Q4. A spring balance is used for years to weigh heavy loads near its maximum. Why might it start giving wrong readings?
Loads near the maximum, repeated for years, can push parts of the spring past its elastic limit, leaving a small permanent set that shifts its zero and its readings. Repeated loading can also start fatigue cracks that may eventually break it.
Q5. A copper wire 2.5 m long is left 1.0 mm longer after a heavy load is removed. Find the permanent set as a fraction of the original length. Is copper brittle or ductile?
1.0 × 10/2.5 = 4.0 × 10, that is, 0.04%. Copper is ductile: it can deform permanently a great deal before breaking, which is why it can be drawn into wires.
Q6. A spring 20.0 cm long stretches to 26.0 cm under a load. After the load is removed it is 20.4 cm long. How much of the extension was recovered, and what is the permanent set as a percentage of the original length?
Extension 26.0 − 20.0 = 6.0 cm; recovered 26.0 − 20.4 = 5.6 cm; permanent set 0.4 cm, which is 0.4/20.0 = 2% of the original length. The spring was loaded beyond its elastic limit.