Question

If you stand on a bathroom scale, the spring inside the scale compresses 0.478mm, and it tells you your weight is 762N. Now if you jump on the scale from a height of 1.18m, what does the scale read at its peak?

Answer 1

so far i first tried finding k by doing \[w/x\] then \[W=\sqrt{2kmgh}\] at the end and the answer has been wrong.

Answer 2

hey...
the first part of the question gives you the K value of the spring:

762N/ 0.478mm= 1594142.259 N/m

the energy stored in a spring can be found by ( d = 0.478 mm)
1/2 * K * d^2= 0.18 joules

the additional energy going into the spring when you jump from 1.2 meters is

=m*g*h
=W*h
=762 N*1.18 m = 899.16 joules.

so the maximum compression will have total energy equal to the sum of the equilibrium energy and the potential energy

1/2 * K * x^2 = E
x= sqrt (2*E/K) = sqrt (2* 899.16 J / 1.594 N/mm) = 33.58mm

the scale is set up to measure W=K*x

so it would show a weight of 53531 N: which is why you should never jump on a scale

hope this will help ya!!