Cycle II Regents Physics

John Dewey High School

Mr. Klimetz

Method and Apparatus for the Demonstration and Calculation

of Centripetal Force

a. Convert the six suspended mass values into kilograms and enter into data table.

b. Calculate the weights (**wt**) of each of the six suspended mass values and enter into data table.

c. Along with your lab partners, use the stopwatch to measure the time it takes to complete 30 full orbits of the rubber stopper. Repeat this three times for each mass increment and average. Enter into data table.

d. Calculate the average orbital period (T) for each mass increment by dividing the average of 30 full orbits obtained in Step C above by 30. Enter into data table.

e. Calculate the orbital frequency (f) for each mass increment by calculating the inverse of the average orbital period, that is, by setting f = 1/T. Enter into data table.

f. Calculate the orbital velocity (**v**) for the given orbital radius and period by setting **v** = 2pr/T, where p = 3.14. Enter into data table.

g. Calculate the centripetal force (**F****c**) from the relationship **F****c** = m**v**exp2/r. Enter into data table.

h. Compare the vertical force (**wt**) of each suspended mass increment to the calculated centripetal force (**F****c**).

1. Plot a graph of centripetal force (**F****c**) versus orbital velocity (**v**) for each of the six individual values of suspended mass (hence weight). Orbital velocity should be regarded as the independent variable and centripetal force should be regarded as the dependent variable. Make sure to set-up your axes properly with each commencing numeration at zero. Create a separate table of values of **F****c** versus **v** __before__ plotting your data.

2. Based on your graph of **F****c** versus **v**, briefly explain the observed relationship between centripetal force and orbital velocity of an object traveling in a circular path at a constant orbital radius.

3. Assuming that the Moon orbits the Earth in a circular path, calculate the Moon's orbital velocity (**v****m**) and orbital period (Tm) given the following data and equations from the *Reference Tables for Physics*:

qMean distance from Earth to Moon: (r) = 3.8 x 10exp8 m

qMass of the Earth (me) = 6.0 x 10exp24 kg

qMass of the Moon (mm) = 7.4 x 10exp22 kg

qUniversal Gravitational Constant (G) = 6.7 x 10exp-11 N-mexp2/kgexp2

qForce of Gravitational Attraction between Earth and Moon (**F****g**) = G x me x mm/rexp2

qCentripetal Force Exerted on Moon by Earth (**F****c**) = mm x (**v****m**)exp2/r

qOrbital Velocity of the Moon (vm) = 2pr/Tm

qOrbital Period of the Moon (Tm) = 2pr/**v****m**

[__Hint__: Set **F****g** = **F****c** and solve for **v****m**. Then solve for Tm.]

Express **v****m** in km/s and Tm in days. How is the length of time Tm more familiarly known?

Cylindrical plastic ballpoint pen casing

1.5 m length of narrow gauge braided nylon cord

00 size single vent rubber stopper with a mass of 0.0045 kg

Adhesive tape

Paper clip

Meter stick

Stopwatch

Set of slotted "coin" type masses from Hooke's Law Apparatus:

1-10 gram mass

2-20 gram masses

2-50 gram masses

1-100 gram mass

50 grams

100 grams

120 grams

150 grams

180 grams

200 grams

For each orbital velocity, the orbital radius (r) of the stopper will assume a constant value (0.50 m) and horizontal orientation, and the suspended masses will occupy a corresponding vertical orientation. Whirl the stopper over your head in a horizontal circular path at such a rate that the paper clip is just pulled up to, but not touching, the bottom of the pen casing. Here, the orbital radius of the rubber stopper should be exactly 0.50 m. Reposition the paper clip on the cord accordingly in order to ensure the 0.50 m orbital radius. Adjust the orbital velocity (faster **v** or slower **v**) so that the radius of the circular path remains at the constant 0.50 m value. This is accomplished by the "limiting" paper clip attached to the cord so that the masses remain suspended a constant distance below the bottom end of the pen casing. The centripetal force (**F****c**) furnished by the weight (**wt**) of the suspended masses is now keeping the stopper moving in a circular path of fixed radius.

It is important to keep two factors constant during the course of this exercise: *the mass of the orbiting object *and* the radius of the orbit. *The centripetal force is varied by *altering the* *amount of mass suspended from the string.* Note that the mass of the rubber stopper is 0.0045 kg and the mass of the cord is neglected.