Batteries in a flashlight must be held in electrical contact even though the outer plastic housing expands differently than the battery and terminals. This is accomplished by having a compliant spring compressed as the cover is screwed on the flashlight. When the cover is screwed on at room temperature (70?F), the spring, with constant 5lb/in., compresses by 0.25in. The plastic casing has a thermal expansion coefficient of 85(10?6)(?F)?1. Let the battery and spring have a single thermal expansion coefficient like that of steel, 6.6(10?6)(?F)?1, and neglect the elastic deformation of the battery.
If the temperature of the flashlight increases to 120?F, does the spring force increase or decrease and by how much? Take the casing wall to have an outer diameter of 1.5 in., thickness 0.125in.,length L = 3 in., and elastic modulus of 300ksi.