Fundamental Forces: Spring Question

[JoeyBob]

Homework Statement

See attached

Relevant Equations

F=lk

ma=-k2l+k1l

(ma-k1l)/l=-k

(-65.12-35.7)/0.51=-k

k=197.69, but answer should be 57.7

 

[Delta2]

Sorry i had some wrong posts here which i deleted... Your mistake is in first line, you take one force as positive and the other as negative. Aren't both forces towards the same direction at position l?

 

[JoeyBob]

Sorry i had some wrong posts here which i deleted... Your mistake is in first line, you take one force as positive and the other as negative. Aren't both forces towards the same direction at position l?

Okay I found out how to do it but am a bit confused. To get the right answer it needs to be

(-ma-lk)/l

This would mean the equation is ma=-k1l-k2l

But doesn't this imply the forces are in the negative i hat direction when they should be in the positive direction??

 

[hutchphd]

On your picture which is the positive i hat direction? Is that the direction of the force when l is positive?

 

[JoeyBob]

On your picture which is the positive i hat direction? Is that the direction of the force when l is positive?

It would be to the right, no?

 

[hutchphd]

So you have to define positive x (you have called it l) in that direction also. Going to the left is negative.

 

[JoeyBob]

So you have to define positive x (you have called it l) in that direction also. Going to the left is negative.

Isnt the change in length an absolute value though when calculating the force?

 

[hutchphd]

No. The force from a spring is opposite from displacement. Hence the minus sign in $F_x=-kx$.