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Auto manufactures study the collisions of moving cars with mounted springs of different spring constants. Consider a car of mass 1500 kg moving with a speed of 36 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant `7.5xx10^(3)N m^(-1)` Find the maximum compression of hte spring.

Text Solution

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At maximum compression, K.E. of car gets converted completely into PE of the spring.
`"KE of car "=K=(1)/(2)mv^(2)=(1)/(2)xx1500xx10xx10" "(v=36xx(5)/(18)=10m//s)`
`"At maximum compression "x_(m), "PE, V of the spring = KE, K of car"`
`V=(1)/(2)kx_(m)^(2)=7.5xx10^(4)J`
`x_(m)=sqrt((2xx7.5xx10^(4))/(7.5xx10^(3)))=4.47m`
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