Final answer:
The work done on compressing a spring is equal to the potential energy stored in the spring, calculated using U = 1/2kx². For a spring compressed 20 cm with a constant of 8.0 N/m, the work done is 0.16 J.
Step-by-step explanation:
The work done to compress a spring can be calculated using the formula for the potential energy stored in a compressed or stretched spring, which is U = 1/2kx², where 'U' is the potential energy, 'k' is the spring constant, and 'x' is the displacement from the equilibrium position.
In this problem, the spring is compressed 20 cm, which is 0.20 m. With a spring constant of 8.0 N/m, the work done to compress the spring is given by:
U = 1/2(8.0 N/m)(0.20 m)² = 0.16 J
This result differs slightly from the provided answer of 0.26 J, indicating a possible error in the student's original data or calculation. It's important to check the values and calculations for accuracy.
Since the work done on the spring is equal to the potential energy stored in the spring, this amount of work (0.16 J) is the correct answer based on the given spring constant and compression distance.