To ensure that a ship is in stable equilibrium, would it be be...

Question

To ensure that a ship is in stable equilibrium, would it be better if its center of buoyancy was above, below, or at the same point as its center of gravity? Explain.

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use. In order to solve this problem. It is established that the buoyant force FB on a floating log found in a lake acts at the center of gravity in the water, which is displayed by the log itself. The this specific point is referred to as the center of buoyancy. In order for the log to be in a state of stable equilibrium, should the center of buoyancy be positioned above below or at the same level as its center of gravity? Explain your reasoning. So that's our angle. Our angle is we're trying to figure out if the center of buoyancy is centered above below or at the same level as its center of gravity. And then we're asked to explain why. And that is our final answer that we're ultimately trying to solve for. So as you can see, we have our diagram and we have our log that's in the water and we have the weight force of the log, which is the mass of the log multiplied by the acceleration due to gravity pointing downwards towards the bottom of this water body is the logs floating in some water. So where it's pointing downwards below the water line below the log pounding, pointing downwards. And then we have our buoyant force which is pointing upwards, pointing away from our weight force. And it's known as vector F subscript B Awesome. And of course, we have a solid blue squiggle line denoting the water, the surface of the water in our diagram. OK. So now that we have an idea of what's going on in this problem visually, let's read off our multiple choice answers to see which answer might be. Our final answer. A is above the two forces will mutually produce a torque that will rotate the log back to its equilibrium position. B below the two forces will cancel out each other. Keeping the log in its equilibrium position. C same level, the two forces will mutually produce a torque that will rotate the log back to its equilibrium position. And finally, D is anywhere the two forces will cancel each other, keeping the log on its equilibrium position. OK. So first off, let us note and recall that the center of buoyancy is the point where the buoyant force which acts upwards is applied. Let us recall that the center of gravity is the point where the weight of the body which acts in the downwards direction is applied. Secondly, let us note that if the center of buoyancy is above the center of gravity and any tilt of the body will create a writing moment, which is a torque or rotational force that will tend to restore the body to its original position. This is because the buoyant force and the weight of the body will create a couple which will produce a torque that will rotate the body back to its equilibrium position. So let us draw a free body diagram to help us better visualize this particular condition. So as we could see looking in our free body diagram, we have our buoyant force which is denoted as vector F subscript boy pointing in the upwards direction and then pointing in the downwards direction. We have our mass multiplied by the acceleration due to gravity where m in this case is the mass of the log. OK. So thirdly let us note that at the center of buoyancy is below the center of gravity. If any kind of tilt occurs, the body will create a capsizing moment that will tend to tip the body over. This is because the buoyant force and the weight of the body will create a couple which will produce a torque that will rotate the body away from its equilibrium position. So let us draw a diagram to help us better visualize this particular condition. So I've gone ahead and made another free body diagram and let's put it next to our other free body diagram that we already have put together here. OK. And then having them side by side here. So now in this condi condition, we have the buoyant force and the weight of the bo. So basically we have, if we have the boy, the center of buoyancy is below the center of gravity, as we could see in our free body diagram. So the buoyant force is below the center of gravity. So now that we can visualize this, we need to note that lastly, we need to see, we need to focus that the center of buoyancy is at the same level as the center of gravity. So the body will be in neutral equilibrium. So any kind of tilt that the body experiences in this particular case will not create a writing or capsizing moment and the body will remain in its new equilibrium position. Thus, for the log to remain in stable equilibrium, the center of buoyancy should be positioned above its center of gravity, which means that our final answer has to be multiple choice answer letter A. So above the two forces will mutually produce a torque that will rotate the log back to its equilibrium position and that's it we've solved for this problem. Thank you so much for watching. Hopefully that helped and I can't wait to see in the next video. Bye.

To ensure that a ship is in stable equilibrium, would it be better if its center of buoyancy was above, below, or at the same point as its center of gravity? Explain.

Key Concepts

Center of Buoyancy

Center of Gravity

Stable Equilibrium

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