# Contradicting conclusions on falling bodies.

rishch
I was recently thinking about potential energy and I came to two conclusions which contradict each other-

1)When a body is falling from a height, the force of gravity is acting on it in the downwards direction. There is displacement in the downwards direction. So as the force and the displacement are in the same direction, some amount of positive work is done on it.

2)When the same body is falling, the potential energy of the body is converted into kinetic energy and the total energy of the ball remains constant. So that means that no work is being done on it.

So in one case there is positive work while in the other no work. How? What's wrong in my reasoning.Please keep the answers as simple as possible because I'm still in secondary school, and won't be able to understand a highly complicated answer. So please keep it as simple as possible.

Gold Member
By the work-energy theorem, $$\frac {1}{2} mv_f^2 - \frac {1}{2} mv_i^2 = W,$$if kinetic energy has increased, then positive work must have been done.

Mentor
1)When a body is falling from a height, the force of gravity is acting on it in the downwards direction. There is displacement in the downwards direction. So as the force and the displacement are in the same direction, some amount of positive work is done on it.
Sure. So the kinetic energy increases. (Note that we do not use the concept of gravitational PE here.)

2)When the same body is falling, the potential energy of the body is converted into kinetic energy and the total energy of the ball remains constant. So that means that no work is being done on it.
Here we account for the effect of gravity and the work it does by using the concept of gravitational PE.

Using the concept of gravitational PE already includes the effect of gravity, so by counting both the work done by gravity and gravitational PE you end up counting it twice.

Work done by all forces (including gravity) = ΔKE

Work done by all forces (except gravity) = ΔKE + ΔPE

rishch
So you're saying that we cannot include the work done by the force of gravity because this work is already included in the potential energy? And for the last sentence where you say "except gravity" that means you are using the concept of PE here?

Mentor
So you're saying that we cannot include the work done by the force of gravity because this work is already included in the potential energy? And for the last sentence where you say "except gravity" that means you are using the concept of PE here?
Right.

Another way to think of it is this:

Work done by all forces (except gravity) + Work done by gravity = ΔKE
Work done by all forces (except gravity) - mgΔh = ΔKE
Work done by all forces (except gravity) = ΔKE + mgΔh