Answer:
The sign of the work done by gravity on a block moving up an inclined plane as the block comes to a rest on the inclined plane is **negative**.
Explanation:
Work is given mathematically as (Force).(displacement) = /F/ /d/ cos θ
where /F/ = magnitude of the force
/d/ = d = magnitude of displacement that the force moves through
θ = angle between the force and the displacement
For gravity Force,
Whenever the angle between the force and the displacement is in the range of 0° and 90°, the workdone is positive.
And whenever the angle between the force and the displacement is in the range of 90°+ to 180°. The workdone is negative.
Better explained,
For gravity, the force of gravity acts in the negative y direction, so, force of gravity is always equal to (-mg î).
If an object is falling downwards, then its displacement is in the negative y direction too; - dî.
Work done by gravity on a falling object = (-mgî).(-dî) = + mg d = mgd cos 0° = + mgd (θ = 0°) in this case
Positive work!
And for an object rising upwards, the force of gravity is still in the negative y direction too and is equal to (-mgî). But the displacement is in the positive y direction; that is, +dî
Work done by gravity on a body moving upwards = (-mgî).(dî) = - mgd = mgd cos 180° = - mgd (θ = 180°)
Negative work done!
So, for a body moving up an inclined plane, the vertical displacement is still upwards and in the positive y-direction. So, the analogy of the 2nd gravity explanation works for it.
