Consider a simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a road and colliding with a horizontally mounted spring of spring constant 6.25xx10^(3)Nm^(-1). Taking the coefficient of friction, mu to be 0.5 What is the maximum compression of the spring ?

Consider a simulation with a car of mass 1000 kg moving with a speed 1

1.	Consider a simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a road and colliding with a horizontally mounted spring of spring constant 6.25xx10^(3)Nm^(-1). Taking the coefficient 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 chenge in kinetic energy is `Delta K = K_(f)-K_(i)=0-(1)/(2) m u^(2)` The work done by the net force is `W=-(1)/(2)kx_(m)^(2)-mu mg x_(m)` Equating we having `(1)/(2)m u^(2)=(1)/(2)kx_(m)^(2)+mu mg x_(m)` Now `mu mg = 0.5xx10^(3)xx10=5xx0^(3)N` (taking `G = 10.0 ms^(-2)`). After rearranging the above EQUATION we obtain the following quadratic equation in the unknown `x_(m)`. `kx_(m)^(2)+2mu m g x_(m)-m u^(2)=0` `x_(m)=(-mu mg +[mu^(2)m^(2)g^(2)+mku^(2)]^(1/2))/(k)` where we take the positive square root since `x_(m)` is positive. Putting in numerical VALUES we obtainthe following quadratic equation in the unknown `x_(m)=1.35m`.