To simulate car accidents, auto manufactrers study the collisions of moving cars with mounted springs of differnet spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant `6.25xx10^(3)N m^(-1)`. What is the maximum compression of the spring ?

Explanation

At maximum compression the kinetic energy of the car is converted entirely into the potential energy of the spring.
The kinetic energy of the moving car is
`K = (1)/(2) mv^(2) = (1)/(2) xx 10^(3) xx 5 xx 5`
`K = 1.25 xx 10^(4) J`
Where we have converted `18 km h^(-1) t o 5ms^(-1)` [It is useful to remember that `36 kmh^(-1) = 10 ms^(-1)` ]. At maximum compression `x_(m) `, the potential energy V of the spring is equal to the kinetic energy K of the moving car from the principle of conservation of mechanical energy
`V = (1)/(2) K x_(m)^(2) = 1.25 xx 10^(4) J`
We obtain `x_(m) = 2.00` m