Immersed Weight Calculator

We’ve all been to the beach, in a pool, or in a bathtub, and we’ve all experienced the feeling of weightlessness when we are immersed in water. But what is this phenomenon? And why is it that we feel our weight much less in water than we usually do? Would we experience the same effects if we were immersed in other liquids? And would other objects be affected in the same way as our human body?

In this immersed weight calculator, we will explain the concepts of weight, density, and buoyancy, then present the notion of immersed weight and answer these questions. We will also give you the tools and methods to set up and carry out your own DIY experiments at home and see what happens to the immersed weight of different objects when you put them in different liquids.

Finally, we show you how the immersed weight calculator works and how to use it with or without experiments. We explain how to calculate the immersed weight for different liquids, verify the theory behind buoyancy, and compute unknown physical properties of liquids and submerged objects.

The weight of an object is equal to the force acting on that object due to gravity. This force is proportional to the mass of the object and the magnitude of gravity where the object is located: you can learn how to find it with our gravitational force calculator. The mass of an object is constant, and the magnitude of the acceleration due to gravity calculator ($g$) on the surface of the Earth can also be considered constant ($g = 9.8\ \mathrm{m/s^2}$, with negligible variation). Therefore, the weight of an object on earth is constant.

When we stand on a scale, it measures the force that we exert on its surface (our weight), and divides that force by the magnitude of gravity, and gives us a reading of our mass in $\mathrm{lb}$ or $\mathrm{kg}$. If we put that scale in the bottom of a pool, the reading would be much lower than what we usually get. But why is that? And how can we explain that difference?

In the following section, we will summarise some concepts necessary for a proper understanding of the subject. I promise it will not be long before we move to the action part, where you get to create your own experiments and see firsthand the results.

Buoyancy:

In the 3^rd century BC, Greek scientist Archimedes of Syracuse explained and formalized a phenomenon called “buoyancy” by what is known as Archimedes’ principle. This principle states that when we immerse an object (partially or fully) in a liquid, the liquid exerts an upward force on the object (opposing its weight). This “buoyant force” is equal to the weight of the liquid occupying the volume of the immersed part of the object. To learn more about buoyancy, check out our Archimedes' principle calculator.

The effect of the liquid's density:

The density of a liquid (or a solid) body is equal to the mass per unit volume of that body.
From Archimedes’ principle, one can see that when we fully immerse the same object (same volume) in two different liquids (different densities), we get two different values for buoyancy; the higher the liquid density, the higher the buoyancy.

In a given liquid, the object's immersed weight is equal to its weight minus the buoyancy. If the density of the object is greater than that of the liquid, it will weigh more than the buoyancy; the immersed weight of this object is positive, and it will sink.

When placed in another liquid of higher density, the object can be immersed up to a point where buoyancy equals its weight; its immersed weight becomes zero, and it will float. If we push down on a floating body and force it into the liquid, the buoyancy becomes greater than its weight, and its immersed weight becomes negative (pointing upward instead of downward). When we release this body, it will bounce back to the surface and float again.

Now that you learned about Archimedes’ principle and the concepts of buoyancy and immersed weight, and saw how the relative densities of objects and liquids relate to their different interactions, it’s time for you to get a firsthand experience of these concepts! Read on if you want to try our DIY experiments and get a practical and intuitive understanding of the immersed weight of different objects in different liquids.

Preparation and set up:

For the purpose of these experiments, you will need the following items:

• 3-4 graduated measuring jugs;
• A high sensitivity ($1\ \mathrm{g}$ or less) hanging hook scale;
• A sewing thread or a fishing line ($3\ \mathrm{yds}$-$4\ \mathrm{yds}$);
• A pair of scissors;
• 3-4 different liquids (water, vegetable oil, rubbing alcohol, dish soap), $20\ \mathrm{fl\ oz}$-$30\ \mathrm{fl\ oz}$ each; and
• Several immersible objects (small rock, egg, small pencil or wooden piece, small plastic toy, wine cork, etc.). It is important for these objects not to be very small so that we're able to measure the change in liquid level when we immerse them, and not to have a lot of holes where air bubbles can get trapped as this will impact the accuracy of the results.

Once you prepare these items, take each of the empty jugs and immersible objects and tie them to a piece of thread, leaving a small tail with a loop that you can hook to the scale. Hook the empty jugs, one at a time, to the scale and measure their mass (we will need that later). Pour each liquid into a jug until it’s about $1/2$-$3/4$ full. That’s it. Now you're ready to start the experiments!

There are many fascinating ways to experiment with this setting, and by all means, feel free to do so, as long as you don’t hurt yourself or make a big mess! 😉 Here’s an example process we recommend to go through to discover some intriguing findings:

Start with the rock:

1. Hook it to the scale and measure its mass in kg;
2. Calculate its weight in $\mathrm{N}$ by multiplying the mass by $g =9.8$;
3. Immerse it in the water jug and measure its displayed "immersed mass" in $\mathrm{kg}$;
4. Calculate its immersed weight by multiplying the immersed mass by $\mathrm{g}$;
5. Calculate the buoyancy (= weight − immersed weight);
6. Calculate the volume of the rock (in $\mathrm{L}$) by measuring the displaced liquid (= water level with immersed rock − water level without the rock);
7. Calculate the density of the rock by dividing its mass by its volume;
8. Calculate the weight of the displaced liquid (= rock volume × water density × g), using water density $= 1\ \mathrm{kg/L}$; and
9. Verify that buoyancy = weight of the displaced liquid.

Congratulations! You just rediscovered the Archimedes principle!

Calculating the density of a liquid:

Use the rock and repeat steps 3, 4, and 5 with all the other liquids. Notice that the immersed weight of the rock varies in different liquids. Now that we know that buoyancy = weight of the displaced liquid, calculate, in each case, the density of the liquid (liquid density = buoyancy / (rock volume × g)).

Well done! You have learned a new way to discover the density of any liquid. Of course, in our case, there's another straightforward way of calculating the liquid density:

1. Hook the full jug to the scale and measure its mass;
2. Subtract the empty jug's mass (previously measured) to get the liquid's mass; and
3. Divide the result by the liquid volume to get the liquid density.

Try to do so and verify that both methods yield the same result!

Other objects:

Once you finish with the rock, you can repeat all the previous steps with the other objects. When an object floats, verify that the "floating buoyancy" (= density × volume of displaced liquid × g) is equal to the object's weight (= object mass × g).

To measure the immersed weight and the immersed buoyancy (that we will simply call buoyancy) of a floatable object:

1. Tie it to the rock (use the rock as ballast) and immerse them together;
2. Measure the immersed mass and calculate the immersed weight of the pair (weight = mass × g);
3. Subtract the (previously calculated) immersed weight of the rock to get the immersed weight of the object; and
4. Calculate the buoyancy by subtracting the immersed weight from the weight of the object.

Notice that the immersed weight of a floatable object is negative, and its buoyancy is greater than its weight (as predicted by theory). You can calculate the volume of a floatable object by measuring the displaced liquid for the pair (object + rock) and subtracting the rock's volume.

Finally, you can calculate its density for each liquid using any object (=liquid density = buoyancy / (object volume × g)). Go ahead and do so if you wish to verify that, for any given liquid, you get the same density value no matter which object you choose to use to calculate it!

In this final section, we will show you how you can use our immersed weight calculator as a stand-alone tool or as a complementary tool to your experiments. It will help you quickly verify the accuracy of your results, or see what happens to the immersed weight with many other common liquids, and even with hypothetical objects (too large or too heavy to be practical). It also allows you to calculate the unknown densities of liquids or objects you may have.

Using the calculator without the experiments:

First, let's suppose that you cannot set up and carry out the experiments. What can you learn from this calculator?

Well, if you provide the weight and volume of an object (any object, real or not) in the fields Object weight and Object volume; the calculator will immediately give you the immersed weight of that object in 12 different liquids.

Remember, when your immersed weight is positive, the object will sink; and when it's negative, the object will float.

Additionally, suppose the liquid you're interested in is not on our list. In that case, you can simply provide the density of your liquid, and the calculator will give you the buoyancy and the immersed weight of your object in that liquid. You can do this by opening the "Custom liquid" section of the calculator.

Using the calculator with the experiments:

If you do the experiments, you can use our calculator to verify that the immersed weights you measure are equal to those calculated here. Or you can measure the immersed weight of your object in one of your available liquids and immediately see what the immersed weight of your object would be in other liquids that you don't have.

When your object floats, and you need to use the ballast to immerse it, provide the measured ballast volume and (ballast + object) volume by opening the "Ballast properties" section of the calculator; the calculator will give you the ballast object's volume, which you can use for your immersed weight calculations.

You can also use our calculator with your experiments when you have a liquid, and you wish to calculate its density. To do so, measure the weight, volume, and immersed weight of your object and input these values in their fields; the calculator will give you the density of your liquid.

Finally, if you wish to know the immersed weight of an object in a hypothetical liquid that you don't have, measure the weight and volume of your object. Input these values, along with the density of your liquid, and the calculator will give you the immersed weight of that object in your liquid.