 GOING IN CIRCLES

NAME ____________________________ PARTNER ________________________ DATE _______

PURPOSE

(1) To study the nature of centripetal force.

(2) To experimentally demonstrate the relationship between centripetal force, mass and velocity.

(3) To use a Traditional Taiwanese Toy called the "Cicada" to experimentally look for a relationship between centripetal force, rotational kinetic energy, velocity and frequency of sound produced by its motion.

MATERIALS

Glass tube 15 cm long; masking tape; nylon fishline; rubber stoppers; masses; paper clip or tape ; clock or stopwatch; triple beam balance.

INTRODUCTION

An object moving with changing speed in the same direction is undergoing acceleration. If an object moves with constant speed but in changing directions, it is also undergoing acceleration. Both types of acceleration require forces. A change in direction is called centripetal acceleration, and the force producing it is called centripetal force. The equation relating centripetal force, mass, and velocity is Fc = mv2 /r where Fc is the centripetal force, m is the mass of the moving object, v is its speed, and r is the radius of the orbit of the object. In this experiment, each of the factors in this equation will be varied as an object is whirled on the end of a string. Centripetal force will be supplied by masses tied to a string that passes through a vertical tube. The effect of gravity on the whirling object is offset by the resulting angle of the string with the horizontal. Thus r can be taken as the length of the string between the tube and the center of the object (even though the string is not perpendicular to the tube) without introducing a significant error. Of course, it is possible for an object to have accelerations of speed and direction at the same time. This is the case with the planets, which move around the sun in elliptic orbits.

PROCEDURE Each group will perform one part of the following procedure. The data will then be shared.

1. Attach a #6 rubber stopper of mass 20 grams (as close as you can make it, by cutting off a little or adding a little tape) securely to one end of a fishline; feed the fishline through the glass tube. Fasten 100 g to the other end, hold it in one hand and hold the glass tube in the other. Fasten a paper clip or tape to the fishline so the radius of the circle will be 60 cm from the top of the tube to the center of the stopper. Whirl the rubber stopper in a horizontal circle by revolving the tube. Slowly release the 100 g mass and adjust the speed of revolution so that the paper clip or tape marker stays just (1-2 mm) below the bottom of the tube. Make several trial runs before recording any data. When you have learned how to keep the horizontal rotational speed and position of the marker constant, have a partner measure the time required for 20 or 30 revolutions. Calculate the time of a single revolution and record as the period. Also record the centripetal force (weight of the 100 g).

Repeat this procedure, but increase the centripetal force by adding about 50 g (two big washers). Record the resulting data. Run four additional trials using still larger centripetal forces in 50 g increments.

2. Run five of trials in which the radius (60 cm) and force (0.980 N) are kept constant, but the mass of the whirling object changes. Use Stoppers from #4 - #8.

3. Run a series of trials in which the mass (use a #6 stopper with a mass 20 grams (as close as you can make it, by cutting off a little or adding a little tape)) of the object and the force (0.980 N) are kept constant, but the radius changes ( use 40 cm, 50 cm, 60 cm, 70 cm, 80 cm). Record the appropriate data.

4. Repeat procedure with the use of the "Cicada" Record all appropriate data.

DATA / RESULTS

 STOPPER MASS _____ # of REVS _____ TIME____ RADIUS _____ SPEED2 = (2p R/t)2 _____ FORCE (Weight) _______ MV2/ R % Difference CICADA MASS ______ # of REVS _______ TIME ____ RADIUS _____ SPEED2 = (2p R/t)2 _____ FORCE (Weight) _______ MV2/ R % Difference

ANALYSIS / CONCLUSION

1. Calculate the velocity from the circumference and period.

2. Using the centripetal force equation, calculate the mass times the acceleration for each trial. Compare these values with the values of force and explain any discrepancies

3. GRAPHS ( do those assigned to you; consider obtaining results from other groups who used the same controls as you did and combine on one graph.)

a) Plot a graph of v2 (y-axis) as a function of the measured Fc (x-axis). (A computer graph is best)

b) Plot a graph of v2 as a function of r.

c) Plot a graph of v2 as some function of mass such that it produces the best linear graph.

Estimate the uncertainty in your measurements and write at the top of the data chart. Find the equation of your graph. Interpret the intercept of your graphs. If it is not zero, should it be zero? Analyze the slope and compare it to what you would expect?

4.Based on the graphs, what is the relationship between the centripetal force, mass, radius and the speed of a body in circular motion? Do your graphs support the textbook equation or do they show it to be wrong?

5. If the tape or marker touches the tube, how does this affect results?

6. If there is a lot of friction between the tube and the sting, how does this affect results?

7. Do a comparative analysis of the two methods used in this lab. Does a mathematical relationship become apparent between the rotational rates and the frequency of sound produced by the Cicada? Explain.

8. Discuss and design other adaptations for the use of the Cicada to experimentally demonstrate the concepts of force, energy, sound and frequency.