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8.1. Concepts: Tension and Compression

Introduction

Tension is the force exerted by a rope, string, or cable on one or more objects. Force of tension appears in flexible elements when an object is being suspended, pulled, swung, etc.

Compression is a force that appears in rigid elements, such as bars, beams, etc., when they are pushed or pressed against.

Examples of situations when force of tension is involved:

  1. A load hanging from a crane’s system of cables
    A crane lifts a bundle of steel beams using a system of tension cables, demonstrating the force of tension in action.
  2. A wagon being pulled by a rope
    A boy pulls a wagon carrying a small house using a rope at an angle θ, demonstrating force of tension and direction.
    Figure 8.1. Examples of force of tension

Concepts

Tension questions with one cable (rope, string) involved

When an object hangs from a rope, a tension will appear in the rope that balances the force of gravity acting on the object. The object will be in equilibrium. To draw a FBD for this situation we can imagine that we cut the rope and replace its effect by a force – force of tension.

A box is hanging from a rope attached to a horizontal beam, with a black downward arrow representing gravity.
A box suspended by a vertical rope, showing an upward arrow labeled Tension and a downward arrow labeled gravity.
Figure 8.3. Solving tension questions with one cable (rope, string) involved

In this situation, the object is in equilibrium on both x and y axes. Therefore:

T=Fg

If the object hung by the rope is now given an upward acceleration, a, then the object will not be in equilibrium on the y axis anymore.

In this case we write the net force using Newton’s second law and using the net force definition:

 

Fnet=m X a

F→net=∑F→

On the y axis:

Fnet=m X a, and

Fnet=T−Fg

So:

T−Fg=m X a,or T=Fg+m X a

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College Physics – Fundamentals and Applications Copyright © by Daniela Stanescu, Centennial College is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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