Consider a 2.0 kg mass on a spring on a horizontal surface. The spring has sprin

ID: 2290597 • Letter: C

Question

Consider a 2.0 kg mass on a spring on a horizontal surface. The spring has spring constant

36 N/m. The static coefficient of friction between the mass and the surface, ?S, is not known, and

the kinetic coefficient of friction is ?K = 0.20. The spring is stretched to 20 cm beyond its

equilibrium position.

(a) If the mass is initially at rest and does not move, what is the minimum value for ?S?

(b) If the mass is given a short push so that its initial velocity is 1.0 m/s to the left, use energy

considerations to determine where the mass first comes to a stop.

Hooke's law

F=k*x

Fr=Ms*N=Ms*m*g

Ms*m*g=K*x

Ms=(K*x)/(m*g)

Ms=(36N/m*0.2m)/(2Kg*9.8m/s^2)

Ms=0.36

Wfr=Mk*N*Xf=Mk*m*g*Xf

Uf=Ui-Wfr

1/2K.(X-Xf)^2=1/2m*Vi^2+1/2K.(X)^2- Mk*N*Xf

18(0.2-xf)^2=1+0.72+3.92Xf

18Xf^2+3.28Xf-1=0

Xf= 0.16159

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