A block of mass `5.7kg` slides on a horizontal frictionless table with a constant speed of `1.2ms^(-1)`. It is brougth momentarily to rest by compressing a spring in its path. By what maximum distance is the spring compressed ? The spring constant `k=1500Nm^(-1).`

Explanation

Here, `m=5.7kg, u=1.2ms^(-1)`
`v=0, x=?, k=1500Nm^(-1)`
When the spring is compressed through a distance x, and block comes momentarily to rest, entire K.E. of block is converted into P.E. of spring `(=(1)/(2)kx^(2))`
`:. (1)/(2)mv^(2)-(1)/(2)m u^(2)=(1)/(2)kx^(2)`
`(1)/(2)mv^(2)-0=(1)/(2)kx^(2)`
`x=sqrt((m)/(k))v`
`x=sqrt((5.7)/(1500))xx1.2`
`=7.4xx10^(-2)m=7.4cm`