A research team investigates the dependence of torque on lever-arm length
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A research team investigates the dependence of torque on lever-arm length. A light rod is pivoted at one end. The team applies a constant force whose line of action is perpendicular to the rod and whose stated magnitude is 40N. They vary the distance r from the pivot at which the force is applied and record the torque τ with a sensor. Their data are shown below.
Distance from pivot r (m): 0.10 0.20 0.30 0.40 0.50
Measured torque τ (N·m): 4.0 8.1 12.0 15.9 20.0
(a) Using the data, construct a graph of τ versus r on your own axes. Describe whether the empirical relationship appears linear and justify your description with reference to specific features of the plotted points.
(b) Determine an experimental value for the perpendicular component of the applied force by calculating the slope of the best-fit straight line through the data. Show all steps.
(c) Compute the percent difference between the experimental force you obtained in part (b) and the stated 40N value.
(d) Propose one plausible systematic experimental error that could account for any deviation from perfect linearity or non-zero y-intercept, and explain qualitatively how this error would influence the recorded torques.