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 o beys 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.?
1 answer:
Answer:
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
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