Calculating Spring Compression from 1m Jump on Scale

[ace123]

If you stand on a bathroom scale, spring inside compresses .6mm, and tells your weight is 710 N. Now if you jump on the scale from a height of 1m, what does the read at it's peak?

This is what I tried to do:

I used Hooke's law: F$$_{}s$$= k*x
and solved for the k which is spring constant.

Then I wasn't too sure of how to find the spring compression when he jumps from a height of 1m. I tried to use conservation of mechanical energy:

I did the potential energy of the the guy at 1m and set it equal to the kinetic energy when he hits the scale.

I then set up another conservation of mechanical energy for the scale. Which was Kinetic energy equal to the compression 1/2kx^2.

This is wrong however and I have no clue what else to try.

Thanks for the help

 

[Hootenanny]

If you stand on a bathroom scale, spring inside compresses .6mm, and tells your weight is 710 N. Now if you jump on the scale from a height of 1m, what does the read at it's peak?

This is what I tried to do:

I used Hooke's law: F$$_{}s$$= k*x
and solved for the k which is spring constant.

Then I wasn't too sure of how to find the spring compression when he jumps from a height of 1m. I tried to use conservation of mechanical energy:

I did the potential energy of the the guy at 1m and set it equal to the kinetic energy when he hits the scale.

I then set up another conservation of mechanical energy for the scale. Which was Kinetic energy equal to the compression 1/2kx^2.

This is wrong however and I have no clue what else to try.

Thanks for the help

Your method seems correct to me, however there is no need for the intermediate step you can just jump straight to setting the gravitational potential energy equal to the potential energy stored in the spring.

Note however, that the question asks for the reading on the scale, not the compression of the spring.

 

[ace123]

I understand that so after I find the compression of the spring i should multiply it by the spring constant. Correct? I threw in the intermediate step because I wasn't sure if you could jump from the gravitational potential energy straight to the spring.

 

[ace123]

Prehaps I made a mathematical mistake. Let me check it again.

 

[Hootenanny]

I understand that so after I find the compression of the spring i should multiply it by the spring constant. Correct?

That is correct. In that case, it is most likely that you have made an arithmetic error; or if you are submitting your answer online your significant figures are out.

 

[ace123]

Well the answer in the book is 4.2*10^4. But I'm not getting that. Can you check my math when I post it? Thanks

 

[Hootenanny]

Well the answer in the book is 4.2*10^4. But I'm not getting that. Can you check my math when I post it? Thanks

No problem

 

[ace123]

Wow you will not believe what I did. I thought .6mm was .6*10^-5. Got it confused with micro. Sorry for bothering you.

 

[Hootenanny]

Wow you will not believe what I did. I thought .6mm was .6*10^-5. Got it confused with micro. Sorry for bothering you.

It usually is the small mistakes that trip you up! Don't worry about it.