91Ó°ÊÓ

• The compression is$0.080\text{m}$ .
• The vertical distance is 2 m.

The work done on a particle by a constant gravitational force is represented as a change in the gravitational potential energy which is given by,

${\mathit{U}}_{\mathbf{\text{grav}}}\mathbf{=}\mathit{m}\mathit{g}\mathit{y}$…â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦.(1)

Here, m is the mass of the object, g is the acceleration due to gravity, and y is height.

When the book is lifted up then the gravitational force will act on the book in the downward direction. So, it can be observed that the displacement and force are in opposite directions.

Therefore, the work done by the gravitational force is negative.

Here, when the book is lifted upwards then the work is done against gravity. It is known that the work done against the gravitational force always gets stored as potential energy.

Hence, the potential energy of the body increases.

This can also be observed from the equation for potential energy, which is given by equation (1).

So the potential energy will increase by 0.8mg.

The displacement and gravitational force on the can are in the downward direction. Since both displacement and force are acting in the same direction.

Therefore, the work done by the gravitational force will be positive.

Here, the work is done by the gravitational not against it. The gravitational force does work atthe expense of potential energy.

Therefore for the falling can, the potential energy decreases. This can also be observed from the equation for potential energy which is given by equation (1).

So, the gravitational potential energy will decrease by $2mg$.

Therefore, the gravitational potential energy will decrease.