Solving Tensions on a Rope: Magnitude of Force and Assumptions

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In summary, the conversation discusses an arbitrary point P dividing a stationary rope into two segments, with one segment exerting a force T on the other. For the first question, the magnitude of the force exerted on the second segment is T. For the second question, the answer is B, as the rope's constant speed and zero net force allows for the assumption that the tensions at both ends are equal. The answer for the first question does not need to include constants like g, and for the second question, the other way for "ma" to equal zero is when the rope is stretched with negligible sag.
  • #1
ysk1
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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.
 

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  • #2
ysk1 said:
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.
 
  • #3
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?
 
  • #4
ysk1 said:
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?
 
  • #5
Is the net force also zero when the rope is stretched with negligible sag?
 

1. What is meant by "tensions" and why is it important to solve them on a rope?

Tensions refer to the forces acting on a rope, causing it to stretch or tighten. It is important to solve tensions on a rope because it helps determine the maximum load that the rope can handle and ensures safety in various applications such as rock climbing, construction, and transportation.

2. How is the magnitude of force calculated in solving tensions on a rope?

The magnitude of force is calculated by using the equation F=ma, where F is the force, m is the mass, and a is the acceleration. In solving tensions on a rope, the mass and acceleration of the object attached to the rope are considered to determine the magnitude of force acting on the rope.

3. What assumptions are made when solving tensions on a rope?

Some assumptions made when solving tensions on a rope include: the rope is inelastic, the weight of the rope is negligible compared to the weight of the attached object, and the rope is under uniform tension. These assumptions help simplify the calculations and provide a basic understanding of the forces at play.

4. How does the angle of the rope affect the magnitude of force?

The angle of the rope affects the magnitude of force as it increases the tension in the rope. The greater the angle, the higher the tension and the greater the force acting on the rope. This is why it is important to consider the angle of the rope when solving tensions.

5. Are there any real-life applications of solving tensions on a rope?

Yes, there are many real-life applications of solving tensions on a rope, such as in construction to determine the maximum weight a crane cable can support, in rock climbing to ensure the safety of the climber, and in transportation to determine the maximum weight a bridge or lift can handle. It is also used in engineering and physics to understand the forces at play in various structures and systems.

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