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

[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.

Thank you for your help.

 

[DrClaude]

What about Newton's 2nd law?

 

[BurpHa]

What about Newton's 2nd law?

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.

 

[Halc]

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

 

[Steve4Physics]

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.

 

[kuruman]

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?

 

[BurpHa]

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.

 

[PeroK]

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.

 

[BurpHa]

What about Newton's 2nd law?

Thank you for your insights! I finally see and understand the problem thoroughly!

 

[BurpHa]

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!

 

[BurpHa]

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!

 

[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?

Thank you for your help! I could understand and do the problem now!

 

[BurpHa]

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!

 

[PeroK]

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.