To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different 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) Nm^(-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)xx10^(3)xx5xx5`
`K= 1.25xx10^(4) J`
where we have converted `18 kmh^(-1)" to "5ms^(-1)`[ It is useful to remember that `36kmh^(-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)kx_(m)^(2)`
`=1.25 xx 10^(4) J`
We obtain `x_(m)= 2.00 m`
We note that we have idealised the situation. The spring is considered to be massless. The surface has been considered to possess negligible friction.