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Mass in Physics

Everyone has at least heard what mass is, and has some intuitive understanding of it. Almost everything has mass, me, you, your house, and the Earth. It's important to know more than just the basics of mass, as so many different formulas and definitions in the field of physics require knowledge on it, as they may very well make use…

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Mass in Physics

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Everyone has at least heard what mass is, and has some intuitive understanding of it. Almost everything has mass, me, you, your house, and the Earth. It's important to know more than just the basics of mass, as so many different formulas and definitions in the field of physics require knowledge on it, as they may very well make use of this variable. So what is mass, and what can we learn about it?

What Is the Definition of Mass In Physics?

Mass describes how much matter something or someone is made up of. Mass can also be defined as the amount of inertia an object will have, which is the value of how resistant it is to a change in velocity, and as a result, a change in acceleration, as acceleration is a rate of change of velocity.

We know that the more matter something or someone has, the harder it is to move. This works the same with mass, the more mass something has the more force needed to be applied to move that mass. Almost everything in existence has mass, from objects as massive as a star to objects as tiny as an atom, all of these and everything in between have mass.

An example of something in the universe that does not have mass is a photon, which is a particle of light.

What is the Unit of Mass?

Mass has many different units, including pounds$\text{(lbs)}$, tons$\left(\text{T}\right)$, and grams$\left(\text{g}\right)$; however, the most widely used measurement for mass is the kilogram$\left(\mathrm{kg}\right)$. The kilogram is defined as the official unit of mass by the International System of Units, which defines the SI units. The kilogram is one of the seven base units that make up the rest of the SI units.

Up until 2019, the official measurement of a kilogram was defined by a very specifically weighed cylinder of metals, which was called the “International Prototype Kilogram”. This cylinder was the one true object on the planet that was exactly a kilogram!

Now, we base it on a constant value known as the Planck constant, which is $6.626·{10}^{-34}\mathrm{kg}{\mathrm{m}}^{2}}{\mathrm{s}}$. This value is used alongside sensitive equipment to determine a more accurate and consistent definition of$\text{1 kg}$.

This is the International Prototype Kilogram, protected from the elements in a glass case, so as not to alter its weight.

There has often been some confusion about mass; particularly, what is different between mass and weight. We said earlier that the more mass something has, the more force is needed to move it. Weight can be explained as a value that describes the force the gravitational pull of the Earth has on mass. At the same time, weight can also be described by the force any gravitational pull has on mass, meaning that if you were to go to a different planet, your mass would stay the same, but your weight would change! The weaker the gravitational pull of the planet or celestial body (such as the Moon), the less you would weigh if you were standing on it. This is why when astronauts were on the moon, they have to bounce along the surface, gravity isn’t pushing down on them as much.

The moon is smaller than Earth, so the gravitational pull is weaker, meaning your weight will be less there than it is here!Wikimedia Commons

The gravitational pull acting on an object or person has a direction, directly down towards the center of the planet or celestial body. This means weight has both magnitude (a quantifiable value) as well as direction. This makes it a vector, whereas mass, which only has a magnitude, is a scalar quantity.

We just mentioned that your mass would stay the same no matter which planet you were on. This is however true in all cases, the mass of any object or person will never change no matter what. This is known as the principle of Conservation of Mass. In more detailed terms, it also states that if an object were to be taken apart, the total mass of that object would be divided exactly within all of its parts, and if they were to be put together again, the sum of all of those parts would equal the mass of the initial object exactly.

Mass in action. We know that the yellow ball must have a higher mass than the blue ball, as it pushes down on the scale more so, due to the force of its weight.ScienceAlert

How Do We Solve a Calculation of Mass?

Mass has a few different ways to be calculated depending on the information that we have at our disposal. One of the primary equations we need to be concerned with is the following:

$m=\rho V$

Where$m$is the mass,$\rho$is the density, and$V$is the volume.

Density

Density defines how much of something there is inside a specific amount of space. Therefore, the denser something is, the heavier it is. For example, imagine we had a ton of feathers and a ton of steel. They both have the same mass, but steel is a lot denser than feathers, so that means that way more feathers are needed than steel to make up that ton. At the other end of the spectrum, volume is quite straightforward. Volume is used to define the amount of space something fills.

Density is typically measured in kilograms per cubic meter (${\text{kg/m}}^{3}$), and volume is typically measured in meters cubed (${\text{m}}^{3}$).

What is an Equation Example of Mass?

We’re now going to look at how this equation may be used in a few different circumstances with some examples, so you’ll know what to look out for and how to solve them:

A box has a volume of$5.2{\mathrm{m}}^{3}$and a density of$15.0\mathrm{kg}}{{\mathrm{m}}^{3}}.$What is the mass of this box?

This is a direct application of our formula. Simply plug in the numbers and solve.

id="2678741" role="math" $\begin{array}{rcl}m& =& \left(15.0\frac{\mathrm{kg}}{\overline{){\mathrm{m}}^{3}}}\right)·\left(5.2\overline{){\mathrm{m}}^{3}}\right)\\ & & \\ m& =& 78\mathrm{kg}\end{array}$

Darren’s oven has a mass of$100\mathrm{kg}$and a density of$75\mathrm{kg}}{{\mathrm{m}}^{3}}$. What is the volume of Darren’s oven?

This question is slightly harder than the previous question, but not by much. All that we need to do is take our equation and rearrange the variables so that volume is the main focus since we need to solve for the value of volume. After this, we just need to plug our numbers in like we did in the last question:

Jane has a table with a mass of$40\mathrm{kg}$and a volume of$8{\mathrm{m}}^{3}.$ What is the density of Jane’s table?

This follows how the previous question was solved, we need to once again rearrange our original equation, and then substitute the values we’ve been given to calculate density:

$\begin{array}{rcl}m& =& \rho V\\ & & \\ \rho & =& \frac{m}{V}\\ & & \\ \rho & =& \frac{40\mathrm{kg}}{8{\mathrm{m}}^{3}}\\ & & \\ \rho & =& 5\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}\end{array}$

Mass in Physics - Key takeaways

• Mass describes how much matter something is made up of.

• Conservation of mass requires that mass can never be created or destroyed. It can only be transferred somewhere else or converted into something else.

• Mass has many units, such as pounds, tons, and grams. However, the main SI unit of mass is kilograms.

• The equation for solving mass is $\mathrm{mass}=\mathrm{density}/\mathrm{volume}$.

Mass in physics is described as how much matter there is in an object or person.

There are many units of mass, such as pounds, tons, and grams. However, the main unit of mass is kilograms (kg).

The mass of something can be found by knowing the volume and density of it, and multiplying these values to together to get its value of mass.

Weight is the value of force an object with mass is applying to the ground because of the gravitational pull acting on it. Multiplying the gravitational pull value on the planet the mass is on by the value of mass will give you the value of weight.

Mass in Physics Quiz - Teste dein Wissen

Question

Describe what mass is in basic terms.

Mass is how much of something there is, or how much matter makes up something.

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Question

Does everything have mass?

No, almost everything has mass, but things such as photons, which are light particles do not have mass.

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What is the official unit of mass according to the International System of Units?

Kilograms.

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Question

What is the difference between mass and weight?

Mass is how much matter something is made up of, whereas weight is used to describe both the mass and the gravitational pull acting on a mass.

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Would you weigh more or less on the Moon?

You would weigh less on the Moon

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Is mass a vector or a scalar unit?

Mass is a scalar unit.

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Is weight a vector or a scalar unit?

Weight is a vector unit.

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What is the principle that states that mass will always stay the same called?

The Conservation of Mass.

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Describe what density is in basic terms.

Density is described as how much of something there is within a specific amount of space, or volume.

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Describe what volume is in basic terms.

Volume is the amount of space something fills.

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Where is the center of mass of a sphere with a uniform mass distribution?

At the center of the sphere.

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A cube and a pyramid both have the same mass and their masses are uniformly distributed. Which is more stable?

The pyramid.

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What is the condition for the center of mass of an object to be at its center?

The object is symmetrical about every axis.

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The center of mass of an object is always inside the object. Is this statement true or false?

False.

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For an object to be the most stable, should it have a wide or narrow base?

A wide base.

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Two glasses have the same mass, but one is thin and tall whereas the other is wide and short. Which glass is more stable (they both have uniform mass distributions)?

The wide and short glass.

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Does a low center of mass or a high center of mass lead to an object being more stable?

A low center of mass.

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At what point do all of the forces acting on a body in a free-body diagram originate?

The center of mass.

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The center of mass of a sphere is always at the center, even if its mass is unevenly distributed. Is this statement true or false?

False.

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When a car drives along a road, its tyres experience friction with the surface of the road. As the force acts at the tyres, we can not consider the force to act at the center of mass of the car in this case. Is this true or false?

False.

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Question

Describe in two sentences or less, why it is difficult to keep your balance while walking on a tightrope?

When you walk on a tightrope, you make a very narrow base with your feet, so it is difficult to keep your center of mass in line with your base and remain stable.

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An object has a T shape and is placed upright on the floor. Will its center of mass be above or below half of its height measured from the ground (the mass is evenly distributed)?

Above.

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A hammer is placed carelessly on the edge of a workbench, with half of it hanging off the bench. The head of the hammer is on the side hanging off. Will the hammer fall to the floor once it is released?

Yes.

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A square piece of card has a circle cut out of its bottom half. Will this cause the center of mass of the card to now be higher or lower?

Higher.

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If a single force acts on an object but causes no moment, at what point on the object does it act through?

The pivot point of the object.

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If you have a group of particles, which of the following quantities is not necessary to be known in order to find the center of mass of the particles at a moment in time?

The velocity of each particle.

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