Centripetal Force

Purpose: To verify Newton’s second law of motion for the case of uniform circular motion.

Introduction: The apparatus that we used in the experiment is the centripetal force apparatus.

A pictoral of what the apparatus looks like

The centripetal force apparatus works so that we can find the centripetal force, F.  By timing the motion for fifty revolutions, and knowing the total distance that the mass has traveled, we can find the velocity. We also already know what the radius is from the apparatus, so therefore, the following equation determines, from Newton’s second law, how much force is necessary to cause the mass to follow its circular path.

The centripetal force equation

Procedure:

1.       For each trial the position of the horizontal crossarm 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 fifty (50) revolutions of the apparatus. Keep the velocity as constant as possible. Use the same mass and radius, measure the time for five different trials. Record the data in a Microsoft Excel sheet.

3.       Using the average time obtained in procedure (2), 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 is positioned over the indicator post (this time at rest).

a.       Calculate this force and compare with the centripetal force obtained in procedure (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 grams to the mass and repeat procedures 2, 3, and 4.

Data:

Our data tables

Calculation:

Calculation when m = .475, v = 1.57, and r = .165

Conclusion:

In the lab, I learned how to obviously find the centripetal force of a mass that follows a circular pattern, which accomplished the purpose of the lab. Also, I learned how to operate a centripetal force apparatus. Although we did not experience a perfect lab, we did brainstorm what could have been sources of error. One thought is that the timer could have started the stopwatch either early or late (or both for that matter). Another thought we had was that the radius could have been off by a couple centimeters. Finally we thought that the calculations can be off because the velocity may have not been constant. This leads me to a way we can improve this experiment. One way is to put a machine that delivers constant energy that moves the bob at a constant speed. Overall, this experiment was very educational and enjoyable at the same time.

Drag Force on a Coffee Filter

Intro:     The purpose of this experiment was to study the relationship between air drag forces and the velocity of a falling body. What we did in this experiment was we started off with nine coffee filters. When we dropped the pack of nine filters over a motion detector, it registered how fast the pack got to the motion detector. After four or five trials, we subtracted a filter and did the four or five trials with the eight filters. We continued to subtract a filter after four or five trials until we had no more filters left. In the end, we analyzed our data and placed it into a graph. The data told us what the terminal speed relative to the number of filters and also, how close to the Power Law fit our numbers were.

Questions: Some questions that were incorporated into the procedure tested our analysis of the procedure.

1) What should the position vs. time graph look like? Explain.   

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  -      I thought the position vs. time graph should look like this because as time elapses, the filters   will get closer to the motion detector. 

2)    From the curve fitting and analysis graph, what should the slope represent? Explain

<!--[if !supportLists]-->-          <!--[endif]-->The slope should equal the terminal velocity of the falling coffee filters.

Results: 

The data table from all our trials. The average terminal velocity is shown on the right side.

This graph shows a representation of what the slope for on of the 8 filters experiment

Conclusion: The actual value of A*x^B is B should equal 2. Our value was 2.55. Therefore, our percentage error was 27.5%. This was a very large error and we contribute the "off-ness" to the shape of the filters. The instructions clearly said to keep the filters straight and we tried, but it was hard when we dropped the last filter more than 50 times. Also, we tried to get the best fit on the slope and the fit was sometimes off by a lot. In the end, I learned about mass and how it affects the velocity of a falling object and also how the air drag force is related to it.

The red points show our data while the solid line shows what the true value of A*x^B is equal to.