Centripital Force

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

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

Introduction:
The centripetal force apparatus is designed to rotate a known mass trough
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.
F=mv^2/r
Where m is the mass, v is the velocity, and r is the radius of the circular
path.
Here we have used the fact that for uniform circular motion, the
acceleration, a, is given by:
a= V^2/r

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 50 revolutions of the apparatus. Keep the velocity as
constant as possible by keeping the pointer on the bottom of the mass aligned with
the indicator post. A white sheet of paper placed as a background behind the
apparatus can be helpful in getting the alignment as close as possible. Using the
same mass and radius, measure the time for three different trials. Record all data
in a neat excel table (see 6).

                                          lab setup during trials, very concentrated individuals here

3. Using the average time obtained above, 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 once again is positioned over the indicator post (this time at rest).
Since the spring is being stretched by the same amount as when the apparatus was
rotating, the force stretching the spring should be the same in each case.
a. Calculate this force and compare with the centripetal force obtained
in part 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 g to the mass and repeat steps 2, 3 and 4 above.
6. The following data should be calculated and recorded in your excel table:
a. Mass and radius for each trial.
b. Average number of revolutions/sec (frequency) for each trial.
c. Linear speed for each trial.
d. Calculated and measured centripetal force for each trial and their percent
difference.

                                            excel spreadsheet with all trials
                            first 5 trails   m=475g r=16.5cm             v=2pi*r*f     a=v^2/r
                             last 5 trails   m=575g r=16.5cm             f=50/t           f=mv^2/r
the percent diff for first 5 trails
1. 0.48% 2. 0.48% 3. 0.48% 4. 12.25% 5. 8.26% AVG 4.44%
last 5 trails
1. 12.52% 2. 1.08% 3.3.83% 4. 2.45% 5. 0.44% AVG 3.83%
Errors: human error in using the stopwatch and keeping the velocity as constant as positive also theres air resistance.
conclusion:
we were able to verify newtons second law of motion for uniform circular motion cause acceleration is proportional to the net force acting on it. thru our results and calculations and can make the assumption that with a constant radius, greater mass the lower the centripetal force is.