# How does water falling down a waterfall gain energy?

I'm kind of a noob in the physics area. But I know that energy cannot be created, it can only be transferred.

So how and what "type" of energy does water get when free-falling?

• The gravitational potential gets converted into kinetic energy, which is the "energy" you are talking about (neglecting air friction, else the waterfall's energy is not conserved - can you see why?).
– user28355
Feb 2, 2014 at 3:19

Since you say you are new to physics first of all let's state what energy is. It is defined as the physical quantity which measures the quantity of work a body can do. Work is the product of a force and a displacement along its direction. It can be thought as the "effort" you (in general the force) have to do to move an objet by pulling it.

In this case the type of energy the water gets when falling is kinetic energy, that is the energy that a body has due its motion. From motion comes a possibility to do work and this happens when the body slows down. As an example you can consider a bullet moving towards a can; when the bullet hits the can it slows down and the can starts to move, what happens is that the bullet decreases his velocity and thus loses kinetic energy while it does work on the can. Doing work on an object entails transferring energy to it.

As you correctly said energy cannot be created, so where does the kinetic energy of the water come from? There must be a force doing work on it and so transferring energy to it. This force is the gravitational force, i.e. the force that "pulls" all the objects towards the ground.

To see this as an energy transfer we can consider an energy that accounts for the possibility the gravitational force has to do work on an object. An object is said to have gravitational potential energy if the gravitational force can do work on it and depends on the mass of the object and height. So what happens during the fall of the water is the transformation of gravitational potential energy in kinetic energy.

To put this into formulas the kinetic energy is given by

$$E_k=\frac{1}{2}mv^2$$

and the gravitational potential energy is given by $$E_g=mgh$$ where m is the mass of the object (here the water), v is his velocity, h is hi height and g is the acceleration due to gravitational force.

While the water falls v increases and h decreases, so the kinetic energy increases and the gravitational potential energy decreases, and this happens in a way that the total energy is always the same. (If there is no friction).

• Wonderful answer! Physics is something I really want to learn and become good at in the future. Thank you. Feb 2, 2014 at 20:20

At the top of the waterfall, the water is higher in the gravitational field of the Earth and has gravitational potential energy. When it falls, the potential energy turns into kinetic energy. So energy is not created, it was there at the beginning, stored as potential energy.

Potential energy = $mgh$ (energy in joules, mass in kg, $g$ is $9.8 m/sec^2$, $h$ is in meters). A parcel of water in free fall or tumbling down substrate accelerates ($K.E. = (mv^2)/2$) until air resistance and frictional loss rates balance rate of potential to kinetic energy conversion. $mgh$ comes out as heat.

Technical aspects: Mass-energy is conserved via the homogeneity of time plus Noether's theorems coupling continuous symmetries to conserved currents (properties). As you are sitting in a gravitational potential well, time is not homogeneous (with altitude, re GPS atomic clock SR and GR corrections). Nobody imagines a way to practically, cyclically exploit the (perhaps possible but very tiny) loophole.