Circular Motion Lab – The Conical Pendulum

Purpose

The goals of this lab are to verify that centripetal acceleration is given by a = v²/r and to show that the period of a conical pendulum is given by .

Procedure

A small mass is suspended by a cord and set into motion above a “target” circle. It then moves in a horizontal circle under the influence of gravity and the tension in the cord. As it moves, the mass and string trace out an imaginary cone – hence it is referred to as a conical pendulum. The radius, r, and length, l, are measured with a ruler or meter stick. Both r and l should be measured to the center of the mass. The period, T, is measured using a stopwatch. It is best to time a certain number of revolutions and divide by this number to get the period. All other values are calculated based on these three measurements.

Part I – Centripetal Acceleration

Vary the value of r and measure the value of T while keeping the ratio of l to r constant. Use a ratio of l/r = 7. (By keeping this ratio constant, the centripetal acceleration will theoretically remain constant according to Newton’s Laws.) Produce a table showing r, l, T, v, and a for six different radii. Produce an appropriate graph – choose one of the following: speed versus radius or speed squared versus radius. Note: if you choose to plot speed squared, this quantity should be included with the data table or in a separate table with the graph. In either case determine the most appropriate best fit equation and plot it against the data keeping in mind the goal of the experiment.

Part II – Period dependence on h

Vary the value of l and measure the value of T while keeping r constant. Produce a table showing r, l, h, T for six different lengths. Produce an appropriate graph – choose one of the following: period versus height or period versus square root of height. Note: if you choose to plot square root of height, this quantity should be included with the data table or in a separate table with the graph. In either case determine the most appropriate best fit equation and plot it against the data keeping in mind the goal of the experiment.

Analyses

Evaluate error and/or deviation. For Part I you should be able to determine the deviation in acceleration values. Determine a theoretical value for the acceleration based on Newton’s Laws and the accepted value for g. Consider this theoretical value to be the “accepted” or “true” value of acceleration and determine the error in the experiment. Remember to consider any constant(s) from the best fit equation. For Part II you should be able to derive the equation for period from theoretical equations and make an appropriate comparison to your best fit equation.

Conclusions

Discuss how well the stated goals of the experiments were achieved. Include in your response an assessment error – referring to evidence of error and the most probable sources.