Question

A 2 kilogram object falls a distance of 5 meters. How much potential energy does this object have before it falls? How much work is done on it by gravity as it falls

Answer 1

1) Potential energy before the fall: 98 J

The gravitational potential energy of an object is given by:

$U=mgh$

where m is the mass of the object, g is the gravitational acceleration and h the heigth of the object above the ground.

In this problem, m = 2 kg, g = 9.8 m/s^2 and h = 5 m: substituting into the equation, we find

$U=(2 kg)(9.8 m/s^2)(5 m)=98 J$

2) Work done by gravity: 98 J

The work done by a force is given by:

$W=Fd cos \theta$

where

F is the magnitude of the force

d is the displacement of the object

$\theta$ is the angle between the direction of the force and the displacement

In this problem:

$F=mg=(2 kg)(9.8 m/s^2)=19.6 N$

d = 5 m

$\theta=0^{\circ}$

Therefore,

$W=(19.6 N)(5 m)(cos 0^{\circ})=98 J$