00:01
Okay, so in this problem, we just want to calculate the speed of the gold sphere.
00:07
But the problem says that the drag force, so let's call this fd, is going to be equal one -fourth of the weight of the sphere.
00:21
So it's just one -fourth of m -g.
00:24
First of all, let's remember what is the drag force.
00:28
So the drag force can be described as 6 pi eta r v of the sphere.
00:43
So this is constant, this is the radius of the sphere, and this is the speed of the sphere, okay? so that is the definition of the drag force.
00:55
The second thing we must remember what is the weight, the weight, m g we can describe as the volume multiplied by the density of the sphere that multiplies the gravitational acceleration so we can describe this first equation here as let's see six by eta r v t the object it's going to be equal the volume and the volume actually one four sorry one fourth of the volume of the sphere which is four divided by three times the radius cubics that multiplies the density that multiplies the gravitational acceleration so we can cross the four and here and we can cross one of the radius in here so we have only radius left and we can simplify this equation through the velocity which is what we want to calculate so that the speed the velocity of the sphere is going to be equal our square to multiply's g ho divided by 18 ata i forgot to put in here the pie because it the volume of the sphere is 4 pi divided by 3.
02:50
So i forgot the pi and we can cross here with here...