A body of mass 100 kg is lifted to a height 10 m from the ground in two different ways as shown in the figure. What is the work done by the gravity in both the cases? Why is it easier to take the object through a ramp?

Explanation

m = 100 kg, h = 10 m
Along path (1): The minimum force `F_(1)` required to move the object to the height of 10 m should be equal to the gravitational force,
`F_(1)=mg=100 times 10=1000N`
`" "` The The distance moved along path (1) is, h = 10 m
`" "` The work done on the object along path (1) is
`" "W = F h = 1000 times 10=10,000J`
Along path (2):
In the case of ramp, the minimum force `F_(2)` that we apply on the object to take it up is not equal to mg, it is rather equal to `mgsintheta.(mgsintheta lt mg)`.
`" "`Here, angle `theta=30^(@)`
`" "`Therefore, `F_(2)=mg sintheta=100 times 10 times sin30^(@)=100 times 10 times 0.5 =500N`
`" Hence", (mgsintheta lt mg)`
`" "` The path covered along the ramp is,
`l=h/(sin30)=10/(0.5)=20m`
`" "`The work done on the object along path (2) is, `W=F_(2)l=500 times 20=10,000J`
`" "`Since the gravitational force is a conservative force, the work done by gravity on the object is independent of the path taken.
`" "`In both the paths the work done by the gravitational force is 10,000 J
Along path (1): more face needs to be applied against gravity to cover lesser distance.
Along path (2): lesser force needs to be applied against the gravity to cover more distance.
`" "`As the force needs to be applied along the ramp is less, it is easier to move the object along the ramp.