Solving Tensions on a Rope: Magnitude of Force and Assumptions

[ysk1]

Question:
(Please look at the attachment picture of the diagram)
Consider a rope subjected to a pulling force on its two ends as shown. The rope is stationary. An arbitrary point P divides the rope into a left-hand segment L and a right-hand segment R.

1. Assume that segment R exerts a force of magnitude T on segment L. What is the magnitude of the force exerted on segment R by segment L?
Give your answer in terms of T and other constants such as g.

2. Which of the following phrases, if they appear in a problem, allow you to assume that T2=T1 in a horizontally oriented rope? (There can be more than one answer)
A. The rope is massless.
B. The rope is moving at constant speed.
C. The rope is stretched with negligible sag.

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For number 1, I think the answer is T because the rope's being stationary indicates that the net force is zero. But should I also include constants like g?
For number 2, I think the answer is all of A, B, and C. Choice C is especially confusing because I don't quite get what "negligible sag" means.


Thank you.

 

[Doc Al]

For number 1, I think the answer is T because the rope's being stationary indicates that the net force is zero. But should I also include constants like g?

What does Newton's 3rd law tell you?

For number 2, I think the answer is all of A, B, and C. Choice C is especially confusing because I don't quite get what "negligible sag" means.

I assume T1 and T2 are the tensions at the ends of that rope?

If the rope had weight, the tension force at each end would have to have a vertical component to balance the weight of the rope--which implies that the rope must sag a bit.

 

[ysk1]

Would the answer for #1 be -T?
But the question asks to only identify the magnitude, not the direction of the force.
Then, isn't the answer just T?

For #2, I think the answer is only B because the fact that the rope is moving at constant speed indicates zero net force, meaning that T2 and T1 are balanced. Am I correct?

 

[Doc Al]

Would the answer for #1 be -T?
But the question asks to only identify the magnitude, not the direction of the force.
Then, isn't the answer just T?

That's right.

For #2, I think the answer is only B because the fact that the rope is moving at constant speed indicates zero net force, meaning that T2 and T1 are balanced. Am I correct?

You are correct that B is a correct answer. In that case, "ma" equals zero because a = 0. What's the other way that "ma" can equal zero?

 

[ysk1]

Is the net force also zero when the rope is stretched with negligible sag?