= This problem introduces the concept of tension. The example is a rope, oriente

Question

    = 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 Fad of the downward force on section a? Express your answer in terms of the tension T1. What is the magnitude Fbu of the upward force on section b? Express your answer in terms of the tension T1.

Explanation / Answer

What is the magnitude Fad of the downward force on section a? Express your answer in terms of the tension T1.

We know from the given information that at point 1 downward force of magnitude Fad acts on section a and that the tension at point 1 is T1. Since the two are the same thing, we know that:

Fad = T1

What is the magnitude Fbu of the upward force on section b? Express your answer in terms of the tension T1.

We know that the downward force (Part 1) is the same as the upwards force

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