Newton's Law question -> Tension

[nguyentech]

Newton's Law question --> Tension

Attached in this message is a question from my school pastpaper... I believe the answer is D... This is because I took John and Joan as one system... Therefore their mass is 130kg (together)...
F = ma
100 = 130*a
a = 0.77 each

However, my teacher says its A, she took the question as two separate systems... I don't think that's right... because it says "inextensible rope" therefore it cannot be stretched.. therefore they can't accelerate at different speeds otherwise it will be stretched... is my logic correct?

 

[HallsofIvy]

No, I'm afraid your teacher is correct.

Don't you hate when that happens?

If you REALLY treated the two as a single system you would have come to the conculusion that there is NO acceleration because there is no external force.

Because there is no external force, the center of mass of the system must remain fixed.

The rope is inextensible so the two cannot move farther apart but they CAN move closer together!

John pulls with (and is pulled by- Newton's third law) a force of 100 N. His mass is 80 kg so his acceleration is 100/80= 1.25 m/sec^2

Joan is pulled by a force of 100 N. Her mass is 50 kg so his acceleration is 100/50= 2 m/ sec^2.

 

[russ_watters]

Its a little bit of a trick question. For starters if Joan is pulling with a force of 100N then John also must be pulling with a force of 100N.

Also, whether or not the rope can stretch is irrelevant - John and Joan are doing whatever is necessary to keep the force a constant 100n (which means reeling it in as they accelerate).