If you stand on a bathroom scale, the spring inside the scale compresses 0.490 m

Question

If you stand on a bathroom scale, the spring inside the scale compresses 0.490 mm, and it tells you your weight is 610 N. Now if you jump on the scale from a height of 1.10 m, what does the scale read at its peak?

Please I tried everything and I can't get it right...

I got 45.24 N which is not the right answer... Please help me with this to get the points, if the answer is wrong or if you just copy and paste a solution with different numbers I will not reward the points to you. Solve this problem with this values please.

I will rate it immdiatelly, thank you.

Explanation / Answer

when the spring is compressed by 0.49 mm

force in the spring will be Kx = k*(0.49 * 10^-3) = mg = W = 610 N

therefore from this we can calculate k = 1244.89 * 10^3 N/m

when he jumps from a height of 1.1m ..

the velocity V of the person just before coming in contact with the scale is calculated as follows :

V^2 = 2*g*s = 2*9.81*1.1

therefore V = 4.64 m/s

therefore now the spring will be compressed till the person comes to rest .

at this point the value will be at its peak

the compression X can be calculated as follows :

1/2 K X^2 = 1/2(m)V^2

m = 610 / g as the original weight is found out to be 610

therefore X = 1.075 mm

therefore KX = the new weight of the person which is (1244.89 * 10^3)(1.075 * 10^-3) = 1338.74 N

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