A block of mas 2.0 kg is pulled up on a smooth incline of angle `30^0` with the horizontal. If the block moves wth an acceleration of `1.0 m/s^2`, find the power delivered by the pulling force at a time 4.0 s after the motion starts. What is the average power delivered during the 4.0 s after the motion starts?

Explanation

Here, the given plane is smooth. Therefore, there is no force of friction. Now,
`m=2kg,theta=30^(@), a=1m//s^(2),P=?`
Force F applied up the plane is such that from figure., `F-mg sin theta =ma`
`F=m(g sintheta +a)`
`=2(9.8 sin 30^(@) +1)`
`F=11.8N`
From `v=u+at`
`v=0+1xx4=4m//s`
`:.` Power delivered by the force at a time 4 second after the motion starts is
`P=Fxxv=11.8xx4=47.2 wat t`
Now, displacement in 4 second is
`s=ut+(1)/(2)at^(2)=0+(1)/(2)xx1xx4^(2)=8m`
work done `= Fxxs=11.8xx8=94.4J`
Average power delivered during 4 second after the motion starts
`P=(W)/(t)=(94.4)/(4)=23.6"watt"`