A bathroom scale is compressed 0.21 in. when a 210 -lb person stands on it. Assuming that the scale behaves like a spring that obeys Hooke's law, how much does someone who compresses the scale 0.06 in. weigh? How much work is done compressing the scale 0.06 in.?

60 lb

1.8 lb-in

Explanation:

Case 1:

F = weight of the person = 210 lb

x = compression of the bathroom scale = 0.21 in

k = spring constant of the spring

Using the equation

F = k x

210 = k (0.21)

k = 1000

Case 2:

F' = weight of the person

x' = compression of the spring = 0.06 in

k = spring constant of the spring = 1000

Using the equation

F' = k x'

F' = (1000) (0.06)

F' = 60 lb

Work done is given as

W = (0.5) k x'²

W = (0.5) (1000) (0.06) ²

W = 1.8