Bobbers Floats
Physics questions about fluids?
Don`t just give me the answer, please show me how you solved the problem.
2. What is the buoyant force acting on a cube of copper(density of 8.96 g/cm^3) that measures 2 cm on each side if it is immersed in water?
3. A piece of alloy “weighs” .086 kg in air and .073 kg when immersed in water. Find its volume and density.
4. A fishing line is attached to a bobber that is .05 m in diameter and has a mass of .005 kg. A lead weight is attached to the line. What is the mass of the lead if the bobber is floating half submerged?
6. A solid chunk of iron(density of 7.8 g/cm^3) is floating in mercury(density of 13.5 g/cm^3). What percent of the iron object is submerged?
It would probably help to know about what exactly goes on when you’re dealing with liquids and things floating or sinking in them.
When you place an object in liquid, let’s say water, why might it be lighter or possibly float?
Well, when we place the object underwater, the object takes up the space the water used to occupy. It displaces it. That volume of water displaced has nowhere to go but up, and the level rises. As we know from experience, things tend to fall down and not rise, because of gravity. Gravity tries to have its way and pulls the water back down.
So we see here that there’s a balance between the object being pulled down, and the displaced water trying to get back into its old spot. Water pushes the object back up as hard as gravity is pulling down on the water. This pushing up is known as the buoyant force.
The key thing to know is that the size of the buoyant force is equal to the **weight of the water displaced**.
You can tell how much water is displaced by realizing that the volume of water displaced is equal to the object’s volume. Using the density of water, you can find the mass, and then the weight of water.
Density = mass/volume
mass = density * volume
2. Buoyant force depended only on the weight of water displaced. What was the cube’s volume? What volume of water was displaced? Using the density of water, what did it weigh?
3. The weight given has some volume that we don’t know. What we do know is that it weighs less under water. Using the masses given, we can figure out the buoyant force. It’s regular weight was .086* 9.8 Newtons, and then the net weight became .073*9.8 Newtons. The difference is from the buoyant force. Once we know that, that can clue us in to the weight of the water, and immediately the mass of the water displaced. Using density, we can figure out what volume of water this is. Realizing this same volume belongs to the object, we can find the object’s density with its mass and volume.
4. The bobber is a sphere and you’re given diameter. That can help you get volume if we need it, but where does it come in? The problem wants us to find the mass of lead. Looking at what’s going on with forces here, we see that gravity pulls down both the bobber and the lead. But then we also have a buoyant force to push them both up. What is the size of the buoyant force? We know that it’s equal to how much water is displaced. That was half the volume of the bobber. So we can find the size of the force.
One last thing is to realize that the the combined weights of both the bobber and the lead is balanced by the buoyant force. In other words, they are equal.
Summing up the forces in the y direction with up as positive (I hope you know about free body diagrams) and down as negative.
Buoyant force(up) – weight bobber (down) – weight lead (down) = 0
so dragging things to the other side
Buoyant force = weight bobber + weight lead
We know the buoyant force, and the weight of the bobber. The only thing left to find is the lead weight. Once we have that, we can get the mass.
6. The fluid in this case is mercury, not water. Once again we’ve got gravity pulling an object down, and then buoyant force pushing up.
The more of the object’s volume that sinks under, the greater the buoyant force. The volume at which the buoyant force matches gravity’s pull on the object is what you’re looking for, compared to the total volume.
Pretend we have 1 cubic cm of iron weighing 7.8 g. What volume of mercury must be displaced to equal that weight? How does this volume compare with 1 cubic cm?
I hope those leading questions get you the answers you seek.
