Understanding Tension: Rope Forces and Equilibrium

[zach3535]

Homework Statement

This problem introduces the concept of tension. The example is a rope, oriented vertically, that is being pulled from both ends. (Intro 1 figure) 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.


question 1. What is the magnitude of the downward force on section a?
question 2.What is the magnitude of the upward force on section b?

 

[tiny-tim]

Welcome to PF!

Hi zach3535! Welcome to PF!

What have you tried? Where are you stuck?

Hint: pretend that there are three separate ropes, joined at points 1 and 2, and apply force diagrams to each rope on its own.