How Much Does the Spring Compress When a Man Jumps on a Scale?

[emilytm]

Homework Statement

As a 75.0 kg man steps onto a scale, the spring inside the scale compresses by 0.65 mm. Excited to see that he has lost 2.5 kg since his last weighing, he jumps 0.3 m straight up into the air and lands directly on the scale.
What is the spring’s maximum compression?
What reading, in kilograms, does the scale give when the spring is at its maximum compression?

Homework Equations

U_s=½k(Δl)²

The Attempt at a Solution

I used U_s=½k(Δl)² to find the spring constant, which I found to be 104.1N/m. Next, I found his total energy while he was jumping in the are, which was all in the form of gravitational potential energy. That was (9.8)(75kg)(.3m)=220.5J. That would also be equal to the kinetic energy of the man right before he makes contact with the scale after he jumps. I am not sure what to do next. Do I use the equation for elastic potential again to find the compression of the spring? I guess I don’t really know what maximum compression means. Thanks!

 

[haruspex]

I used Us=½k(Δl)2 to find the spring constant,

You did? But you you are not given initial energy, you are given a mass. You can do it with that equation but it seems a bit of a long way around. How about F=kx?

104.1N/m.

kN/m?

Do I use the equation for elastic potential

Yes, but be careful...

equal to the kinetic energy of the man right before he makes contact with the scale after he jumps.

Ok, but bear in mind that gravity does not switch off at that point.