Question

If you stand on a bathroom scale, the spring inside the scale compresses 0.530 mm, and it tells you your weight is 632 N. Now if you jump on the scale from a height of 1.12 m, what does the scale read at its peak?

Answer 1

here,

the compression in the spring , x1 = 0.53 mm = 5.3 * 10^-4 m

W = 632 N

the mass , m = W /g = 64.42 kg

let the spring constant of the spring be K

equating the forces vertically

W = K * x1

632 = K * 5.3 * 10^-4

K = 1.19 * 10^6 N/m

height , h0 = 1.12 m

let the new compression be x2

using conservation of energy

0.5 * K * x2^2 = m * g * ( h + x2)

0.5 * 1.19 * 10^6 * x2^2 = 64.42 * 9.81 * ( 1.12 + x2)

solving for x2

x2 = 3.5 * 10^-2 m

the peak reading , R = W *(x2 /x1)

R = 632 * ( (3.5 * 10^-2) /(5.3 * 10^-4))

R = 4.17 * 10^4 N