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Suppose there is a sprig of spring constant k and a box of mass m attached to it.This system is placed on a horizontal smooth plane.Suppose a constant force F is applied on the box so that spring contract. Let the mass is displaced by a distance x.I have to find this x(maximum displacement)Since work done by F is stored as potential energy of box,Fx=1\2kx^2x=f/2kNow I`ll try to find this by different approach.When box is displaced, it will stop n will be in equilibrium.So applied force will be equal to restoring forcei.e F=kxx=F/kWhy this is different from first solution?Where am I going wrong?

Suppose there is a sprig of spring constant k and a box of mass m attached to it.This system is placed on a horizontal smooth plane.Suppose a constant force F is applied on the box so that spring contract. Let the mass is displaced by a distance x.I have to find this x(maximum displacement)Since work done by F is stored as potential energy of box,Fx=1\2kx^2x=f/2kNow I`ll try to find this by different approach.When box is displaced, it will stop n will be in equilibrium.So applied force will be equal to restoring forcei.e F=kxx=F/kWhy this is different from first solution?Where am I going wrong?

Grade:12

3 Answers

Vikas TU
14149 Points
7 years ago
It is so because the Force U wrote as F =kx is the spring force due to F is the restoring firce at any displacement x which we could not sure that it would be maximum compression in the spring.
The answet that came from conservation of energy gives u the compression x as maximum value as it is clear that all the work done due to force F would be stored to the elastic potential energy. 
Awasthî Shußham
23 Points
7 years ago
So the point where the two forces are equal n opposite, need not to be the point of maximum displacement?
Awasthî Shußham
23 Points
7 years ago
If we are applying force in such a way that its not converting into kinetic energy then the object will stop (at max displacement) when both(restoring n applied) forces are equal. (As I think)

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