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This article was co-written by Bess Ruff, MA. Bess Ruff is a graduate student in geography at Florida. She received her Master’s degree in Environmental Science and Management from the Bren School of Environmental Science & Management, UC Santa Barbara in 2016. She has conducted survey work for marine spatial planning projects in the coastal area. Caribbean and support research as a contributor to the Sustainable Fisheries Group.
There are 9 references cited in this article that you can view at the bottom of the page.
This article has been viewed 21,174 times.
Buoyancy is the force acting on an object submerged in a fluid in the opposite direction of gravity. When an object is placed in a fluid, its weight pushes down on the fluid (liquid or gas) while buoyancy pushes the object upwards, in the opposite direction of gravity. In general, this buoyancy force can be calculated using the equation F b = V s × D × g , where F b is the buoyancy force, V s is the volume of the submerged part, and D is the density of the enclosing fluid. around the object, and g is the force of gravity. To learn how to determine the buoyancy of an object, start by watching Step 1 below.
Steps
Using the buoyancy equation
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Find the volume of the submerged part of the object. The buoyant force acting on an object is directly correlated with the submerged volume of that object. In other words, the larger the submerged part of a solid body, the stronger the buoyant force acting on the object. That is, even if the object is completely submerged in the liquid, there is still a buoyant force acting on it. To begin to calculate buoyancy forces acting on an object, the first step is usually to determine the volume of volume submerged in the fluid. In the equation for the buoyancy force, this value must be written in terms of m 3 .
- For an object that is completely submerged in the fluid, the submerged volume will be equal to the volume of the object itself. For bodies floating on the surface of a fluid, we only consider the volume below the surface of the fluid.
- For example, suppose we want to find the buoyant force acting on a rubber ball floating in water. If the ball is a perfect sphere with a diameter of 1 m and it floats with exactly one half submerged, we can find the volume of the submerged part by calculating the volume of the whole ball and dividing it by two. Since the volume of the sphere is (4/3)π(radius) 3 , we have the volume of the ball as (4/3)π(0.5) 3 = 0.524 m 3 . 0.524/2 = 0.262 m 3 sunk .
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Find the density of the fluid. The next step in the process of finding buoyancy is to determine the density (in kg/m 3 ) of the liquid surrounding the object. Density is a quantity measured by the ratio of the mass of an object or matter to its corresponding volume. With two objects of equal volume, the one with the higher density will weigh more. The general rule is that the higher the density of the fluid, the greater the buoyant force acting on the object submerged in it. With fluids, usually the easiest way to determine density is to look it up in the reference literature.
- In the example above, the ball floats in the water. Refer to the study material that tells us that water has a density of 1,000 kg/m 3 .
- The densities of many common fluids are given in the technical literature. You can find this list here.
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Find the force of gravity (or other downward force). Whether an object sinks or floats in a fluid, it is always under the influence of gravity. In fact, this downward force constant is about 9.81 Newton/kilogram . However, in cases where there is another force acting on the fluid and the object immersed in it, such as the centripetal force, we must also consider this force when calculating the total “downward” force for the system as a whole.
- In the above example, if we have an ordinary static system, it can be assumed that the only downward force acting on the fluid and the body is the standard gravitational force — 9.81 Newton/kilogram .
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Multiply volume by density and gravity. When you have the values of the body volume (in m 3 ), the density of the fluid (in kg/m 3 ), and gravity (or the downward force of the Newton/Kilogram system), finding buoyancy becomes easy. Simply triple this quantity to find the buoyancy force in Newtons.
- Solve the example problem by substituting the values into the equation F b = V s × D × g. F b = 0.262 m 3 × 1,000 kg/m 3 × 9.81 N/kg = 2,570 Newtons . The other units will cancel each other out, leaving only the Newton unit.
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Determine if an object is floating by comparing it to gravity. Using the buoyancy equation, you will easily find the force that pushes the object out of the liquid. However, you can also determine whether the object floats or sinks in the fluid if you take an extra step. Find the buoyant force acting on the whole body (i.e. use the entire volume of the object V s ), then find the gravity that pulls the object down using the equation G = (mass of the object)(9.81 m/s 2) ). If the buoyant force is greater than gravity, the object will float. On the other hand, if gravity is greater then the object will sink. If these two forces are equal, we say that the body is suspended .
- A suspended object will not float on water or sink to the bottom while in water. It will be suspended in the liquid halfway between the surface and the bottom. [1] X Research Source
- For example, suppose we want to know whether a cylindrical wooden crate weighing 20 kg with a diameter of 0.75 m and a height of 1.25 m can float in water. We have to perform many steps for this problem:
- The first is to find the volume using the formula for the volume of a cylinder V = π(radius) 2 (height). V = π(0.375) 2 (1,25) = 0.55 m 3 .
- Next, assuming the standard gravity and density of the water are known, we solve for the buoyant force acting on the barrel. 0.55 m 3 × 1000 kg/m 3 × 9.81 N/kg = 5,395.5 Newton .
- Now we have to find the gravity acting on the wooden crate. G = (20 kg)(9.81 m/s 2 ) = 196.2 Newtons . This result is much less than the buoyancy force, so the barrel will float.
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Use the same calculation when the fluid is a gas. When solving problems with buoyancy, do not forget that a fluid is not necessarily a liquid. Gases are also considered fluids even though they have a very small density compared to other types of matter, and gases can still repel some objects floating in it. The helium bubble is proof of this. Since the helium in the bubble is lighter than the fluid around it (air), the balloon will rise!
Do a simple experiment on buoyancy
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Place a small bowl in a larger bowl. With just a few household items, it’s easy to see the effect of buoyancy in practice. In this experiment, we show that when an object is submerged, it experiences buoyancy force, since it displaces a fluid equal to the volume of the submerged object. During the experiment, we also show how to find the buoyancy force of the object in practice. First you put a small container without a lid, like a bowl or cup, in a larger container like a large bowl or bucket of water.
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Pour water into the small container up to the edge. You must pour the water to the very edge without overflowing. Be careful at this step! If you let water spill, you must empty the large container and do it again.
- For this experiment, we assume water has a density of 1000 kg/m 3 . Unless you use brine or a completely different liquid, most waters have a density close to this reference value so the results should not be affected.
- If you have a dropper, you can use it to drip water into the container inside so that the water level is close to the edge.
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Submerge a small object. Next, you find an object that can fit in a small container but won’t be damaged by water. Find the mass in kilograms of this object (you should use a scale to give the reading in grams and then convert to kilograms). Then slowly press the object into the water without getting your fingers wet until it starts to float or you can barely hold it, and then release the object. You should see some water spill over the edge of the inner container into the outer container.
- For this example, let’s say we’re pressing a 0.05 kg toy car into its inner container. We don’t need to know the volume of the car to calculate the buoyancy force, as we will in the next step.
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Collect and measure spillage. When you press an object into water, it displaces a certain amount of water — otherwise there would be no space for you to dip it into the water. As it pushes the water out of the passage, the water pushes back and creates buoyancy. Collect the spilled water from the inner container and pour it into the small measuring cup. The volume of water in the beaker should be equal to the volume of the submerged object.
- In other words, if the object is floating, the volume of water that spills out will be equal to the volume of the object that is submerged below the surface of the water. If the object sinks, the volume of water that spills out will be equal to the volume of the entire object.
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Calculate the volume of water spilled. Since you know the density of water and can measure the volume of water that overflows in the measuring cup, the volume of water will be calculated. Convert the volume to m 3 (an online unit converter like this one can help here) and multiply it by the density of water (1,000 kg/m 3 ).
- In the example above, assume the toy car is submerged in its inner container and displaces about 2 tablespoons of water (0.0003 m 3 ). To find the mass of water, you multiply this value by the density: 1,000 kg/m 3 × 0.0003 m 3 = 0.03 kg .
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Compare the mass of water displaced and the mass of the object. Now that you know the mass of both the submerged object and the displaced water, compare these two values. If the mass of an object is greater than the mass of the volume of water displaced, the object will sink. On the other hand, if the volume of water displaced is greater, the object will float. This is the principle of buoyancy in practice — for an object to float, it must displace a mass of water greater than the mass of the object itself.
- Therefore, objects with light mass but large volume are the ones that can float best. This property shows that hollow objects can float very well. Let’s take a look at the canoe — it floats well because it’s hollow inside, so it can take up a lot of water, but it’s not too heavy. If the canoe is solid inside, it can’t float well.
- In the above example, the vehicle has a mass of 0.05 kg which is 0.03 kg more than the displaced water mass. This is consistent with what we observe: the car has sunk.
Advice
- Use a scale that automatically zeroes after each weighing for accurate readings.
Things you need
- Small cup or bowl
- Large bowl or pail
- Small objects that can be submerged in water (such as rubber balls)
- Measuring cup
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This article was co-written by Bess Ruff, MA. Bess Ruff is a graduate student in geography at Florida. She received her Master’s degree in Environmental Science and Management from the Bren School of Environmental Science & Management, UC Santa Barbara in 2016. She has conducted survey work for marine spatial planning projects in the coastal area. Caribbean and support research as a contributor to the Sustainable Fisheries Group.
There are 9 references cited in this article that you can view at the bottom of the page.
This article has been viewed 21,174 times.
Buoyancy is the force acting on an object submerged in a fluid in the opposite direction of gravity. When an object is placed in a fluid, its weight pushes down on the fluid (liquid or gas) while buoyancy pushes the object upwards, in the opposite direction of gravity. In general, this buoyancy force can be calculated using the equation F b = V s × D × g , where F b is the buoyancy force, V s is the volume of the submerged part, and D is the density of the enclosing fluid. around the object, and g is the force of gravity. To learn how to determine the buoyancy of an object, start by watching Step 1 below.
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