Consider an ideal spring with k = 200.0N/m. One end of the spring is attached to the ceiling, and at the bottom of the spring is a basket (you can assume the basket has zero mass)

(a) Calculate the amount of work done by the spring as the basket is pulled down from 0cm to 10cm, from 10cm to 20cm, and from 20cm to 30cm.

(b) Now calculate the amount of work done by the spring as the basket is pulled from 0cm to 30cm in two ways:

(1) by adding up your answers to part (a) above;

(2) by using equation ( w= -1/2k (x_f-x₀)²-(xi-x0)²) directly with x _i x ₀ = 0 and x _f x ₀ = 30cm. Check to make sure your answers agree with each other and that the sign makes sense for the work done by the spring.

(c) A tennis ball with m = 59.0g is placed in the basket, which is then pulled downward to a displacement of 1.50m and then released. What will be the work done by the spring on the tennis ball as the ball moves up to the equilibrium point? Is this work positive, zero, or negative?

(d) What will be the amount of work done by gravity on the tennis ball over this same displacement? Is it positive, zero, or negative?

(e) Is the net work done on the ball positive, zero, or negative over this displacement? Describe how this relates to the direction of the net force on the tennis ball during this period.