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

Let d be the distance travelled by block along the plane Height it comes down in downward direction, `h=d sin 30^(@).`
When block comes to rest, decreases in its PE will be stored in the spring.
`mgh1/2ky^(2)` (y is the compressin in t he spring)
Let d be the distance travelled by the block along the plane and height it comes in downward direction is `h=d sin30^(@)`
When block comes to rest, the decreases in its PE will be stored in the spring.
`thereforemgh=1/2ky^(2)` (y is compression in spring)
`mgd sin30=1/2ky^(2)`
`4xx10xxd/2=1/2xx100xx1^(2)`
`impliesd=2.5m`