Explanation:
It is given that,
Weight of the person, W = F = 846 N
When the person steps onto a spring scale in the bathroom, the spring compresses by 0.574 cm, x = 0.00574 m
(a) The force acting on the spring is is given by Hooke's law as :
[tex]F=-kx[/tex]
[tex]k=\dfrac{F}{x}[/tex]
[tex]k=\dfrac{846\ N}{0.00574\ m}[/tex]
k = 147386.7 N/m
(b) If the spring is compressed by 0.314 cm or 0.00314 m, weight of the person is given by again Hooke's law as :
[tex]F=kx[/tex]
[tex]F=147386.7\ N/m\times 0.00314\ m[/tex]
F = 462.7 N
Hence, this is the required solution.
