Centripetal Force

Introduction:
The purpose of this lab is to experiment with Newton's second law of motion for uniform circular motion. Using a centripetal force apparatus to rotate a known mass around a known radius. The velocity can be calculated by timing the number of revolutions the object travels and the total distance the mass has traveled. To determine the centripetal force to maintain the object in the circular path can be calculated by F = mv^2/r.

Materials:
Centripetal force apparatus, metric scale, vernier caliper, stop watch, slotted weight set, triple beam balance.

Procedure:
1. Assemble the centripetal force apparatus so that when the weights rotate around the mass hangs right over the vertical cross arm that indicates the radius.

2.Spin the apparatus 50 times and time how long it takes while maintaining a constant speed. Use the same mass and radius for all the the first four trials.

3. Obtain the average time to calculate the velocity of the weights. Then you can calculate the centripetal force exerted on the mass during the rotation.

4. Determine the centripetal force by attaching a hanging weight to the mass until it is position over the radius indicator post. The force should be about the same.

5. Add 100 g and repeat steps 2, 3, and 4.

centripetal force apparatus

Formulas:
f = 50/t
v = 2pi*r*f
F = mv^2/r 


Data:

Table1.2

*top 5 trials are with the first mass and the bottom was added 100 g. Note: radius is in meters.

 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%

Force Diagram 

Tension force

  *net force = 0

gravity

Conclusion: 

The lab shows that while keeping the radius constant, the centripetal force becomes lower as the mass of the object increases. The results that we obtained were closed to the measured centripetal force. The percent difference for most of them was between 0.19% and -7.1%. There was one trial where we got a percent difference that was high (-23.7%) but we kept it as an example of source of error. The reason for such a difference is because of confusion between the number of rotations and time, and the revolutions not being constant. Some of the sources of error which we came across were that at moments the revolutions didn't seem as if they were going at a constant velocity. When the revolutions are too fast the object overpasses the radius generating some different results.Another source of error is not remembering to use unit conversions if you used something else than meters..