A hollow plastic sphere is held below the surface of a freshwater lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.650 m^3 and the tension in the cord is 1120 N. (a) Calculate the buoyant force exerted by the water on the sphere. (b) (b) What is the mass of the sphere?

Video transcript

Everyone. So for this problem we are going to be working with buoyancy. Let's see what they're asking and then jump into it. A wooden block is suspended in a tank of fresh water using a string fixed to the bottom Of the tank. The tension in the string is 805 newtons. And the block has a volume of 0.425 m cubed, determine the buoyant force experienced by the block from the water and the blocks mass. So a two part question. So let's write down our givens first. We know the tension in the string is newtons And our volume is 0.4 - five m cubed. Let's recall that the buoyancy force equation is ro G V where rho is the density of the um fluid that we're working with in this case water, That's a constant recall, that is um kg per meter cubed. And then gravity are constant is 9.8 m/s squared. Um We also need to draw our free body diagram to some the different forces working here. So let's do that. Next. We've got our masks, the block, we know that the string is at the bottom of the tank. That means it's a downward force. The tension. And we also know the weight of the block is going to be, you know, force, the force is downward and then the buoyancy force is acting in an upward direction. So we're going to some some of our forces equals mass times acceleration and it's not moving. So that's just zero. So our positive force is our buoyancy force that equals the sum of our attention plus our weight. We are asked for the blocks mass. Um so what we're and we have everything we need to solve for the buoyancy force. So the first thing we're going to do is solve for the weight and then we're going to use that to solve for the mass. So let's recall that the weight is just mass times gravity. Right? So we know that um our buoyancy force is 1000 kg Per meter Cube Times 9.8 m/s squared Time 0.4-5 m cubed. Let's just do a quick unit. Check everything is in the room units there. And so our buoyancy forest close that into our calculator and that is 4165 newtons. We know our attention. We're gonna plug that back into this equation here. So 4165 Newtons equals 805 newtons minus weight. We're gonna solve this for the weight that comes out to 30 Newtons. So again, recall that weight is just the mass times of gravity. So we have 33 60 newtons divided by 9.8 m per second squared equals the mass. You plug that into your calculator and get kg. Alright, so the answer to the first part, the buoyant force Is 65 Newtons. So off the bat, we can eliminate a couple of these answers And the answer to the second part of the question. Your mass is 343 kg. And so, looking at the answers we have left, the correct answer is C Point Force is 4,165 Newtons, and the mass is 343 kg. Okay, that's all for this problem. We'll see you in the next video.