Final answer:
4 joules of work is required to stretch a spring from 38 cm to 48 cm, as the work needed is equal to the previous work done for the same 10 cm stretch.
Step-by-step explanation:
Given that 4 joules of work is needed to stretch a spring from its natural length of 35 cm to 45 cm, we can determine the work needed to stretch the same spring from 38 cm to 48 cm using the principle of conservation of energy and Hooke's Law. According to these laws, the work required to stretch or compress a spring can be calculated by the formula ½ kx², where k is the spring constant, and x is the displacement from the equilibrium position. Notably, the work done on the spring depends on the square of the displacement from its natural length.
The original 10 cm stretch (from 35 cm to 45 cm) needed 4 joules, so an additional 10 cm stretch (from 38 cm to 48 cm) would also require 4 joules of work. This is because the amount of stretch from the equilibrium length is the same in both cases, regardless of the initial length of the spring. Hence, the work done is only dependent on the magnitude of the stretch, not on the initial position from which it is stretched.