Figure shows a spring fixed at the bottom end of an incline of inclination `37^0`. A small block of mass 2 kg starts slipping down the incline from a point 4.8 m away from the spring. The block compresses the spring by 20 cm, stops momentarily and then rebounds through a distance of 1 m up the incline. Find a. the frictioin coefficient between the plane and the block and b. the spring constant of the spring. Take `g=10 m/s^2`.

Explanation

Between (1) and (2)
`mg(5sin37^@)=(1)/(2)k(0.2)^2+mumgcos37^@(5)` .(i)
between (2) and (3)
`(1)/(2)k(0.2)^2=mg(1sin37^@)+mumgcos37^@` (1) .(ii)
Adding (i) and (ii) we get
`4mgsin37^@=6mumgcos37^@`
`impliesmu=(2)/(3)tan37^@=(2)/(3)xx(3)/(4)=0.5`
Putting `m=2kg`,`mu=0.5` in (ii)
`(1)/(2)k(0.2)^2=2xx10xx(3)/(5)+(1)/(2)xx2xx10xx(4)/(5)`
`0.02k=12+8=20impliesk=1000(N)/(m)`
`mu=(1)/(2)`,`k=1000(N)/(m)`