CENTRIPETAL FORCE

 

GOAL

            To verify the second Newton’s law for the uniform circular motion.

 

PREREQUISITES

                                 R.D. Knight, Physics for scientists and engineers, chapter 7.

 

EQUIPMENT

                         Centripetal Force Apparatus

                         Slotted Mass Set

                         Vernier Caliper

                         Stopwatch

                         Scale

                         Ruler

 

THEORY

                 An object moving in a circle of radius r at constant speed v (and a period of motion T)

v=2π·r/T,

 

has an acceleration whose direction is toward the center of the circle and whose magnitude is

ar=v2/r.

 

According to Newton’s second law, an object that is accelerating must have a net force acting on it

Fnet=m·ar=mv2/r

 

This net force must be directed toward the center of the circle.

 

PROCEDURE

                        

 

Trial 1

Trial 2

Trial 3

Trial 4

Radius of rotation, r (m)

±

±

±

±

Displacement mass, md (kg)

 

 

 

 

Displacement force, Fd (N)

 

 

 

 

Heavy mass, m (kg)

±

Period of rotation, T (s)

 

 

 

 

Speed of rotation, v (m/s)

v=2π·r/T

±

±

±

±

Force from Newton’s law, F (N)

F=m·ar=mv2/r

 

 

 

 

Difference between forces (%)

|F-Fd|/F*100%

 

 

 

 

 

  1. Determine the value of the heavy mass m with a scale balance. Note, that you have to do that measurement only one time. Record that value in fifth raw of the Table.
  2. Disconnect the spring from heavy mass. Adjust the radius of rotation to a minimum possible value. Tighten the knurled screw on top of the vertical shaft. Measure the radius of rotation and record data in the Table.  Adjust the radial indicator rod to be vertically under the heavy mass m and fix its position. Connect the spring to the heavy mass m.
  3. Connect hanger to heavy mass m via a string over the pulley. Add mass to hanger until the radial indicator rod is aligned vertically with the heavy mass m. Record the displacement mass md and displacement force Fd=md·g in the Table. Remove hanger, displacement mass, and string from heavy mass m. Rotate the system by applying torque with your fingers on the knurled poetion of the shaft. With a little practice the rotation rate can be adjusted to keep the heavy mass m passing directly over the radial indicator rod. Measure the time necessary for 5-10 rotations. Calculate the period of rotation T and record it in the Table.
  4. Repeat all previous steps for the maximum possible radius of rotations.
  5. Repeat all previous steps for two arbitrary values of the rotation radius between minimum and maximum values.

 

ANALYSIS

1.      Make all necessary calculation to fill the Table completely.

2.      Why the difference between two forces is rather large? Give your explanation.