Consider Example 22. Takin the coefficient of friction, mu to be 0.5, calculate the maximum compression of the spring.

Consider Example 22. Takin the coefficient of friction, mu to be 0.5,

1.	Consider Example 22. Takin the coefficient of friction, mu to be 0.5, calculate the maximum compression of the spring.
Answer» Solution :In the PRESENCE of friction, boththe SPRING force and the frictional force f act so as to oppose the COMPRESSION of the spring. WORK done by the two forces `W=-(1)/(2)kx_(m)^(2)-f(x_(m))` `W=-(1)/(2)kx_(m)^(2)-mumg(x_(m))` `( :' f=muR=mumg)` and change in K.E. `DeltaK=K_(f)-K_(i)=0-(1)/(2)mv^(2)` Applying work energy theorem, `DeltaK=W` `:. -(1)/(2)mv^(2)=-(1)/(2)kx_(m)^(2)-mumg(x_m)` `:.kx_(m)^(2)+2mumg(x_(m))-mv^(2)=0` It is a quadratic equation in `x_(m)` `:. x_(m)=(-2mumg+[4mu^(2)m^(2)g^(2)+4mkv^(2)]^(1//2))/(2K)` Putting the numerical values and solving, we get `_(m)=1.35m`