Experiment 6
Centripetal Force
Objectives:
The objectives are to experimentally verify the formula for centripetal force and learn how to determine the linear speed of an object from its angular speed as it performs uniform circular motion.
Equipment:
A centripetal force apparatus, a set of assorted weights, a weight hanger, one meter of strong thin string, a stop watch, a ruler, a mass balance, and a calculator
Theory:
An object performing uniform circular motion is constantly under the action of a force that acts toward its center of rotation and has a magnitude of
where M is the mass of the object, v its liner speed of the mass as it travels along the circular path, and R its radius of rotation.
An object tends to move along a straight line if it is under the action of a force that has a constant direction, but if the direction of the force keeps changing such that it is always directed toward the center of a circle, the object is then forced to follow a circular path. Fig. 1 shows a small object of mass M that is connected to a string of length R and is spun in a horizontal plane at constant linear speed, v. Note that the velocity is not constant. This is because of the fact that the direction of velocity keeps changing in circular motion. The velocity vector v is always perpendicular to the radius of rotation R at any point on the circular path, as shown.
Fig. 1
Procedure:
Follow instructions given by your instructor as how to use the centripetal force apparatus and how to twirl its rotor such that it’s pointed mass (bob) lines up with the stud below it as it rotates. See Fig. 2.
Measure the rotation radius (R) and mass (M) of the bob by using a ruler and a mass balance. Choose a radius between 16 cm to 19 cm and set it. The radius does not have to be exactly 16.0, 17.0, 18.0, or 19.0cm. Any value between 16cm and 19cm will do.
Measure the period of rotation (T) for a high number of revolution of the pointed mass, at least 30 revolutions. 50 revolutions is better.
Use the radius of the circle to calculate the circumference and multiply the result by the number of revolutions in order to find the total distance traveled. Divide this total distance by the total time (that you measured by the stop watch) to find the average linear speed (v) of the revolving mass.
With the values of M, V, and R measured, calculate F_{c }by using the centripetal force formula:
This gives you the measured value for F_{c} because your calculation is on the basis of the measured values of M, V, and R.
Direct Measurement of F_{c}:
Your instructor will show you how to attach a string to the mass and pass it over the pulley and connect it to the weight hanger. Stack enough slotted weights on the weight hanger to cause the same extension in the spring as the centripetal force causes during the uniform circular motion. Note that you are putting mass on the weight hanger (including the hanger itself) in order to generate force and stretch the spring. You should find the weight of the hanging mass. That gives the accepted value for F_{c}.
Calculate a %error on F_{c}.
Repeat the experiment (All steps) for two more values of R between 16 and 19cm.
Fig. 2
Data:
Given: g = 9.8 m/s^{2}.
Measured:
Trial | R (meter) | M (kg) |
t = total rotation time (seconds) | N Number of rotations |
v = 2πRN/t | Measured F_{c} F_{c} = Mv^{2}/R |
Accepted F_{c} F_{c} = M_{1}g |
% error |
1 | ||||||||
2 | ||||||||
3 |
Calculation(s):
Comparison of the results:
Write down the percent error formula used as well as the calculated percent errors.
Conclusion:
State your conclusions of the experiment.
Discussion:
Provide a discussion if necessary.
Questions:
Give two examples on objects that perform circular motion and determine the source of centripetal force for each.
Suppose you tie a rock to a string and spin it in a vertical plane. In what direction will the rock move if the string breaks exactly when the rock is passing the lowest point?
Using v = 2πRf, derive a formula for F_{c} in terms of M, R, and frequency, f. Simplify the formula after you substitute for v in the centripetal force formula.