Centripetal Force

Introduction 
This lab was done to verify Newton’s second law of motion for the case of uniform circular
motion. The materials used were a Centripetal force apparatus, metric scale, vernier caliper, stop watch, slotted weight set, weight hanger, and a 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.

Data 
 Our data was collected manually (without graphical analysis or lab vernier pro). We would count the revolutions, record the time and measure the radius.

Here is the set up for the centripetal force measurement.

Below the centripetal force measurement is in action. 

Force Diagrams

Below is the data for the weight of 0.4745(g)

Above is the data for the weight of 0.5745 (g)

Calculations

Formulas

f= 50/t

V= 2pi*r*f

F = mv^2/r

Known mass = 474.5g (475g)

Revolutions (t) = 50

*convert units

f = 50/t   so, f = 50/32.06 s    (revolutions over time)

                     = 1.56 Hz

linear speed

v = 2pi*r*f so, v = 2pi(0.18542)(1.56)

                         = 1.817 m/s

Calculated cf

F = mv^2/r so, F= (0.4745mg)(1.817 m/s)^2/0.18542m

                        = 8.444 N

Measured cf 8.428 N 

Percent difference

(8.444-8.428/8.428)* 100 = 0.19%

Conclusion
From this lab we learned how to find the centripetal force of an object in uniform circular motion. We compared our experimental values with actual values to see if our results were reasonable. They were relatively consistent with the actual forces exerts o the spring. I learned that the higher the velocity of an object the more force it exerts to the center. Our percent error ranged from 1% to a major outlier of 23%. This large error was due to the frequency not being constant since it was operated manually and was thus susceptible to human error. In this lab we saw how Newton 2nd Law applies to objects in uniform circular motion. The results showed that in this experiment the acceleration was directly proportional to the Force exerted by the object to the center bu ii is inversely proportional to the mass of the object. Some things that could be done to reduce the percent error would be to have the object spin my some type of motor that will keep the force constant. Also a device that could just measure the frequency would be good. In conclusion, this lab reinforced Newton 2nd Law.

Drag Force on A Coffee Filter

Introduction

The purpose of this lab is to study the relationship between air drag forces and the velocity of a falling body.When an object moves through a medium such as air, a force know as drag opposes its motion. This force increases  with the velocity of the object. In this lab we studied the relationship between velocity and drag force. We assumed that the drag force FD = k (|v|^n) where we had to find n. We investigated the drag forces on falling coffee filters. 

Data
Our data was collected using Graphical Analysis. The number of coffee filters was reduced by one during every run. The terminal velocity was obtained by taking the slope of the Time vs. Position Graph recorded in graphical analysis. Every run was conducted 4 trials for every number of coffee filters to obtain an average terminal velocity. From this we saw a trend because the surface area was the same but the only thing that changed was the number of filters, the force to the ground.

Here is a table of data collected. The trend that observed that the coffee filters fall faster with more weight because there is the same amount of drag but less weight to accelerate it to the ground, so in turn the velocity is lowered with less weight.

Number of Filters	Trial 1 (m/s^2)	Trial 2 (m/s^2)	Trial 3 (m/s^2)	Trial 4 (m/s^2)	Average (m/s^2)
9	2.009	1.925	2.053	2.081	2.017
8	1.981	1.612	2.031	2.061	1.921
7	1.878	1.955	1.837	1.925	1.898
6	1.694	1.756	1.685	1.743	1.719
5	1.422	1.6	1.501	1.428	1.481
4	1.337	1.303	1.309	1.353	1.325
3	1.176	1.167	1.24	1.269	1.213
2	1.009	1.067	0.985	0.982	1.011
1	0.776	0.672	0.721	0.866	0.758

Conclusion 
In this lab we observed the relationship between velocity of a falling (accelerating) object and drag.
From our data we came to the conclusion that when the coffee filters fell they accelerated like any other object but then the drag came into effect. The velocity remains relatively the same because as the objects increases in acceleration the drag also increases. So as the drag increases on the object the acceleration decreases. When the drag comes to equilibrium with the mass of the falling object then the acceleration will be zero and the velocity will be constant and will not change.

We plotted the Number of coffee filters vs. Average terminal velocity and then analyzed it with a power law fit to obtain the value of our experimental n value. The n value resulted in n=2.075 which is relatively close to the actual value of n=2. We had a error of  3.61%. It was very important for the shape of the coffee filters to stay the same because if the shape changed the surface area would change thus changing the drag force. The Position vs. Time graph was linear with a constant slope, where the slope represented the terminal velocity. The trend that was seen was that as the velocity increased the drag also increased.