28-Sept-2016: Centripetal Force Lab

Lab 8: Centripetal Force with changing mass, radius, and angular velocity
Name: Andrew Martinez
Lab Partner: Professor Phillip Wolf

Purpose: To determine the relationship between centripetal force and mass, centripetal force and radius, and centripetal force and angular velocity.

Theory/Introduction: To find centripetal force the formula F_centripetal = mrw^2 is used where w is the angular velocity, r is the radius, and m is the mass. By varying the values on m, r, and w separately and then graphing in a centripetal force vs (varying variable) our slope will equal our constant values and prove their relationship to one another and to the formula.

Apparatus: Was a custom made motor that spun in a circular motion. A time gate with some mass was fasted to the spinning panel and measured for the varying variables.

Measured Data

Trail 1: M=200 g, R= 19 cm, V=6.1 Volts, Delta Theta = 20pi, Delta T=.43s-20.63s, F=0.392 N
Trail 2: M=200 g, R= 28.5 cm, V= 6.1 V, Delta Theta= 20pi, Delta T=1.27s-19.28, F=0.837 N
Trail 3: M=200 g, R=40 cm, V=6.1 V, Delta Theta= 20pi, Delta T=.55s-16.7s, F=1.39 N
Trail 4: M=200 g, R=54 cm, V=6.1 V, Delta Theta= 20pi, Delta T=.94s-17.47s F=1.65 N
Trail 5: M=200 g, R=54 cm, V=6.6 V, Delta Theta=20pi, Delta T=.2s-13.1s F= 2.61 N
Trail 6: M=200 g, R=54 cm, V=7 V, Delta Theta= 20pi, Delta T=.7s-12.5s, F=3.37 N
Trail 7: M=200 g, R=54 cm, V=7.7 V Delta Theta=20pi, Delta T=.32s-10.04s, F=4.79 N
Trail 8: M=100 g, R=54 cm, V=7.7 V, Delta Theta=20pi, Delta T=.6s-10.4s, F=2.3 N
Trail 9: M=50 g, R=54 cm, V= 7.7 V, Delta Theta=20pi, Delta T=.31s-10.54s, F=1.14 N

Graphing Analysis

In this Force vs Rw^2 graph the variable m for mass is kept constant. By comparing the slope to the actual M one can see how accurate the equation F=mrw^2 is.  In this case the slope of mass is 0.21 when our actual mass is 0.2 which means we had a 5% percent error which is an acceptable margin of error.

In this Force vs w^2 graph the variable mr for mass and radius is kept constant. By comparing the slope to the actual mr one can see how accurate the equation F=mrw^2 is.  In this case the slope of mass and radius is 0.117 when our actual is 0.108 which means we had a 8.3% percent error which is admittedly pushing the acceptable margin of error.

In this Force vs mw^2 graph the variable r for radius is kept constant. By comparing the slope to the actual r one can see how accurate the equation F=mrw^2 is.  In this case the slope of radius is 0.393 when our actual radius is .54 which means we had a 27.22% percent error which is too large of an error to be consider acceptable.

Conclusions:

Based on the data and graphing analysis we can conclude that the equation F=mrw^2 does indeed work. While both graphs Force vs w^2 and Force vs Rw^2 slope and actual were within acceptable percent error range the graph Force vs Mw^2 was not. This can be contributed to a number of things from random errors such as changes in voltage or the friction on the mass as it was accelerated to systematic errors suchs as inaccurate measurements or timing. If the lab were to be redone I am confident that all three graphs of data can be brought into reasonable range of percent error.