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In this video, we’re going to learn about weight and mass.
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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.
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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.
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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.
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When it comes time to auction off the golden monkey, the auctioneer comes on stage and makes an unexpected announcement.
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The monkey will be priced according to its weight based on the cost of gold per unit weight.
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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.
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To understand the reason behind this request, we’ll want to learn about weight and mass.
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Mass and weight are two terms that sometimes are used interchangeably as those are the same thing.
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Mass is defined as the amount of material in a body, whereas weight is a measurement of how much gravity pulls on a body.
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Mass is typically measured in units of kilograms, whereas weight is measured in units of force such as newtons or pounds.
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It turns out that mass and weight are different from one another.
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And we can understand the difference by looking closely at these definitions.
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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.
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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.
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But now, look at the definition for weight.
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Weight is the measurement of how much gravity pulls on a body.
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This means that if gravity changes, the weight of an object changes as well.
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Let’s say we were to take our one-kilogram mass and set it at rest on the surface of the Earth.
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On Earth, the weight of this mass would equal its mass multiplied by the acceleration due to gravity on Earth’s surface 𝑔.
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Say that we change locations of our mass.
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Now, we put it to rest on the surface of the Moon.
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Now, the weight of the mass is equal to its mass times the gravity of the Moon.
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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.
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All this means there are a few more things we can say about mass and weight.
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An object’s mass doesn’t change.
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It’s always the same no matter where the object is located.
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An object’s weight on the other hand equals its mass times acceleration due to gravity.
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If gravity changes, so does the object’s weight.
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This by the way is the reason behind the request to relocate the auction to a spot along the equator of the Earth.
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The acceleration due to gravity 𝑔 is not constant over the Earth surface, but is highest at the poles and smallest at the equator.
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So an object will weight least when it’s located along the equator and if it’s being sold by weight will cost less.
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Let’s get some practice working with mass and weight through a couple of examples.
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The mass of a particle is 15.0 kilograms.
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What is its weight on Earth?
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On the Moon, the acceleration produced by gravity is 1.36 meters per second squared.
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What is the weight of the particle on the Moon?
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What is its mass on the Moon?
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What is its weight in outer space far from any celestial body?
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What is its mass at this point?
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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.
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We can recall that weight 𝑤 is equal to an object’s mass multiplied by the acceleration it experiences due to gravity.
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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.
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When we calculate this product, if we assume that 𝑔 is exactly 9.8 metres per second squared, our answer is 147 newtons.
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That’s the weight of the object on Earth.
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Next, we want to calculate the weight of the particles not on Earth, but on the Moon.
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Here, the acceleration due to gravity is no longer 9.8 metres per second squared, but it’s 1.63 metres per second squared.
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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.
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This is 24.5 newtons.
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Notice how much less this particle weighs on the Moon than the Earth.
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It’s about six times less.
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Next, we want to solve for the particle’s mass on the Moon.
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This will be simple because mass doesn’t change regardless of our location.
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It’s always the same.
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The mass of the particle on the Moon or anywhere else is 15.0 kilograms.
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Next, we want to solve for weight in the case of being in outer space far from any celestial body.
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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.
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If we’re far from any celestial body, that means that the acceleration due to gravity is effectively zero.
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This means that the object’s weight which will be equal to its mass times 𝑔 which is zero is itself zero.
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Far away from any mass, the particle can truly be said to be weightless.
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And, finally, far away from any celestial body, we want to know the particle’s mass.
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Well, this is the same as it has been before.
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Since mass is a measure of the amount of material in an object, it doesn’t depend on the environment of the object.
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This means that the mass of the particle as before is 15.0 kilograms.
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We’ve learned the equation for calculating an object’s weight based on its mass and acceleration due to gravity.
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Now, let’s look at an example that involves solving for the object’s mass through an equation.
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Astronauts in orbit are apparently weightless.
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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.
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One way to do this is to exert a known force on an astronaut and measure the acceleration produced.
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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.
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Knowing the force exerted on an astronaut as well as the astronaut’s resulting acceleration, we want to calculate the astronaut’s mass.
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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.
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For our scenario, we can write that 𝑚 is equal to 𝐹 divided by 𝑎.
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And when we plug in for these two values and calculate this fraction, we find it’s equal to 56.0 kilograms.
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That’s the measured mass of the astronaut based on the astronaut’s response to an applied force.
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Let’s summarize what we’ve learnt so far about weight and mass.
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We’ve seen that weight and mass are related to one another, but they’re not the same.
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Mass is the amount of material in a body and weight is the measure of how much gravity pulls on a body.
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And we’ve seen that weight is equal to the product of mass times gravity.
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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.