PHYSICS .k12.ca.us
Chapter 7: ROTATIONAL MOTION LAB
Purpose
Prove relationship between centripetal force and period. Calculate value of acceleration due to gravity.
Theory
It turns out that when objects (like a mass on a string swinging around your head) undergo uniform circular motion they are moving with a constant speed (notice I didn’t say velocity) and also constant acceleration. Because the mass on the end of the string is always changing direction, the velocity of the mass is always changing (remember that velocity is a vector quantity), and therefore the mass is accelerating. The velocity of the mass is always changing direction toward the center of the circle. It follows then that the mass is always accelerating toward the center of the circle.
[pic], where [pic]
We all know that ΣF=ma, so if you know the centripetal acceleration you also know the centripetal force.
[pic]
[pic]
In the above diagram, the centripetal force is equal to the tension in the string; the same tension that holds m2 up, such that:
[pic]
[pic]
In this experiment, m2 will be out independent variable and T will be our dependent variable. With all other variables left constant, we will observe the following relationship:
[pic]
Materials
• A piece of string, about 2 meters long
• 6 washers to use as weights
• Masking tape
• Electronic balance
• Meter stick
• Stopwatch
• Paper clip
• Plastic pipe, about 60 cm long
Procedure
1. This lab requires you to swing masses on the end of a string with uniform circular motion.
2. Number each washer 0 - 5.
3. Record the mass of washer 0 as m1.
4. Record the mass of washer 1 and the paper clip in the table as m2.
5. Record the mass of washers 1 and 2 and the paper clip in the table as m2.
6. Record the mass of washers 1, 2 and 3 and the paper clip in the table as m2.
7. Record the mass of washers 1, 2, 3 and 4 and the paper clip in the table as m2.
8. Record the mass of washers 1, 2, 3, 4 and 5 and the paper clip in the table as m2.
9. To get started, tie a knot at the end of your string that will act as a stop. It is important to make a good stop so that your masses do not fly off when you start swinging your string. We don’t want anyone getting hurt.
10. Attach washer 0 to the end of the string and slide string through plastic pipe. Attach a paper clip to the other end.
11. Lay the apparatus on a table and adjust until the center of washer 0 is 1 m from the center of the pipe. Mark the other end of the string with a piece of masking tape just below the bottom of the pipe so you know when the washer is being swung around with a radius of 1 m.
12. Place washer 1 on the paperclip.
13. Get far enough away from any obstacles and people and swing washer 0 around in a circle at a constant speed such that the tape just touches the bottom of the pipe.
14. Record the time it takes for 10 revolutions.
15. Repeat measurement for a total of 5 trials.
16. Add washer 2 and repeat measurement process.
Results
Raw Data
radius =
m1 =
|Mass 2 (kg) |Time 1 (s) |Time 2 (s) |Time 3 (s) |Av. Time |
| | | | |(s) |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
Processed Data
|Mass 2 (kg) |Av. Time |Period |1/Period2 |
| |(s) |(s) |(1/s2) |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
• Create a graph of your processed data using a computer spreadsheet program showing the relationship between your two variables. Must include a best fit line and the equation of the line.
Conclusion
• Calculate the value of g from the slope.
• Don’t forget units.
• Compare your result with an accepted value, say where this value is from.
• Calculate the percent error.
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