A block of mass 4 kg is released from the top of an inclined smooth surface as shown in figure If spring constant of spring is `100N//m` and block comes to rest after compressing spring by 1 m, find the distance travelled by the block before it comes t o rest.

Explanation

Hint : Let d be the distance travelled by block along the plane. Height it comes down in downward direction, `h=dsin 30^(@)`.
When block comes to rest, decrease in its PE will be stored in the spring .
`mgh=(1)/(2)ky^(2)` (y is the compression in the spring)
Let d be the distance travelled by the block along the plane and height it comes in downward direction is `h=d sin 30^(@)`
When block comes to rest, the decrease in its PE will be stored in the spring.
`therefore " "mgh=(1)/(2)ky^(2)" (y is compression in spring)"`
`mgd sin 30=(1)/(2)ky^(2)`
`4xx10xx(d)/(2)=(1)/(2)xx100x1^(2)`
`rArr" "d=2.5m`