Question

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. (Figure 1) LetFu and Fd (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 Fad acts on section a.

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

• At point 1, the tension in the rope is T1.

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

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

• At point 2, the tension in the rope is T2.

Assume, too, that the rope is at equilibrium.

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

What is the magnitude F_bu of the upward force on section b? express in terms of T_1.

Answer 1