a. A `2-kg` situated on a smooth fixed incline is connected to a spring of negligible mass, with spring constant `k=100Nm^-1`, via a frictionless pulley. The block is released from rest when the spring is unstretched. How far does the block moves down the incline before coming (momentarily) to rest? What is its acceleration at its lower point?

b. The experiment is repeated on a rough incline. If the block is observed to move `0.20m` down along the incline before it comes to instantaneous rest, calculate the coefficient of kinetic friction.

Answer

a. `24m`; `6ms^-2`, b. `1/8`

Explanation

(a) At the extreme position blocks stops.
Applying work-energy theorem, we get
`mg sin 37^@=1/2ks^2`
`2xx10xxsxx3/5=1/2xx100xxs^2`
On solving `s=0.24m`
Acceleration at its lowest point, `a=(ks-mg sin 37^@)/(m)`
`=(100xx0.24-2xx10xx3/5)/(2)=6ms^-2`
(b) `W_g+W_(f riction)+W_(spri ng)=DeltaKE`
`mg sin 37^@+mumgcos37^@xxs=1/2ks^2`
`mgsin37^@-1/2ks=mumgcos 37^@`
`2xx10xx3/5-1/2xx100xxs=muxx2xx10xx4/5`
Gives `s=0.020m`
`mu=(12-50s)/(16)impliesmu=1/8`