Question

To stimulat car accidents, the auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000kg moving with a speed of `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?

Answer 1

Here, `m=1000kg`,
`v=18.0km//h=5m//s, k=6.25xx10^(3)Nm^(-1), `
`x_(m)=?`
At maximum compression of the spring, the K.E. of the car s converted entirely into P.E. of the spring i.e.,
`(1)/(2)mv^(2)=(1)/(2)kx_(m)^(2)`
`x_(m)=sqrt((m)/(k))xxv=sqrt((1000)/(6.25xx10^(3)))xx5`
`=0.4xx5=2.00m`