Ph201: General Physics Laboratory1

Instructor: Tony Zable

Experiment #8: Centripetal Force

Preliminary Questions:

1) A 0.10 kg mass travels in uniform circular motion, at constant speed of 1.5 m/s. The radius of the path traveled by the mass is 0.3 m.

a) What is the centripetal force that keeps the mass traveling in the circular path?

b) What is the centripetal acceleration that keeps the mass traveling in the circular path?

c) How far does the mass travel during one complete revolution?

d) How long does it take for the mass to complete one revolution?

2) A 0.060 kg mass travels in uniform circular motion, where radius of the path traveled is 0.40 m. The mass completes one revolution in 0.25 seconds.

a) What is the number of revolutions completed per second?

b) How far does the mass travel during one complete revolution?

c) How fast (speed) is the mass traveling during this motion?

d) What is the centripetal acceleration of the mass?

e) What is the centripetal force acting on the mass?

Objectives:

  • To measure the centripetal acceleration associated with a rotating object using the centripetal force apparatus, for various values of m and r.
  • To compare the calculated centripetal force directly with the static force required to pull the object to the same radial position.

Theory:

When a body is caused to revolve in a circle with uniform velocity, the resultant inward force on the body is called centripetal force. The centripetal force produces an inward radial acceleration, a, Starting with Newton’s 2nd Law, the centripetal force can be written:

(1)Fc = mv2/r

in which m is the mass of the revolving object.

Consider one revolution of the mass. The distance traveled is 2r and the time it takes to go one revolution is the period, T. Since v = distance/time, the velocity of the mass is 2r/T. The centripetal force equation becomes:

(2)Fc = 42m r/ T2

where r is the radius of the circular path.

Equation (2) is the working equation for this apparatus. Remember to convert to SI units for all measurements (m, kg, s)

Procedure:

  1. Measure T: Let the heavy mass hang freely with the spring detached. Adjust the indicator beam to be exactly under the mass. Now reattach the spring to the mass. Begin spinning the axle so that the mass swings out over the indicator, just as it was before the spring was attached. Maintain this speed while a lab partner times for 50 revolutions. Repeat this measurement 3 times, each time letting a different person spin the mass and time 50 revolutions. Use this data to calculate the period. . Average the results over the 3 trials. (You have the time for 50 revolutions so just get the time for one revolution.) Record your results below.
  2. Measure r: The radius of rotation is the distance from the center of the top of the radius indicator to the axis of the vertical shaft. To obtain this value, add one half the diameter of the shaft to the distance from the shaft to the center of the top of the indicator. Record your results below.
  3. Measure m: Determine the mass of the revolving object using a balance in the lab. Record your results below.
  4. With the mass attached from the spring, guide the free string that is attached to the mass over the pulley (little wheel). Hang masses on that string until the mass is pulled directly over the indicator, just as it was when it was being spun. Record the amount of hanging mass below.

Time for 50 revolutions:Trial 1______

Trial 2______

Trial 3______

Average period (T):______s

Mass of weight:______kg

Radius of rotation:______m

A) Centripetal Force from Eqn 2:______N

Amount of hanging mass over pulley______kg

B) Force (weight) ofhanging mass:______N

Percent Diff between A and B:______%

Final Questions:

  1. When the radius is constant, does the centripetal force vary when the mass of the rotating object is increased? Why or why not?
  2. When the mass of the object is same, does the centripetal force vary when the radius of rotation is increased or decreased? Why or why not?
  3. Do your calculations for centripetal force agree with your direct measurement of static force? What are possible reasons why the results would disagree?
  4. What is responsible for generating the centripetal force experience by the rotating object? Be specific.