Learning Goal: To understand the concept of tension and the relationship between tension and force.

This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. Let and (with u for up and d for down) represent the magnitude of the forces acting on the top and bottom of the rope, respectively. Assume that the rope is massless, so that its weight is negligible compared with the tension. (This is not a ridiculous approximation--modern rope materials such as Kevlar can carry tensions thousands of times greater than the weight of tens of meters of such rope.)

Consider the three sections of rope labeled a, b, and c in the figure.

At point 1, a downward force of magnitude acts on section a.

At point 1, an upward force of magnitude acts on section b.

At point 1, the tension in the rope is .

At point 2, a downward force of magnitude acts on section b.

At point 2, an upward force of magnitude acts on section c.

At point 2, the tension in the rope is .

Assume, too, that the rope is at equilibrium.

What is the magnitude of the downward force on section a?

Express your answer in terms of the tension .

=

Try Again; 5 attempts remaining

FeedbackThe correct answer does not depend on the variable: .

Part B

What is the magnitude of the upward force on section b?

Express your answer in terms of the tension .

=

Part C

The magnitude of the upward force on c, , and the magnitude of the downward force on b, , are equal because of which of Newton's laws?

1st

2nd

3rd

Correct

Part D

The magnitude of the force is ____ .

equal to

Correct

It is important to realize that and are not a Newton's third law pair of forces. Instead, these forces are equal and opposite due to the fact that the rope is stationary () and massless(). By applying Newtons first or second law to this segment of rope you obtain , since and . Note that if the rope were accelerating, these forces would still be equal and opposite because .

Part E

Now consider the forces on the ends of the rope. What is the relationship between the magnitudes of these two forces?

Correct

The forces on the two ends of an ideal, massless rope are always equal in magnitude. Furthermore, the magnitude of these forces is equal to the tension in the rope.

Part F

A massless rope is attached at its ends to two stationary objects (e.g., two trees or two cars). For this situation, which of the following statements are true?

Check all that apply.

The tension in the rope is everywhere the same.

The magnitudes of the forces exerted on the two objects by the rope are the same.

The forces exerted on the two objects by the rope must be in opposite directions.

The forces exerted on the two objects by the rope must be in the direction of the rope.