# Centripetal Force and Speed

## Purpose:

The purpose of this lab is to investigate the relationship between the speed of an object in uniform circular motion (UCM) and the centripetal force on the object.

## Equipment:

 centripetal force apparatus washers or weights meter stick stopwatch data & analysis sheet

## Discussion:

A force which pulls an object toward the center of a circle is called a centripetal force. How much centripetal force needs to be exerted to cause an object to move in a circle? Your experience should tell you that the amount of centripetal force that you need to exert depends on

1. the mass of the object you are whirling - heavier objects require more force,
2. how fast you are whirling it - going faster requires more force, and
3. the radius of the circle.

The textbook says:

but how can we verify the quantitative relationship between centripetal force and mass, speed, and radius? This question can't be answered all at once, since a scientific experiment is designed to vary one quantity (holding all others constant) and measure its effect on one other quantity. The most difficult quantity (of mass, speed, and radius) to hold constant from trial to trial in an experiment is the speed of the object, so it is easiest to study the effect of speed on centripetal force, since it is relatively easy to hold the mass of the object and the radius of the circle constant.

You will use an apparatus similar to the one pictured above to measure the effect of speed on centripetal force. You can hold the mass constant during a set of trials by always whirling the same object. You can keep the radius of the circle constant (with a little practice) by keeping the upper clip a fixed distance below the glass tube while whirling the object.

# Procedure:

1. Place a small number of weights or washers (be sure that all of the washers you use are the same size.) on the bottom clip of the apparatus. This part of the apparatus hangs straight down, and the weight of the washers supplies the centripetal force.
2. Practice whirling the stopper (or ball) until you can keep the top clip a short distance below the bottom of the glass tube while the stopper whirls. IMPORTANT! If the clip touches the bottom of the glass tube, the weights are no longer supplying the centripetal force! If the clip rises or falls appreciably as the stopper whirls, the radius of the circle is changing. Practice!
3. Use a stopwatch to measure the time taken for a reasonable number of revolutions (20 - 30 perhaps). Record your data.
4. Change the number of washers on the bottom clip (centripetal force) and repeat steps 3 and 4. Repeat for several different weights. Record the data.
5. Change the position of the top clip to change the radius of the circle. Repeat the experiment for this radius. Be sure to indicate where the radius changes in your data table.
6. If you have time, you might try to determine the relationship between mass and centripetal force. In order to do this, you need to keep both the radius of the circle and the speed constant while you vary the mass and the centripetal force. You can design your own data table for this. You could also investigate the relationship between the radius and the centripetal force.

## Results:

1. Calculate the period of revolution, T (the time to go around once) for each trial. Show a sample calculation.
2. Calculate the linear speed, v, of the stopper for each trial. Include a sample calculation. (Note:  )
3. Theoretically, the centripetal force should be directly proportional to the square of the speed. To check this, add a column to your data table for v2. Construct a graph of centripetal force versus v2. Remember that it is customary to put the quantity you change (force, in this case) on the horizontal axis, and the quantity that changes by itself (speed) on the vertical axis. Be sure that you pick the largest convenient scale for your graph and draw the best smooth curve through your data points.

## Conclusions:

Is the graph of centripetal force versus speed squared a straight line? So, what can you say about the relationship between centripetal force and speed, then?

last update January 24, 2007 by JL Stanbrough