Find Unknown Weight w/ Ideal Spring Problem

[Potatochip911]

Homework Statement

An ideal spring hangs next to a scale, when a 100N weight the scale reads 40, when a 200N weight is attached it reads 60. Using an unknown weight reads 30.

Homework Equations

F=-kx

The Attempt at a Solution

I attempted to find the value of k for the spring however when calculating k for the 100N it is 2.5N/m and for the 200N it is 3.3N/m which doesn't make sense to me since I would've thought k would be constant. I also tried using F/x=F/x but this also didn't work so I'm completely lost.

 

[haruspex]

Homework Statement

An ideal spring hangs next to a scale, when a 100N weight the scale reads 40, when a 200N weight is attached it reads 60. Using an unknown weight reads 30.

Homework Equations

F=-kx

The Attempt at a Solution

I attempted to find the value of k for the spring however when calculating k for the 100N it is 2.5N/m and for the 200N it is 3.3N/m which doesn't make sense to me since I would've thought k would be constant. I also tried using F/x=F/x but this also didn't work so I'm completely lost.

Hint: you are not told what the scale reads when no weight is attached.

 

[Potatochip911]

Hint: you are not told what the scale reads when no weight is attached.

Thanks! I solved for the constant weight that is being applied to the scale.
(100+c)/40=(200+c)/60
This gave c=100
Including this constant weight in the equations gave the correct scale reading of 50.
I'm assuming this is how you would solve it because it produced the correct answer although there might be a different way.

 

[haruspex]

Thanks! I solved for the constant weight that is being applied to the scale.
(100+c)/40=(200+c)/60
This gave c=100
Including this constant weight in the equations gave the correct scale reading of 50.
I'm assuming this is how you would solve it because it produced the correct answer although there might be a different way.

That's as good a way as any.