Respuesta :
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.
The effort done is negative because the angle between both the component of gravitation and displacement is 180 degrees.
Gravitation and displacement:
If the inclination is 0 degrees, which means the force is parallel to the motion, the force exerts positive work on the item. If the inclination is 180 degrees, the force is acting in the reverse direction as the motion, doing negative work on the item.
Negative is the correct answer to the following question.
Find out more information about 'inclination'.
https://brainly.com/question/6104900?referrer=searchResults
