To stimulate car accidens, auto manufactures study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulations with a car of mass 1000kg moving with a speed 18.0km/h on a smooth road and colliding with a horizontally mounted spring of spring constant `6.25 xx 10^(3)` N`m^(-1)`. What isthe maximum compression of the spring?

Explanation

At maximum compression `x_(m)`, the potentia energy V of the spring is equal to the kinetic energy K of the moving car from the principle of conservation of mechanical energy.
`K = UrArr (1)/(2) m u^(2)=(1)/(2) kx_(m)^(2)`
`rArr x_(m)= u sqrt((m)/(k)) rArr x_(m)= u sqrt((m)/(k))`
We obtain `x_(m)=2.00m`