car 1 by moving forward with the same amount of force from the beginning. So it is reasonable, at least to my intuition, that the force of the engine on car 1 is equal to the force of car 1 on car 2. However, it turns out that my intuition is wrong. I have reviewed the definition, but I still don't see any flaws in my thinking.
BurpHa
Homework Statement
A train engine pulls two identical cars behind it. Car 1 is
attached directly to the engine, and car 2 is attached to car 1.
The engine and cars are speeding up. The force of the engine on
car 1 is _____ the force of car 1 on car 2.

A. greater than
B. less than
C. equal to
D. There is no force on either car.
Relevant Equations
I would say a relevant law: Newton's third law.
My choice is C, which is "equal to." Here is my reasoning:

The engine pulls on car 1, so car 1 is having a force acting on it, which pulls car 1 forward. Likewise, the same amount of force is applied on car 2 by car 1 by moving forward with the same amount of force from the beginning. So it is reasonable, at least to my intuition, that the force of the engine on car 1 is equal to the force of car 1 on car 2.

However, it turns out that my intuition is wrong. I have reviewed the definition, but I still don't see any flaws in my thinking.

BurpHa and topsquark
DrClaude said:
Newton's second law is F = ma.
So the engine applies the force on car 1, car 1 travels forward with an acceleration. When car 1 does so, it also applies the same force upon car 2, which also makes car 2 travels forward with the same acceleration.

Perhaps draw a free body diagram for car 1, using the forces you specify. What is the net force acting on car 1?

topsquark and BurpHa
BurpHa said:
The engine pulls on car 1, so car 1 is having a force acting on it, which pulls car 1 forward. Likewise, the same amount of force is applied on car 2 by car 1 by moving forward with the same amount of force from the beginning. So it is reasonable, at least to my intuition, that the force of the engine on car 1 is equal to the force of car 1 on car 2.

However, it turns out that my intuition is wrong. I have reviewed the definition, but I still don't see any flaws in my thinking.
Your analysis hasn’t included all forces.

If car-1 exerts a force on car-2, what does Newton’s 3rd law tell you.?

It helps to draw free body diagrams for both car-1 and car-2. Remember there must a net force on each car acting in the direction of the acceleration – so draw the arrows on your diagrams with appropriate lengths.

topsquark and BurpHa
The tow bar connecting the engine to cars 1 and 2 provides a net force to 1 and 2 that accelerates mass ##2m## with acceleration ##a##. The tow bar connecting car 1 to car 2 provides a net force to 1 that accelerates mass ##m## with acceleration ##a##. Which of the two is greater?

berkeman, Steve4Physics, topsquark and 2 others
Steve4Physics said:
Your analysis hasn’t included all forces.

If car-1 exerts a force on car-2, what does Newton’s 3rd law tell you.?

It helps to draw free body diagrams for both car-1 and car-2. Remember there must a net force on each car acting in the direction of the acceleration – so draw the arrows on your diagrams with appropriate lengths.
If car 1 exerts a force on car 2, then car 2 also exerts the same magnitude of force but in the opposite direction. I'm analyzing the free body diagram.

BurpHa said:
Newton's second law is F = ma.
So the engine applies the force on car 1, car 1 travels forward with an acceleration. When car 1 does so, it also applies the same force upon car 2, which also makes car 2 travels forward with the same acceleration.
What if car 2 was a hundred times more massive than car 1?

Hint: consider this scenario from the engine's point of view.

topsquark and BurpHa
DrClaude said:
Thank you for your insights! I finally see and understand the problem thoroughly!

Halc said:
Perhaps draw a free body diagram for car 1, using the forces you specify. What is the net force acting on car 1?
Thank you! Yes, drawing out the scenario helps!

PeroK said:
What if car 2 was a hundred times more massive than car 1?

Hint: consider this scenario from the engine's point of view.
Thank you! If car 2 was a hundred times more massive than car 1 then the acceleration of the system of the whole (the engine and the cars) is divided by 100! Now I could understand the problem!

kuruman said:
The tow bar connecting the engine to cars 1 and 2 provides a net force to 1 and 2 that accelerates mass ##2m## with acceleration ##a##. The tow bar connecting car 1 to car 2 provides a net force to 1 that accelerates mass ##m## with acceleration ##a##. Which of the two is greater?
Thank you for your help! I could understand and do the problem now!

kuruman
Steve4Physics said:
Your analysis hasn’t included all forces.

If car-1 exerts a force on car-2, what does Newton’s 3rd law tell you.?

It helps to draw free body diagrams for both car-1 and car-2. Remember there must a net force on each car acting in the direction of the acceleration – so draw the arrows on your diagrams with appropriate lengths.
Thank you! Yes, I indeed missed out some critical forces in my drawing! And drawing out really helps!

BurpHa said:
Thank you! If car 2 was a hundred times more massive than car 1 then the acceleration of the system of the whole (the engine and the cars) is divided by 100! Now I could understand the problem!
The point is that the engine must be pulling car1 with all the force needed to accelerate car2 as well. The engine doesn't really know how many cars there are. It only knows how much total mass it's trying to accelerate.

topsquark and BurpHa

## 1. What is meant by "a greater force" in this scenario?

The term "a greater force" refers to the amount of energy or power needed to move an object. In this scenario, the train engine is exerting a greater force than the two identical cars in order to pull them along the tracks.

## 2. How does the train engine exert a greater force than the two cars?

The train engine is able to exert a greater force due to its larger size and more powerful engine. It has the ability to generate more energy and apply more force to the cars, allowing it to pull them along the tracks.

## 3. Why do the two cars need to be identical?

The two cars need to be identical in order to ensure that they have the same weight and resistance. If one car was heavier or had more resistance, it would require a greater force from the train engine to pull it along with the other car.

## 4. What factors affect the force needed to pull the two cars?

The force needed to pull the two cars can be affected by several factors, including the weight and resistance of the cars, the condition of the tracks, and any external forces such as wind or inclines on the track.

## 5. How is the force of the train engine calculated in this scenario?

The force of the train engine can be calculated using Newton's Second Law of Motion, which states that force equals mass times acceleration. In this scenario, the mass of the train engine and the acceleration it can achieve determine the amount of force it can exert on the two cars.

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