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.