Work done a gravitational field
Work Done by a Gravitational Field
Gravitional Field:
“The or region around the earth in which it can exert its gravitional force on other bodies is called gravitional field”.
When an object is moved in the graviyional field, the work is done by the gravitional force.
• If displacement in the direction of the gravitional field, the work is positive.
• If displacement is against the gravitional force, the work is negative.
Explanation:
Consider an object of mass ‘m’ being displaced with constant velocity from point ‘A’ to ‘B’ along various paths in the presence of a gravitional force. In this case, the gravitional force is equal to the weight ‘mg’ of the object which always act vertically downwards towards the earth.
Work done along the path adb:
The work done by the gravitational force along the path ADB can be split into two parts.
(Work)ᴀᴅʙ = (Work)á´€→á´… + (Work)á´…→Ê™
= F.d + F .d
=(mg) (AD) Cos 90֯ +(mg)(DB) Cos180֯
= 0 + (mg) (h) (-1)
(Work)ᴀᴅʙ= -mgh
Work done along the path acb:
The work done by the gravitional force along the path ADB can be split into two parts.
Work)ᴀᴄʙ = (Work)á´€→á´„ + (Work)á´„→Ê™
= F.d +F . d
=(mg)(AC) Cos 180֯ + (mg)(CB) Cos 90֯
= (mg) (h)(-1) + 0
(Work)ᴀᴄʙ= -mgh
Work done along the path ab:
Calculate the work done along the path AB which is curved one,we divide it into a large number of horizontal and vertical steps as shown in the below fig.
There is no work done along the horizontal steps, because mg is parpendicular to the displacement for these steps. Work is done by the force of gravity only along the vertical steps.
“Work done in the earth’s gravitational field is independent of the path followed”.
Conservative field:
“ The field in which the work done is independent of the path followed or work done in a closed path be zero, is called a conservative field”.
Examples:
(1)Gravitional field
(2)magnatic field
(3)Electric field
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