A Rough inclined plane with inclination `30^(@)` with the horizontal has a block of 1 kg being pushed up the plane by a force of 10 N acting parallel to the plane. If the coefficient of friction between the block and the plane is 0.1 and block is pushed through a distance of 10 m along then incline. What are the increases in the (1) potential energy and (ii) kinetic energy of the block ? 

Options

A. 50 J: 41.3J
B. 40 J: 31.6 J
C. 100 J, 81.8 J
D. 25 J, 20.7 J.

Answer

a

Explanation

Here let `DeltaU` to be the change is P.E. then
`DeltaU=mgh`
=`1xx10xx5`
=50 J …(i)
(`because(h)/(10)=sin 30^(@)` and h=5m)
COD
Also cceleration along the plane
`a=("Force")/("mass")=([F-mg sin theta+mu mg cos theta])/(m)`
=`([10-(10xx1/2+0.1xx10xx(sqrt3)/(2))])/(1)`
=`[10-(5+0.5xx1.732)]`
=`10-5.87=4.13 ms^(-2)`
Applying `v^2-u^2=2 a S`
We have `1/2mv^2-1/2mv^2=m a s`
`:. DeltaE_k=m a s`
=`1xx4.13xx10=41.3 J` ...(ii)