Re: What is the height of bottom of ball submerged below water surface

Hi Azhan,

Interesting question... Are you, by chance, a floating ping pong aficionado?

The first thing you need to do is figure out which forces are acting on the ping pong ball to keep it afloat. Draw a force diagram. There's a gravitational force pulling it down (that would be your m*g). There's a buoyancy force, caused by the displaced water, pushing it up (your rho*V*g). There's also surface tension along the interface between the ping pong ball and the water. Surface tension is often overlooked when solving simple buoyancy problems, in which case you'd get your first answer [(m divide V) = rho]. However, since the ping pong ball is very light compared to the surface area it offers the water, surface tension is likely non-negligible in determining how deep the ball will sink.

Surface tension is more complicated geometrically, acting perpendicular to the surface of the ping pong ball at all points where it is in contact with the water. Luckily balls are spherical, so all the lateral forces cancel out. It then works out that the upwards vertical force due to surface tension is (sigma/r)*A (where sigma is surface tension in N-m^-1, something you'll have to look up because it's different for different materials).

You're now on your way to predicting how a ping pong ball will float.

Cheers, Tetjana