Fundamental Forces: Spring Question

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SUMMARY

The discussion centers on the correct formulation of the spring force equation, specifically addressing the equation ma = -k1l - k2l. Participants clarify that both forces should be considered in the same direction when analyzing the spring's behavior at position l. The correct interpretation of the forces leads to the conclusion that the spring force is opposite to the displacement, as indicated by the equation F_x = -kx. The confusion arises from the sign convention used for the forces in relation to the defined positive direction.

PREREQUISITES
  • Understanding of Newton's Second Law (ma = F)
  • Familiarity with Hooke's Law (F = -kx)
  • Knowledge of vector direction and sign conventions in physics
  • Basic algebra for manipulating equations
NEXT STEPS
  • Review the principles of Hooke's Law and its applications in spring mechanics
  • Study the concept of force vectors and their directionality in physics
  • Explore the implications of sign conventions in mechanical systems
  • Practice solving problems involving multiple forces acting on a spring
USEFUL FOR

Physics students, mechanical engineers, and anyone studying dynamics and spring systems will benefit from this discussion.

JoeyBob
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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
 

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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?
 
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Delta2 said:
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??
 
On your picture which is the positive i hat direction? Is that the direction of the force when l is positive?
 
hutchphd said:
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?
 
So you have to define positive x (you have called it l) in that direction also. Going to the left is negative.
 
hutchphd said:
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?
 
No. The force from a spring is opposite from displacement. Hence the minus sign in ##F_x=-kx##.
 
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