Lab 7 - Centripical Force

Objective: 
To verify Newton's second law of motion for the case of uniform circular motion.

Procedure: 
The equipment used for this lab are as follows:
1. Centripetal force apparatus
2. Metric scale
3. Vernier Caliper
4. Stop Watch
5. Slotted weight set
6. Weight hanger
7. Triple beam balance


The idea of this lab was to manually spin the centripetal force apparatus so the weight is close to the marker, time 50 rotations for each weight to figure the velocity using Newton's second law.   After a few practice runs with the apparatus, we were ready to begin.  While one of the lab partners counted, one manually spun the apparatus another used the stop watch to track the time it took for 50 rotations.  The hard part of spinning the apparatus is that the weight had to match with the indicator post on the apparatus as it spun.  Spinning it too fast would make the weight pass the post, while spinning too slow would not reach the post.  This was repeated 4 more times for a total of 5 runs.  With all of this data, we were able to calculate a relatively accurate average of the velocity.

The cetripetal force apparatus also had another post that would let us calculate the cetripetal force of the bulb by attaching weight to a string until the bulb was even with the indicator post.  The amount of weight that was attached to the bulb to get it to center over the indicator post was .6kg.  This is illustrated below.



Apparatus with the weight to measure the Centripetal force needed to center the bulb over the indicator post

After the first set of runs, we added another .1kg of weight to the bulb and started the experiment over.  In the end, we had data to calculate the cetripetal force for a .5 kg and .6 kg bulbs, along with the measured centripetal force that it took to center the bulb over the indicator post.

Data: For both of the experiments, the information was entered into Excel to do the calculations.

Data captured from the experiments and information derived from formulas used

Trial - The number of the trial out of the 5
Time - The amount of seconds that it took for 50 revolutions
LDT - 2PIr - 2*pi*.1754 measured in meters
Mass - the mass of the spinning bulb
Radius - The measurement from the center of the spinning pole to the center of the indicator post
Average Velocity - LDT / Time measured in m/s
Calculated Centripetal Force - (mass - Velocity ^2) / Radius measured in Newtons
Measured Centripetal Force - the mass of the weight it took to hold the bulb over the indicator post * 9.8(gravitational measurement) measured in Newtons
Percent Error = Absolute value of ((Measured C force - Calculated C force) / Measured C Force )* 100

Possible Sources Of Error:  Timing was the key with this experiment.  If the person spinning the bulb could not keep the bulb over the indicator post, the timing would be off.  If the bulb spun too fast, the time would be less, and if the bulb spun too slow the time would be too much.  In addition, the timer had to be paying attention to the person counting the rotations to ensure that the stop watch was started and stopped at the correct times.  This was the cause for most of the trials that were done a second time.  We tried to ensure that the count was correct by having 2 of the lab partners counting at the some time.  This prevented us from starting over at least 2 times.

Questions:
1. Calculate this force and compare with the centripetal force obtained in part 3 by finding the percent difference.  This was completed with the excel data.  The percent difference at .5 kg was 1.42, and at .6 kg it was 1.95.
2. Draw a force diagram for the hanging weight and draw a force diagram for the spring attached to the hanging mass.

Conclusion:  I feel that the lab overall was successful.  We were very close to the measured centripetal force with very little difficulty.
The purpose of this lab was to verify Newton's second law of motion in a uniform circular motion using the formula F = (mv^2) / r.  Using this formula I was able to calculate the centripetal force of the bulb as it spun on the apparatus.  This was a great way to see the calculations that we do in the problems in action with the spinning bulb.
If the force and radius are the same, and only the weight changed, then the only other variable that effect the net force is the velocity of the spinning bulb.