5
$\begingroup$

The Situation:

A ball is placed in a beaker filled with water and floats. It is also attached to the bottom of the beaker via a string.

The Question:

The ball is attached to the beaker, thus making the ball and beaker (and string included) a system. However, it is floating. Does the ball add to the weight of the beaker?

$\endgroup$
1
  • $\begingroup$ It looks like putting a 1 kg hollow steel ball in a trough of water attached to a string and floats doesn't add weight to the trough when measured as a whole ;-) $\endgroup$ May 1, 2013 at 5:38

1 Answer 1

7
$\begingroup$

Yes, it does. When an object floats, its mass is not affected. It only affect the force experienced by it, as the water exerts a "buoyant force" on the object:

enter image description here

Basically, there is a pressure difference between the top and bottom surfaces, and this corresponds to a force difference, leading to a net upwards force:

enter image description here

However, remember that the force exerted by the water on the object leads to an equal and opposite force exerted by the object on the water. Since at equilibrium, $m_{obj}g=\text{buoyant force}$, a force equal to the weight of the body is exerted on the water. When the beaker is weighed, this extra force is balanced by the normal force.

Here are some free body diagrams. BF is the buoyant force, T is the string tension. Note that N is the weight that the weighing platform measures. enter image description here

$\endgroup$
2
  • $\begingroup$ beautiful diagrams, did you do them all yourself? $\endgroup$ Jul 11, 2013 at 14:19
  • $\begingroup$ @LarryHarson Not the first two, I got them from somewhere. The FBDs were made in LibreOffice Draw. $\endgroup$ Jul 11, 2013 at 15:16

Not the answer you're looking for? Browse other questions tagged or ask your own question.