00:02
This problem involves the buoyant force, which we're going to calculate using archimedes principle.
00:09
But first, let's draw a free body diagram so we understand what forces are involved here.
00:15
When the crown is suspended in water by a string, the force is acting on it are a tension force going up, which i'll label t.
00:23
And they have a buoyant force going up as well.
00:27
I'll label that fb.
00:29
And we also have a force of gravity acting down.
00:32
Call that fg.
00:35
Now, because the crown is an equilibrium in that situation, when it's to suspended at rest underwater, we know that the tension plus the buoyant force minus the force of gravity equals zero.
00:55
And this allows us to solve for the buoyant force.
00:57
The buoyant force then must be the force of gravity minus the tension force.
01:06
If we plug in the numbers which they gave us, we're told the force of gravity is 8 .3 newtons, and we are told the tension is 7 .81 neutins, and therefore we know that the buoyant force is 0 .49 neutins.
01:28
Now, let's take that buoyant force and see how we would calculate it using archimedes ' principle.
01:35
Archimedes principle says that the buoyant force should equal the weight of the fluid that is displaced.
01:43
And the weight of the fluid that displaced is the mass of that fluid times g, the gravitational field strength or acceleration of gravity.
01:52
So therefore, and the mass of the fluid should be the density of the fluid.
01:59
So we'll say the buoyant force is the density of water.
02:05
And then that's times the volume that is displaced.
02:10
And the volume that's displaced is the volume of the crown itself...