Consider with a car of mass 1000 kg moving with a speed 18.0 km/h on a road and colliding 6.25 xx 10^(3) Nm^(-1). Taking the coeffici-ent of friction, mu to be 0.5 what is the maximum compression of the spring?

Consider with a car of mass 1000 kg moving with a speed 18.0 km/h on a

1.	Consider with a car of mass 1000 kg moving with a speed 18.0 km/h on a road and colliding 6.25 xx 10^(3) Nm^(-1). Taking the coeffici-ent of friction, mu to be 0.5 what is the maximum compression of the spring?
Answer» Solution :In presence of friction, both the spring force and the frictional force act so as to oppose the compression of the spring. We invoke the WORK - energy theorem, rather than the conservation of mechanical energy. The CHANGE in kinetic energy is `DeltaK=K_(f)=0-(1)/(2)m u^(2)` The work done by the net force is `W=-(1)/(2)kx_(m)^(2)-mumgx_(m)` Equating we have `(1)/(2)mu^(2)=(1)/(2)kx_(m)^(2)+mumgx_(m)` Now `mu MG=0.5xx10^(3)xx10=5xx10^(3)N` `("taking g" = 10.0s^(2))`. After rearranging the above equation we obtain the following quadratic equation in the unknown `x_(m)`. `kx_(m)^(2)+2mu mgx+_(m)-m u^(2)=0` `x_(m)=(-mu mg+[mu^(2)m^(2)g^(2)+mku^(2)]^(1//2))/(k)` Where we take positive square root since `x_(m)` is positive. Putting in numerical values we obtainthe following quadratic equation in the unknown `x_(m) = 1.35m.`