To simulate car accidents , auto manufactures 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 roadand colliding with a horizontally mounted spring of spring constant 6.25 xx10^(3) Nm^(-1) .What is the maximum compression of the spring ?

To simulate car accidents , auto manufactures study the collisions of

1.	To simulate car accidents , auto manufactures 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 roadand colliding with a horizontally mounted spring of spring constant 6.25 xx10^(3) Nm^(-1) .What is the maximum compression of the spring ?
Answer» Solution :At maximum compressionthe kinetic energy of the car is converted entirelyinto the potentialenergy of the spring. The kinetic energy of the moving car is , `K = 1/2 mv^(2)` `=1/2 xx10^(3)xx(5)^(2)` ` = 1.25 xx10^(4)J` `V = 18 "kmh"^(-1)` ` = (18 xx1000)/(3600)` ` = 5 ms^(-1)` From the law of the conservation of MECHANICAL energy potential energy of spring = kineticenergy of moving car `V = 1/2 kx_(m)^(2)` Where k = spring CONSTANT , `x_(m) ` = maximum COMPRESSION ` 1.25 xx10^(4) =1/2 xx6.25 xx10^(3) xxx_(m)^(2)` ` =(2xx1.25 xx10^(4))/(6.25 xx10^(3)) =x_(m)^(2)` ` :. x_(m) = sqrt((2.5xx10^(4))/(6.25xx10^(3))` ` sqrt(4)` ` :. x_(m) = 2m ` ` :. ` Since spring will be compressed by 2 m .