Important Cases of Work

by • 04/07/2012 • GeneralComments (0)533

Important Cases of Work

Work can be positive or negative depending upon the angle θ between F and d.


Case I

When θ = 0º i.e., when F and d have same direction.

W = F . d

W = F d cos 0º ………….. {since θ = 0º}

W = F d …………………….. {since cos 0º = 1}

Work is positive in this case.
Case II

When θ = 180º i.e., when F and d have opposite direction.
W = F . d

W = F d cos 180º ………………………. {since θ = 180º}

W = – F d ………………………………….. {since cos 180º = -1}

Work is negative in this case
Case III

When θ = 90º i.e, when F and d are mutually perpendicular.

W = F . d

W = F d cos 90º ………………………. {since θ = 90º}

W = 0 ……………………………………. {since cos 90º = 0}
Work Done Against Gravitational Force

Consider a body of mass ‘m’ placed initially at a height h(i), from the surface of the earth. We displaces it to a height h(f) from the surface of the earth. Here work is done on the body of mass ‘m’ by displacing it to a height ‘h’ against the gravitational force.

W = F . d = F d cos θ

Here,

F = W = m g

d = h(r) – h(i) = h

θ = 180º

{since mg and h are in opposite direction}

Since,

W = m g h cos 180º

W = m g h (-1)

W = – m g h

Since this work is done against gravitational force, therefore, it is stored in the body as its potential energy (F.E)

Therefore,

P . E = m g h

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