A mass-spring system with recoil and friction

AI Thread Summary
The discussion centers on analyzing a mass-spring system where an object with mass m encounters a spring after traveling on a surface with kinetic friction. The key equations involve the conservation of energy, accounting for energy lost due to friction. The user attempts to derive the spring constant k in terms of the coefficient of friction mu, mass m, initial speed v, and gravitational acceleration g. They apply the work-energy theorem but initially arrive at an incorrect expression for k. The conversation emphasizes the importance of correctly incorporating frictional work into the energy balance to find the accurate spring constant.
Trojanof01
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An object of mass m is traveling on a horizontal surface. There is a coefficient of kinetic friction, mu , between the object and the surface. The object has speed v 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.


Find k, the spring constant.
Express k in terms of mu, m, v, and g .

Any ideas how on setting this up? KE1 + SPE1 = KE2 + SPE2 is where I'm headed...
 
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Your on the right track with conservation of energy, however, don't forget the energy dissapated due to friction.
 
This is what I've done so far

Work-energy theorem: E_f-E_i=W_fr:

0-(1/2)*m*v^2=- mu*m*g*2*x

x = .5v^2 / (2g(mu)) Max compression of spring

W=-mu*m*g*x

E_i=(1/2)*m*v^2 )

E_f=(1/2)*k*x^2

Work-energy theorem:

(1/2)*k*x^2-(1/2)*m*v^2=-mu*m*g*x

Plugged into x and solved for k and got 2m(mu)g...answer was incorrect. Any ideas?
 

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