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 in watt during the 4.0 s after the motion starts?

Answer

24

Explanation

The forces acting on the block are shown in ure. Resolving the forces parallel to the incline, we get
`F-mg sintheta=ma`
`or, F=mgsintheta+ma`
`=(2.0)(9.8 m/s^2)(1/2)+1.0m/s^2]=11.8N`

The velocity at t=4.0 s is
`v=at=(1.0 m/s^2)(4.0s)=4.0m/s`
The power delivered by the force at t=4.0s is
`P=vecF.vecv=(11.8N)(4.0m/s)~~47W`
The displacement during the first four seconds is
`x=1/2at^2=1/2(1.0m/s^2)(16s^2)=8.0m`
The work done in these four seconds is therefore
`W=vecF.vecd=(11.8N)(8.0m)=9.44J`
The average power delivered `=(94.4J)/(4.0s)`
`=23.6W~~24W`