# Physics 1 Dynamics Activity Tension in a String

## Purpose:

To investigate the concept of tension in a string:

• If 2 equal forces pull on opposite ends of a string, what is the tension in the string?
• Is the tension in a string different in different parts of the string?

## Discussion:

The concept of tension in a string can be very difficult for beginning physics students to grasp. (Actually, it can be a very difficult concept for advanced physics students to grasp...)

If you hold a length of string taut between your hands, any force that you exert on one end of the string is transmitted through the string to the other hand. This "force" transmitted by the string is called the tension in the string. How does the tension in different parts of the string compare?

Suppose you hang a 5 Newton weight from a string, and hold the other end of the string in your hand. If the weight (and the string and your hand) is at rest, then the weight exerts a 5 Newton downward force on the lower end of the string, and you exert a 5 Newton upward force on the upper end of the string. What is the tension in the string? It is possible to build very plausible arguments that the tension in the string is 10 Newtons, or that it is 0 Newtons, or that it is 5 Newtons - but what is it, really, and why?

A key to the puzzle is the realization that tension is not force. A force always has a very definite direction - up, to the left, North, etc. The tension in a string or rope must follow the rope! The tension may have to extend around corners, over and under pulleys, etc. So, tension transmits a force through a string or rope, but tension is not force. Tension doesn't work exactly the way force does.

In this activity, you will use rubber bands as "miniature spring scales". The rubber bands can be inserted at various points in the string to measure the force at that point - without adding a lot of extra weight, as a "regular" spring scale would do.

## Equipment:

 1/2 meter of string ruler or meter stick three identical rubber bands pen small mass - 0.5 to 1.0 kg. spring scale ring stand ring stand clamp c-clamp four paper clips

## Safety Notes:

• Be sure to keep your feet out of the area in which the mass will fall if the string or rubber band breaks!

• Be sure to clamp the ring stand to the lab table, or weight it with several books so that the mass does not pull it off the table.

## Procedure:

### Setting Up the Apparatus:

1. Using a pen, carefully put 2 marks on each rubber band some convenient distance apart - a centimeter or two will do. You will use these marks to tell how far each rubber band has stretched, which, according to Hooke's Law, is proportional to the force on the rubber band. Be sure that you don't stretch the rubber bands when you do this. Check to be sure that the marks are the same distance apart on all three rubber bands.

2. Measure and record the distance that each rubber band stretches when you hang the mass from it. If the stretches aren't pretty close to equal, try different rubber bands.

3. Bend the paper clips into S-shaped hooks to be used to conveniently link strings and rubber bands together.

4. Cut the string in half, and tie a small loop in each end.

5. Hang the spring scale from the ring stand. Be sure to clamp the ring stand to the table or weight it with books.

### The Nitty-Gritty:

Set up each situation in the table below, and record the spring scale reading, as well as the stretch of each rubber band, where appropriate. In the table, "band1 + string + band2" means "Hang a rubber band from the spring scale (which is always attached to the ring stand). Use a paper-clip hook to suspend a string from this rubber band. Use another paper-clip hook to suspend a second rubber band from the string. Attach the mass to the lower rubber band." Get it?

Trial

Setup

Spring Scale
(N)

Band 1 Stretch
(cm)

Band 2 Stretch
(cm)

Band 3 Stretch
(cm)

1

Scale (only)

________

XXX

XXX

XXX

2

Scale + string

________

XXX

XXX

XXX

3

Scale + band1

________

________

XXX

XXX

4

Scale + band1 + band2

________

________

________

XXX

5

Scale + band1 + string + band2

________

________

________

XXX

6

Scale + band1 + band2 + band3

________

________

________

________

7

Scale + band1 + string + band2
+ string + band3

________

________

________

________

## Conclusions:

1. How does the tension in a string compare to the forces pulling on its ends? Please cite evidence for your conclusions.

2. How does the tension in a string vary along the length of the string? Please cite evidence for your conclusions.

adapted from Robinson, Conceptual Physics Laboratory Manual, Addison-Wesley - Experiment 14 - "Tension"

last update November 10, 2007 by JL Stanbrough