Question

The gravitational potential difference between the surface of a planet and a point `20m` above is `16J/kg`. The work done in moving a `2kg` mass by `8m` on a slope of `60^@` from the horizontal is ??

Answer 1

It required 11 J.

Explanation:

First a tip on formatting. If you put parentheses, or quotes, around kg, it will not separate the k from the g. So you get `16 J/(kg)`.

Let's first simplify the relationship between gravitational potential and elevation. Gravitational potential energy is mgh. So it is linearly related to elevation.

`(16 J/(kg))/(20 m) = 0.8 (J/(kg))/m`
So after we calculate the elevation that ramp gives us, we can multiply that elevation by the above `0.8 (J/(kg))/m` and by 2 kg.

Pushing that mass 8 m up that slope gives it an elevation of
`h = 8 m*sin60^@ = 6.9 m` of elevation.

By the principle of conservation of energy, the gain of gravitational potential energy is equal to the work done moving the mass up there. Note: nothing is said about friction, so we have to pretend it does not exist.

Therefore the work required is

`0.8 (J/(kg))/m * 6.9 m * 2 kg = 11.1 J ~= 11 J`