PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
A nonlinear spring is stretched, and the force F(x) (in newtons) required to hold the spring at an extension of x centimeters is measured.
x (cm)
0
1.5
3.5
5.0
6.5
8.0
F(x) (N)
0
52
127
180
250
330
(a) Treat the force as varying linearly between the recorded extensions. Approximate the work, in joules, needed to stretch the spring from x=0 cm to x=8 cm.
(b) Use the same data to determine an experimental estimate of the spring’s effective constant k by finding the slope of the best-fit line through the origin for the ordered pairs (x,F(x)).
(c) A manufacturer claims that the spring obeys Hooke’s law with k=350 N/cm. Evaluate the reasonableness of this claim using your answers from parts (a) and (b). Discuss at least two factors that could account for any discrepancy.