(a) The spring constant of the slingshot is 400 N/m.
(b) The child needs to do 1.875 J of work to stretch the slingshot back 15 cm from equilibrium.
The spring constant of the slingshot is the slope of the force-displacement graph. The slope is calculated by taking the change in force divided by the change in displacement. We can see from the graph that the force increases from 0 N to 80 N as the displacement increases from 0 m to 0.20 m. Therefore, the spring constant is:
k = (80 N - 0 N) / (0.20 m - 0 m) = 400 N/m
To calculate the work done to stretch the slingshot back 15 cm from equilibrium, we can use the following equation:
W = 1/2 * k * x^2
where:
W is the work done in Joules
k is the spring constant in Newtons per meter
x is the displacement in meters
We can see from the graph that the displacement at equilibrium is 0.10 m. Therefore, the work done to stretch the slingshot back 15 cm from equilibrium is:
W = 1/2 * 400 N/m * (0.15 m - 0.10 m)^2 = 1.875 J