# Pull-ups in water

I realized a couple days ago that I honestly did not learn in school why it is easier to do pull-ups in water than out of it. The only answers that I found are "because you're in water so there is less gravity". That answer does not suffice at all.

• Why did this get downvoted? It's a basic question but a perfectly reasonable one. – John Rennie Jul 17 '15 at 6:00

To expand on @CoilKid's answer, the buoyant force that makes it easier to do pullups in water is due to the pressure gradient in water. In simple terms, the pressure in water increases as you go down, because as you go down, there is more water above being pulled down by gravity. This pressure gradient is also why it hurts your ears if you swim down to the bottom of the pool without equilibrating the pressure in your ears as you descend.

The fact that the pressure steadily increases with depth means that the water pushing on your lower body exerts more force than the water pushing on your upper body. On balance, this means there is more force from the water pressure pushing up than down - this overall force that results is known as the "buoyant force".

If you were on the space station where there the effect of gravity is negligible, water would form giant globs floating around or sticking to surfaces, and doing a pullup with half your body inside such a glob of water would not help; without the effect of gravity, the water glob has the same pressure throughout, so on balance the force on you from the water pressure is zero; no buoyant force.

Interestingly, such a pressure gradient also exists in the air, and as such the air exerts a buoyant force on you as well, but since the density of air is so much less than that of water, the pressure changes much more gradually with height, so the buoyant force on you from the air is far smaller.

It's because unlike in air, the density of a human is less than the the density of the fluid around it. This causes you to float a bit, or be buoyant.

When there is a large difference in buoyancy, you will float on the surface of the fluid. This is why big aircraft carriers made of steel float. While they are made of steel, they are also full of air, which makes them have an overall density much less than that of the water.

As a human, you are made of, on average, ~65% water. This means that your overall density is just a bit less than that of water. When the densities are very close to one another, you will float just a bit. Not enough to make you pop to the surface (For the average person. This can change with an above average BMI.), but enough that the buoyancy offsets the pull of gravity just a bit. Gravity does not change just for you, you're still being pulled toward Earth's center of mass at ~$9.8m/s^2$ just like always.

Hopefully you find this explanation to be more satisfying than "because you're in water so there is less gravity".

Another way to see this is to consider the work needed to do a pull up. In the water you will do less work; while your body will be lifted up by the same distance, water will be displaced from a different height, so water moves down if you move up. The total change in the potential energy of your body and the water in the Earth's gravitational field is thus less.