Students investigate uniform circular motion by tying a mass to a light string and…

PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

Students investigate uniform circular motion by tying a

0.12\,\text{kg}

mass to a light string and swinging it in a horizontal circle of unknown radius above their heads. A force sensor in the string measures the tension

F_T

, which equals the net force toward the center. The students vary the speed

v

and obtain a straight-line graph when plotting

F_T

(vertical axis) versus

v^{2}

(horizontal axis). The slope of the best-fit line is

0.45\,\text{N}\,\text{s}^{2}\,\text{m}^{-2}

. (a) Show that the ratio

m/r

can be obtained from the slope of the graph, and determine its numerical value and units using the given data. (b) Using the known mass of

0.12\,\text{kg}

, calculate the radius

r

of the circular path. (c) The radius is measured directly with a tape measure as

0.25\,\text{m}

with an uncertainty of

\pm0.02\,\text{m}

. Compare the two determinations of

r

by calculating the percent discrepancy, and comment on whether they agree within experimental uncertainty. (d) Discuss qualitatively how air resistance acting on the mass would influence the slope of the

F_T

versus

v^{2}

graph. Would neglecting air resistance cause the radius determined in part (b) to be overestimated, underestimated, or unchanged? Explain your reasoning.

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