Final answer:
The work done by the woman compressing a spring is calculated using the formula W = 1/2 k x^2, resulting in 1.215 J. The spring does an equal amount of work but in the opposite direction, so it's considered -1.215 J.
Step-by-step explanation:
You've asked about the work done by a woman while compressing a spring and the work done by the spring itself. The work done on a spring when it is compressed by a distance x can be calculated using the formula W = 1/2 k x^2, where k is the spring constant, and x is the compression distance in meters. In this case, the compression distance is 9 cm, which is 0.09 m.
Work done by the woman: This will equal to the potential energy stored in the spring, which is W = 1/2 k x^2. Therefore, the work done by the woman is W = 1/2 * 300 N/m * (0.09 m)^2 = 1.215 J.
Work done by the spring: As the spring pushes back, it performs work on the block which will be negative since it's in the opposite direction to the displacement caused by the woman. Hence, the work done by the spring is -1.215 J.