PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Solids · Mechanical Properties of Solids
Problem
In a follow-up investigation, another student records many force–extension pairs for a different spring and plots the results on graph paper. The plotted points lie close to a straight line that passes through the origin within experimental uncertainty. From the student’s graph, two points that lie on the best-fit line are clearly readable:
• Point P: extension Δx=0.020m corresponds to force F=1.5N
• Point Q: extension Δx=0.080m corresponds to force F=6.1N
Each plotted point carries an uncertainty of ±0.2 N in force and ±0.002 m in extension due mainly to the resolution of the spring scale and ruler.
(a) Use points P and Q to compute a best estimate for the spring’s stiffness. Show all steps.
(b) Using the stated uncertainties, determine the maximum and minimum possible slopes consistent with the data. Hence obtain an uncertainty range for the spring’s stiffness.
(c) A manufacturer’s rating for the same model spring is 76 N·m⁻¹. Discuss whether the experimental value you obtained is consistent with the manufacturer’s value, citing quantitative evidence.