(b) Below what speed does a 3.0-mm-diameter ball bearing in 20°C air experience linear drag?

Video transcript

Hey, everyone. So this problem is working with drag forces. Let's see what they're asking us. We have a bead of radius 2 mm thrown with an initial speed of V in castor oil at a temperature of 25°C. They tell, they tell us that uh the viscosity given by A is 585 times 10 to the negative three pascal seconds. And our density given by row is 958 kg per meter cubed. We're asked to determine the maximum speed of the bead at which the bead will encounter linear drag. And our multiple choice answers here are a one point a sorry, 0.15 m per second. B 0.30 m per second, C 2.4 m per second or D 6. m per second. The first thing we're going to do here is recall that the maximum Reynolds number where an object will experience this linear drag is equal to one. So therefore, we can solve the Reynolds equation with the Reynolds number equal to one. Let's recall that the Reynolds equation is given by R E equals row V D divided by A where row is our density V is our speed D is our diameter and ada is our viscosity. We are solving for the speed. So V and we can rearrange this equation um plugging in all of the values that we know. So we've already said that for linear drag, our Reynolds number is going to equal one. Our density was given to us. And the problem as 958 kg per meter cubed. Our diameter we weren't given, but we know that diameter is two times the radius and the radius is 2 mm. So we have two multiplied by 2 mm which is 2 times 10 to the -3 m. So our density is four times 10 to the -3 times 10 to the -3 m. And then our data is given to us in in the problem our viscosity of 585 times 10 to the negative three pascal seconds. So we will rearrange our equation to solve for V and then plug in chug. So speed equals our Reynolds number multiplied by our viscosity over our density multiplied by our diameter. So one multiplied by 585 times 10 to the negative three pascal seconds divided by 958 kilogram per meter cubed multiplied by four times 10 to the -3 m. Plug that into our calculator and we get 0.15 m/s. And so that is our answer and that aligns with answer choice. A so that's all we have for this one. I'll see you in the next video.