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CENTRIPETAL FORCE I

Purpose

To measure the centripetal force acting on a mass and compare the measured force to the force calculated from the formula Fc = mv2/r.

Apparatus

Centripetal force apparatus (see fig. 1), meter stick, stop watch, weight hanger, weights and a scale.

Theory

Centripetal force acting on a mass will be measured and compared to a measured force, using the formula Fc = mv2/r. m is the mass of a rotating body, v is the speed of rotation of the mass in revolutions per second and r is the radius of the circle, r and m are determined by direct measurement.

A mass is hung from a rotating head (see diagram 1). The head consists of a frame to which the mass is attached by a horizontal spring. It rotates about a vertical shaft in a horizontal plane which is turned manually.

As the mass rotates the spring exerts a centripetal force in the mass. The mass exerts and opposite force which stretches the spring. By measuring the amount of stretch and using a static load to reproduce the amount of stretch the centripetal force can be measured.

Procedure

Rotate the mass until it is opposite the pointer. Keeping the speed constant have your partner time a predetermined number of revolutions. Make measurements for at least three different number of revolutions and calculate the average number of revolutions per second.

Attach a string to the mass and hang it over the pulley. Using a mass hanger add weights until the pointer is opposite the indicator. The spring tension is now the same as when the mass was in motion. Convert this value to Newtons and compare it to the value from the formula Fc = mv2/r. Measure the radius and the mass.

Repeat the procedure by adjusting the position of the cross arm and pointer. This changes the tension on the spring.

Comparison / Error Analysis

The results from the two trials varied greatly. In the first trial the calculated centripetal force was only -2.8% less than the measured force. While in the second trial the calculated centripetal force was -41.6% less than the measured force.

I believe human error was the primary reason for the disparity in the two results. Timing and maintaining a constant rotation each added to the error rate. For each trial different people were responsible for the timing and rotating the mass. This lack of consistency probably added to the error rate.

When adding weights to the mass hanger it was noticed that large weight increments were needed to make the spring respond. Missing the true mass by +/-25 grams would have been possible when determining the static mass. This was especially true in the second trial when the spring had to be stretched the longest.

It is obvious that the centripetal force calculated in the second trial was inaccurate as it was less than the force in trial one although it should have been higher as the mass rotated at a greater radius.

I feel that a combination of errors compounded themselves in the formula creating a grossly inaccurate answer.

Question In Book

Could a horizontal axis of rotation be used for this experiment?

A horizontal axis of rotation would bring the affect of the force of gravity into the experiment. The mass would accelerate on the downward portion of the rotation and conversely decelerate on the upward potion of the rotation. Therefore accurate results would not be possible. To negate the effect of gravity a vertical rotation is necessary.

Conclusion

The experiment met its purpose in deterring the centripetal force of a moving object. The principles involved as well as the effect of varying the various factors in are clarified.

To obtain greater accuracy I feel that more than two trails should be made. This would help minimize and identify any errors made. If possible a more sensitive spring could be used and a mechanical method of rotating the mass would improve accuracy.