Question

A bathroom scale is compressed 0.11 in. when a 110​-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 0.05 in.​ weigh? How much work is done compressing the scale 0.05 ​in.?

Answer 1

Answer:

(a) 220 lb

(b) 10.75 in-lb

Explanation:

(a) We know that if a 110 lb person compresses the spring 0.11 inches, then a person weighing double that amount will compress the spring double, i.e. the person would weigh 220 lb.

(b) The amount of work done in compressing the spring 0.11 inch is given by the integral:  

110/.11=1210

$\int\limits^\frac{1}{20} _0 {1210x} \, dx$

=10.75 in-lb