To test how well a laboratory spring follows a power-law relationship
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Solids · Mechanical Properties of Solids
Problem
To test how well a laboratory spring follows a power-law relationship, a team measures the force required to produce several extensions that are well within the spring’s safe operating range.
Table 2 – Force and Extension Data
| Extension Δx (m) | 0.005 | 0.010 | 0.020 | 0.030 | 0.050 |
| Force F (N) | 0.38 | 0.78 | 1.56 | 2.40 | 4.00 |
Assume gravity and friction do not affect the horizontal setup used.
(a) For each data pair, calculate a value of the ratio F/Δx. Record your results and comment on their consistency.
(b) Transform the data by taking the base-10 logarithm of both F and Δx. Using the first and last data points, determine the slope of a straight line that would fit a plot of logF versus logΔx. Show all calculations.
(c) Explain what the numerical value of the slope found in part (b) implies about whether the spring obeys a linear force–extension relationship over the measured range.
(d) If each force measurement carries an uncertainty of ±0.05 N, calculate the percentage uncertainty in the ratio F/Δx for the largest extension. Discuss how this uncertainty affects the confidence in your conclusion from part (c).