Centripetal Force
Purpose:
To verify Newton's second law of motion for the case of uniform circular motion.
Equipment:
- 1 Centripetal Force Apparatus
- 1 Metric Scale
- 1 Vernier Caliper
- 1 Stop Watch
- 1 Slotted Weight Scale
- 1 Weight Hanger
- 1 Triple Beam Balance
The centripetal force apparatus is designed to rotate a known mass through a circular path of known radius. By timing the motion for a definite number of revolutions and knowing the total distance that the mass has traveled, the velocity can be calculated. Thus, the centripetal force, F, necessary to cause the mass to follow its circular path can be determined from Newton's second law:
F= (mv^2)/r
Where m is the mass, v is the velocity, and r is the radius of the circular path. Here we have used the fact that for uniform circular motion, the acceleration, a, is given by the formula:
a= (v^2)/r
Procedure: (from lab handout)
1. For each trial the position of the horizontal cross-arm and the vertical indicator
post must be such that the mass hangs freely over the post when the spring is
detached. After making this adjustment, connect the spring to the mass and
practice aligning the bottom of the hanging mass with the indicator post while
rotating the assembly.
2. Measure the time for 50 revolutions of the apparatus. Keep the velocity as
constant as possible by keeping the pointer on the bottom of the mass aligned with
the indicator post. A white sheet of paper placed as a background behind the
apparatus can be helpful in getting the alignment as close as possible. Using the
same mass and radius, measure the time for three different trials. Record all data
in a neat excel table (see 6).
3. Using the average time obtained above, calculate the velocity of the mass. From
this calculate the centripetal force exerted on the mass during its motion.
4. Independently determine the centripetal force by attaching a hanging weight to
the mass until it once again is positioned over the indicator post (this time at rest).
Since the spring is being stretched by the same amount as when the apparatus was
rotating, the force stretching the spring should be the same in each case.
a. Calculate this force and compare with the centripetal force obtained
in part 3 by finding the percent difference.
b. Draw a force diagram for the hanging weight and draw a force
diagram for the spring attached to the hanging mass:
5. Add 100 g to the mass and repeat steps 2, 3 and 4 above.
6. The following data should be calculated and recorded in your excel table:
a. Mass and radius for each trial.
b. Average number of revolutions/sec (frequency) for each trial.
c. Linear speed for each trial.
d. Calculated and measured centripetal force for each trial and their percent
difference.
Setup:
Pictures of Lab Equipment and Demonstrations
 |
| Hanging Bob Aligned with Marking Rod |
 |
| Keeping a Rhythm while I spin the Centripetal Force Apparatus |
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| Measuring Expected Radius and Tension by Hanging mass off of Pulley |
Data:
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| Force Diagram for the Hanging Weight |
mass = 446.1 g = .4461 kg
radius = 16.6 cm = .166 m
frequency = 50/s
F = (m*v^2)/r
Conclusion:
In this lab I learned how to measure centripetal force and how to properly use a vernier caliper. According to our table of data and results, we can say that when the radius is kept constant and the mass increases, the centripetal force increases. Our average calculated centripetal force when added the 100 g is very close to the measured centripetal force. The last one (added 50 g) is much closer than the first one. We can say that our results are accurate and convincing. In this lab, we verify Newton's second law of motion (uniform circular motion). The acceleration (a) of the object is directly proportional to the net force, and is inversely proportional to the mass (m). F= ma. In this particular case, the direction of net force points to the center of the circle, where a=v^2/r. Possible sources of error in this lab were when I was spinning the mass on the string, I didn't always spin it with a constant velocity, the person timing the fifty revolutions might not have stopped the stopwatch exactly when the mass made its fiftieth revolution, and the string and spring have mass as well, but we do not really compare to the weight we had attached so we could say we neglected those masses. To improve the lab, we could maybe use something like a Doppler Radar or something to precisely measure the time it takes for one revolution and would therefore decrease human error by a substantial amount.
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