Q4. A rubber band stretches 1.0 cm under 1 N, 2.2 cm under 2 N and 3.7 cm under 3 N. Does it obey Hooke’s law?
No. The extension per newton is 1.0, 1.1 and about 1.23 cm, rising with the load, so extension is not proportional to load. These data are nonlinear; whether the band recovers on unloading requires a separate observation.
Q5. A copper wire is 3.0 m long, with a cross-section of 2.0 mm, and the modulus of copper is 1.1 × 10 Pa. What force stretches it by 1.5 mm?
F = ksΔL = kAΔL/L = 1.1 × 10 × 2.0 × 10 × 1.5 × 10/3.0 = 110 N.
Q6. A wire is cut in half. How does the spring constant of each half compare with that of the whole wire?
The spring constant is ks = kA/L. Halving L doubles it: each half is twice as stiff, and under the same load stretches half as much.