A Question about Hooke's Law...

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  • Thread starter Kaneki123
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Okay...Hook's Law is stated as ''the force (F) needed to extend or compress a spring by some distance X is proportional to that distance. That is: F = kX (Wikipedia)'' And further on this topic there is a statement that
''Hooke's law for a spring is often stated under the convention that F is the restoring (reaction) force exerted by the spring on whatever is pulling its free end''...
My question is that, Is the force F the force which we apply continuosly for some time to extend the spring upto some distance X, or is it the force needed to ''hold'' the stretched spring at the distance X (the former force will obviously be greater than the second)??? If it is the first force than should'nt it be the second one???
 

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  • #2
sophiecentaur
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the former force will obviously be greater
hmmm. What is your argument to justify that statement? Do you just mean that it would be necessary to accelerate the mass of the spring by a finite amount`?
 
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sophiecentaur
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Is the force F the force which we apply continuosly for some time to extend the spring upto some distance X,
If you apply a constant force, starting from zero extension, you will end up with an oscillation around the equilibrium position. (If the spring has finite mass).
 
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  • #4
Chandra Prayaga
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If you want to state Hooke's law in terms of a force that YOU apply, then the force necessary to KEEP the spring compressed (or extended) by a distance x is proportional to x. Obviously then, if you extend it more, you will need to apply a larger force to keep it extended by that amount.
Of course, nothing prevents you from exerting whatever force you want. As sophiecentaur said, you could just apply a constant force, for example, by hanging a mass from a vertically suspended spring. In which case, the mass will oscillate about the equilibrium position.
You could also apply a force varying sinusoidally with time, and force the spring to oscillate at the same frequency as the applied force.
In all cases, the RESTORING force exerted by the spring will be proportional to the extension or compression, provided the amplitude of oscillations is small.
 
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My question is that, Is the force F the force which we apply continuosly for some time to extend the spring upto some distance X, or is it the force needed to ''hold'' the stretched spring at the distance X (the former force will obviously be greater than the second)??? If it is the first force than should'nt it be the second one???
The force is only dependent on the current position, not the change in position. For each value of x, the law applies. The final value, X, will need a force of kX to prevent it from moving. Any force greater than kX will stretch the spring past X. Similarly, for any value of x<X, a force of kX will accelerate the mass to X.
 

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