The question is An object of mass m is traveling on a horizontal surface. There is a coefficient of kinetic friction u between the object and the surface. The object has speed when it reaches x = 0 and encounters a spring. The object compresses the spring, stops, and then recoils and travels in the opposite direction. When the object reaches x = 0 on its return trip, it stops.(adsbygoogle = window.adsbygoogle || []).push({});

The question then asks me to find the spring constant k.

The answer to the problem has to be in terms of the following symbols:

u = coefficient of kinetic friction

m = mass of block

g = acceleration due to gravity

v = initial velocity of the block

I used conservation of energy

E(final) = E(initial) + W(nonconservative forces)

E(final) = 0 because the block is at rest (i think)

E(initial) if trying to find k could probably only be found if E(initial) = 1/2*k*x^2 right?

and then the W(nonconservative forces) = -m*g*u*x

then in order to find x I'd have to find how far the block would go with initial velocity v along the surface with u being the friction. So I'd get x = (v^2)/(2*u*g).

And then plugging everything back in and solving for k i get:

(4*g^2*m*u^2)/(v^2)

I figured that'd be the answer but when I put it into the online answer it says that its off by a multiplicative factor. Where did I go wrong?

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# Spring + Friction system equation

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