Video: Weight and Mass

In this video we learn what mass and weight are and how they are different, as well as calculating their values in examples.

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Video Transcript

In this video, we’re going to learn about weight and mass. We’ll learn what these two terms mean, how they’re different from one another, and we’ll also get some practice using them in examples.

To start out, imagine that as a collector of fine works of art you are waiting with great anticipation in an auction where some collectibles will be offered to the highest bidder. In particular, you’ve had your eye on a statue of a monkey rumored to be hundreds of years old and made of solid gold. When it comes time to auction off the golden monkey, the auctioneer comes on stage and makes an unexpected announcement. The monkey will be priced according to its weight based on the cost of gold per unit weight. Based on this information, thinking quickly, you raise your hand and ask the auctioneer if the auction can be moved to some spot along the Earth’s equator. To understand the reason behind this request, we’ll want to learn about weight and mass.

Mass and weight are two terms that sometimes are used interchangeably as those are the same thing. Mass is defined as the amount of material in a body, whereas weight is a measurement of how much gravity pulls on a body. Mass is typically measured in units of kilograms, whereas weight is measured in units of force such as newtons or pounds. It turns out that mass and weight are different from one another. And we can understand the difference by looking closely at these definitions.

Looking at the definition for mass, we can see that the amount of material in a body in theory doesn’t change regardless of the body’s position or location. If we have a one-kilogram block for example, then that block will have the same amount of mass one kilogram regardless of where it is. But now, look at the definition for weight. Weight is the measurement of how much gravity pulls on a body. This means that if gravity changes, the weight of an object changes as well.

Let’s say we were to take our one-kilogram mass and set it at rest on the surface of the Earth. On Earth, the weight of this mass would equal its mass multiplied by the acceleration due to gravity on Earth’s surface 𝑔. Say that we change locations of our mass. Now, we put it to rest on the surface of the Moon. Now, the weight of the mass is equal to its mass times the gravity of the Moon. And if the gravity on the Moon is different from the gravity on Earth which it is, then the weight of this mass will be different in those two locations.

All this means there are a few more things we can say about mass and weight. An object’s mass doesn’t change. It’s always the same no matter where the object is located. An object’s weight on the other hand equals its mass times acceleration due to gravity. If gravity changes, so does the object’s weight. This by the way is the reason behind the request to relocate the auction to a spot along the equator of the Earth. The acceleration due to gravity 𝑔 is not constant over the Earth surface, but is highest at the poles and smallest at the equator. So an object will weight least when it’s located along the equator and if it’s being sold by weight will cost less.

Let’s get some practice working with mass and weight through a couple of examples.

The mass of a particle is 15.0 kilograms. What is its weight on Earth? On the Moon, the acceleration produced by gravity is 1.36 meters per second squared. What is the weight of the particle on the Moon? What is its mass on the Moon? What is its weight in outer space far from any celestial body? What is its mass at this point?

In the first part of this exercise, after having been told that we’re working with a particle of mass 15.0 kilograms, we want to solve for its weight on Earth. We can recall that weight 𝑤 is equal to an object’s mass multiplied by the acceleration it experiences due to gravity. So the weight of the particle on Earth is equal to 15.0 kilograms times 𝑔, where 𝑔 we know to be 9.8 metres per second squared. When we calculate this product, if we assume that 𝑔 is exactly 9.8 metres per second squared, our answer is 147 newtons. That’s the weight of the object on Earth.

Next, we want to calculate the weight of the particles not on Earth, but on the Moon. Here, the acceleration due to gravity is no longer 9.8 metres per second squared, but it’s 1.63 metres per second squared. This means that the weight of the particle on the Moon we can call it 𝑤 sub 𝑀 is equal to its mass 15.0 kilograms multiplied by 1.63 meters per second squared. This is 24.5 newtons. Notice how much less this particle weighs on the Moon than the Earth. It’s about six times less.

Next, we want to solve for the particle’s mass on the Moon. This will be simple because mass doesn’t change regardless of our location. It’s always the same. The mass of the particle on the Moon or anywhere else is 15.0 kilograms.

Next, we want to solve for weight in the case of being in outer space far from any celestial body. As we think about the particle being far away from any large mass, we consider that it’s those large masses that the source of acceleration due to gravity 𝑔. If we’re far from any celestial body, that means that the acceleration due to gravity is effectively zero. This means that the object’s weight which will be equal to its mass times 𝑔 which is zero is itself zero. Far away from any mass, the particle can truly be said to be weightless.

And, finally, far away from any celestial body, we want to know the particle’s mass. Well, this is the same as it has been before. Since mass is a measure of the amount of material in an object, it doesn’t depend on the environment of the object. This means that the mass of the particle as before is 15.0 kilograms.

We’ve learned the equation for calculating an object’s weight based on its mass and acceleration due to gravity.

Now, let’s look at an example that involves solving for the object’s mass through an equation.

Astronauts in orbit are apparently weightless. This means that a clever method of measuring the mass of astronauts is needed to monitor their mass gains or losses and adjust their diet. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 newtons is exerted and an astronaut’s acceleration is measured to be 0.893 metres per second squared, calculate her mass.

Knowing the force exerted on an astronaut as well as the astronaut’s resulting acceleration, we want to calculate the astronaut’s mass. If we call that mass we want to solve for 𝑚 and record the force and acceleration as 𝐹 and 𝑎, respectively, we can recall from Newton’s second law of motion that an object’s mass is equal to the net force acting on it divided by its acceleration. For our scenario, we can write that 𝑚 is equal to 𝐹 divided by 𝑎. And when we plug in for these two values and calculate this fraction, we find it’s equal to 56.0 kilograms. That’s the measured mass of the astronaut based on the astronaut’s response to an applied force.

Let’s summarize what we’ve learnt so far about weight and mass. We’ve seen that weight and mass are related to one another, but they’re not the same. Mass is the amount of material in a body and weight is the measure of how much gravity pulls on a body. And we’ve seen that weight is equal to the product of mass times gravity. All this means that an object’s mass is constant or another way of saying it is invariant, while weight changes with acceleration due to gravity 𝑔.

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