Centripetal Action: What is the relationship between distance and force in circular motion?
(Excerpted from Experiment Central, published by U·X·L; also available in Science Resource Center, a Gale online database)
Purpose/Hypothesis
Centripetal force is any force that acts on an object at a right angle to its path of motion. The constant right angle force results in the object moving in a circular path. In this experiment, you will examine how altering the force and radius will affect the acceleration of an object. Radius is the distance from the center to the outer point of a circle. The object's mass will stay the same.
A piece of string will have a mass attached to one end and washers creating the force attached to the other end. You will first alter the radius, and then alter the force. For a more accurate measure of how many times the mass completes a circle or revolution, you will count how many times it revolves in 30 seconds. That number will then be divided by 30 to give its revolutions per second. Another way to increase accuracy is to complete three trials of each experimental trial.
Comparing the results to a control experiment will help you isolate each variable and measure the changes in the dependent variable. In this experiment there will be two variables that you will change, one at a time. Only one variable will change between the control and the experimental setup each time. In the first part, the distance will change when the radius increases. In the second part, the force will change. At the end of the experiment you can compare each of the results to the standard experiment.
Before you begin, make an educated guess about the outcome of this experiment based on your knowledge of centripetal force. This educated guess, or prediction, is your hypothesis. A hypothesis should explain these things:
- the topic of the experiment
- the variable you will change
- the variable you will measure
- what you expect to happen
A hypothesis should be brief, specific, and measurable. It must be something you can test through further investigation. Your experiment will prove or disprove whether your hypothesis is correct. Here is one possible hypothesis for this experiment: "The greater the force, the greater the acceleration; the greater the radius; the lower the acceleration."
In this case, the variable you will change is the force and the distance, one at a time. The variable you will measure is the acceleration of the mass.
What Are the Variables?
Variables are anything that might affect the results of an experiment. Here are the main variables in this experiment:
- the force
- the radius
- the mass
In other words, the variables in this experiment are everything that might affect the acceleration of the mass. If you change more than one variable at the same time, you will not be able to tell which variable had the most effect on centripetal force.
Level of Difficulty
Easy to Moderate.
Materials Needed
- spool of thread with narrow hole
- ruler
- ten metal washers of equal size
- 3 feet (90 centimeters) of string
- masking tape
- watch with second hand
- bobbin, small spool of thread, rubber stopper or other lightweight object that can be easily tied
- helper
Approximate Budget
$2.
Timetable
30 minutes.
How to Experiment Safely
Be careful when swinging the mass and check to ensure the knot is tight. Make sure you are working in an open area.
Step-by-Step Instructions
- Slide the string in the large spool of thread and move the spool up 2 feet (0.6 meters).
- On the long side of the string, attach four metal washers (this is the force) to the end and secure with a knot.
- Tie the bobbin or rubber stopper to the end of the short side of the string. This is the mass.
- Wind a piece of tape about 1 inch (2.5 centimeters) below the spool to make sure it does not slide down and change the radius. Mark the string at the point above the tape.
- Hold the washers with one hand and begin to swing the mass until it is moving parallel to the floor. Practice swinging at a steady rate.
- While you are swinging, have your helper time 30 seconds and count the number of revolutions the bobbin makes.
- Repeat Step 6 two more times so that you have three trials. This is your standard experiment.
- Remove the tape and slide the spool down 1 foot (0.3 meters) towards the washers. Reattach the tape about 1 inch (2.5 centimeters) below the spool.
- Again, time the number of revolutions in a 30-second period, then repeat for two more trials. Note the results.
- Return the spool to its beginning position, reattaching the tape at the marked point on the string.
- Double the number of washers to eight. Support the washers until you have a steady swing and then have your helper time 30 seconds while you count the revolutions. Repeat two more times and note the results.
Summary of Results
Determine the time for each revolution per second by dividing the total revolutions by 30. Once you have the revolutions per second for each trial, average the three trials. Make a chart of your data. Compare how long it took to complete a full circle when the radius lengthened. How much force would it take to have the revolutions of different radiuses be the same. Look at how the increased force compares with the acceleration of the lesser force? What would happen to the acceleration if you halved the force? Hypothesize how the force and/or radius would need to change if the mass was doubled and you wanted to keep the acceleration equal.
Troubleshooter's Guide
Below is a problem that may arise during this experiment, a possible cause, and a way to remedy the problem.
Problem: The radius looked like it was changing.
Possible cause: The paperclip might have slid loose. Use a tight paperclip and make sure it is attached firmly, then repeat the experiment.
Change the Variables
You can continue to experiment on changing the variables in this experiment in new ways and new combinations. Try to halve the force and halve the radius. Look at what occurs if the radius is tripled and the force remains constant. You can also change the mass of the object, making it lighter or heavier. Make sure you secure the mass tightly to the string and try to work in an open area.