Consider a simulation with a car of mass 1000kg moving with a speed 18.0 km/h on a road and colliding with a horizontally mounted spring of spring constant 6.25 xx 10^(3)N m^(-1). Taking the coefficient of friction, mu to be 0.5 What si the maximum compression of the spring?

Consider a simulation with a car of mass 1000kg moving with a speed 18

1.	Consider a simulation with a car of mass 1000kg moving with a speed 18.0 km/h on a road and colliding with a horizontally mounted spring of spring constant 6.25 xx 10^(3)N m^(-1). Taking the coefficient of friction, mu to be 0.5 What si 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 teh net force is `W= -(1)/(2) kx_(m)^(2)- mu mgx_(m)` Equating we have `(1)/(2) m u^(2) = (1)/(2) kx_(m)^(2)- mu mgx_(m)` Now `mu mg = 0.5 xx 10^(3) xx 10= 5 xx 10^(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 mgx_(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`