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A two-cart train

The cars in Figure 5.6 are speeding up as they are pulled to the right with increasing speed across a frictionless surface. The ropes have negligible mass. We can concule that

A. The pull of rope 1 on cart A has greater magnitude than the pull of rope 1 on cart B. B. The pull of rope 2 on cart B has greater magnitude than the pull of rope 1 on carb B. C. The pull of rope 1 on cart A has greater magnitude than the pull of rope 2 on cart B.

Conceptual image of Figure 5.6:-

|Cart A|-----rope 1-----|Cart B|-----rope 2-----

Cart A looking considerablly smaller than Cart B.

Solution (according to the book): Answer B is correct: For cart B to accelerate there must be a net force to the right. Answer A cannot be right; if the rope is massless, the forces acting on its two ends must add to zero. (etc...)

My attempt:-

I have drawn Free Body Diargrams, and so, I could analyze the forces on each object:-

Rope 2:-

A) Force pulling Rope 2 to the right, what is pulling it is unknown.

B) Force pulling Rope 2 to the left, by Cart 2.

Cart 2:-

A) Reaction force pulling Cart 2 to the right, by Rope 2. Since it's a reaction force, it's equal to "Rope 2 Force B".

B) Force pulling Cart 2 to the left, by Rope 1.

Rope 1:-

A) Reaction force pulling Rope 1 to the right, by Cart 2. Since it's a reaction force, it's equal to "Cart 2 Force B".

B) Force pulling Rope 1 to the left, by Cart 1.

Cart 1:-

A) Reaction force pulling Cart 1 to the right, by Rope 1. Since it's a reaction force, it's equal to "Rope 1 Force B".

I've started with the first Option (A. The pull of rope 1 on cart A has greater magnitude than the pull of rope 1 on cart B.)

Net force on F_rope1 = Force_rope1_A - Force_rope1_B

Since Net F_rope is greater than zero: Force_rope1_A > Force_rope1_B

Since Force_rope1_A = Force_cart2_B: Force_cart2_B > Force_rope1_B

Since Force_rope1_A = Force_cart1_A: Force_cart2_B > Force_cart1_A

So, I came to the conclusion that the pulling force in the direction of Cart 2 is greater than the pulling force in the direction of Cart 2. (Answer A).

What is wrong with my solution?

share|improve this question
Welcome to Physics! Generally we discourage questions that just ask for someone to check your work. Once you have identified the specific concept that you're not sure about, that's the point at which it's appropriate to ask a question here. – David Zaslavsky♦ Feb 27 '12 at 18:21
Somehow it seems to me that you think of solid rods connecting the carts instead of ropes. In any case, a rope or rod (neglecting elasticity or weight) will always exert the same force in both directions. Otherwise it would accelerate things by itself which is not possible. That is why A) is cannot be true. – Alexander Feb 27 '12 at 18:21

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