00:01
In this question, we have an object whose weight is known, and then when we submerge it in two different fluids, i'm gonna call it fs for submerged in water, and fso for submerged in oil.
00:21
When we submerge this object into two different fluids, we have a new scale reading, and we're gonna use this information to determine the density of the object and the density of the oil.
00:38
So our key idea is archimedes ' principle, which is that the buoyant force fb is equal to the weight of the displaced fluid.
00:54
Excuse me.
00:55
And when we think about, now if we have an object inside a container, and here's some liquid, and our object is fully submerged, oh yeah, it's attached to a spring.
01:11
That's attached to a scale, right? so a spring scale so we can get readings.
01:15
There we go.
01:17
When we think about the forces acting on our object, we are going to have, of course, the weight downward, and then we're gonna have a fs, actually, s, as i think about it, i meant fs to be the scale reading in water, and the scale reading in oil not submerged.
01:44
I don't know what i was thinking there when i was speaking earlier.
01:46
And then we're gonna have our buoyant force is gonna make up the difference so that the object is in equilibrium, that force equals zero.
01:54
So buoyant force plus the scale reading will be equal to the weight.
02:01
And so we can find our buoyant force with the weight in air minus the scale reading.
02:09
Excuse me.
02:10
And so for the buoyant force in water, we can say it's the gravitational force minus the scale reading in water.
02:26
And then how to calculate the weight of the fluid, we need the density of the fluid.
02:31
So rho w is density of water times v.
02:34
It's usually the volume of the displaced fluid, but in this case, the volume of the water is equal to the volume of our object.
02:47
So i'm just gonna call it v, quick note on that, and then times g.
02:53
So density times volume gives us mass.
02:56
And then g of course is gravitational acceleration that gives us a weight.
03:02
So we'll take our 343 newtons minus our 214 newtons.
03:07
And then we are going to use 1000 kilograms per cubic meter for the density of water...