A student investigates the oscillations of a thin uniform hoop of radius RRR suspended from a narrow peg at its inner rim.
Describe how to determine accurately the period TTT of oscillations of this hoop.
The relationship between the frequency fff of the oscillations of the hoop and its radius RRR is given by:
f=12πg2R f = \frac{1}{2\pi}\sqrt{\frac{g}{2R}} f=2π12Rgwhere ggg is the acceleration of free fall.
The student varies the radius RRR of the hoop and determines the period TTT for each radius. The student plots a graph of T2T^2T2 against RRR.
Show that the gradient of the graph is given by the equation:
gradient=8π2g \text{gradient} = \frac{8\pi^2}{g} gradient=g8π2The gradient of the line of best fit on the student's graph is 8.15 s2 m−18.15\text{ s}^2\text{ m}^{-1}8.15 s2 m−1. Use this value to determine ggg.
The student draws a line of worst fit and determines its gradient to be 8.56 s2 m−18.56\text{ s}^2\text{ m}^{-1}8.56 s2 m−1. Use this line of worst fit to calculate the percentage uncertainty in ggg.
Use the accepted value of g=9.81 m s−2g = 9.81\text{ m s}^{-2}g=9.81 m s−2 to evaluate the accuracy of the student's experimental value of ggg. Include a calculation of the percentage difference in your answer.
