Lesson Video: Weight Science

Video Transcript

In this video, we will learn how to distinguish between the mass of an object and the gravitational force that acts on the object, the weight of the object.

The word “weight” is used quite a lot in everyday language. A doctor might ask us to step on some scales so they can weigh us. Or when we’re cooking, we might say that we weigh out our ingredients. In everyday language, the word “weight” is often used in a way that is incorrect in physics. This is because in everyday language, weight is often confused with mass. If we measure out a kilogram of sugar for a cake, we’re actually measuring the mass of the sugar, not its weight. Anytime we have a value in units of kilograms or grams, that’s a mass and not a weight.

Mass and weight are closely related quantities, but they are not the same thing. When we pick up a very heavy object, we feel a force from the object pulling it towards the ground. This force is the weight of the object. The weight of an object is related to its mass. A greater mass means the object has a greater weight.

But weight is a force and mass is not. And weight doesn’t only depend on the mass of the object. Weight also depends on Earth. It might seem strange to say that the weight of an object depends on something other than the object itself. But we know that the weight of an object always acts downwards, towards the Earth’s surface. This is because weight is actually the gravitational force of Earth acting on an object and attracting it towards the center of Earth. When we stand on Earth’s surface, the center of Earth is always below us. This is why no matter where we are in the world, weight always acts towards the ground.

So we’ve seen that weight always acts towards the center of Earth. But where in the object does weight act from? Weight acts from every part of an object. For example, think about lying on the beach, in the sand. When you stand up, you’ll see an impression made by your whole body, because of the force of weight acting from every point. But if we were to think about weight acting from every single point of an object, things would get very complicated very quickly. It’s much easier to think of weight as acting at a single point of an object. We call this point the center of mass.

The center of mass of an object is the average point at which weight acts on the object. So, instead of thinking about weight acting from every point, we think of it as acting from a single center of mass. Remember, even though this is called the center of mass, we’re still thinking about weight here. For simple uniform objects, the center of mass is always exactly in the center of the object. So, when we use arrows to represent the weight of these objects, we draw them starting from the center of mass and pointing towards the center of Earth.

It’s important to understand that the weight of an object does not depend on whether or not the object is moving. Let’s think about this person, who’s standing still, and imagine that we know what their weight is. Now imagine that they started to run. Their weight doesn’t change and still has the same value as when they were standing still. If they jump into the air, their weight doesn’t change. When they’re falling back down, their weight doesn’t change.

The motion of an object does not change the object’s mass or the gravitational force that acts on the object. Since weight only depends on these things, the weight of the object doesn’t change either. However, gravity can cause things to move. For example, imagine holding a ball above the ground and letting it go. If there are no objects in the way, the ball will start to fall. It’ll keep falling until it reaches the ground. As the ball falls, it accelerates. This means that its speed increases over time.

To understand this, let’s go back to the moment at which the ball is first dropped. Initially, the ball has no speed. But once it’s released, gravity will cause it to accelerate. Let’s say that a short time later, the ball has reached this position. And the same amount of time after that, the ball has reached this position. So we know the position of the ball at three equally spaced moments in time.

But if we compare the positions of the ball, we see that equal changes in time do not correspond to equal changes in distance. We can see that the distance between the third position and the second position is greater than the distance between the second position and the first position. Since the ball has traveled a greater distance in the same amount of time, we know that its speed must have increased.

So we have seen that the speed of the ball increases because gravity causes the ball to fall towards the ground. Because gravity causes things to accelerate, we can use this acceleration as a measure of gravity’s strength. Near Earth’s surface, gravity causes things to fall towards the ground with an acceleration of 9.8 meters per second squared. We call this value the acceleration due to gravity. It’s usually represented by a lowercase 𝑔.

When gravity acts on an object, that object is said to have a weight, a force which pulls it towards the center of Earth. It’s important to understand that gravity acts on all objects, even objects that aren’t falling to the ground. For example, imagine we have two identical balls held at the same height above the ground, like so. Now let’s imagine that we place a table directly underneath one of the balls so that the bottom of the ball is touching the surface of the table. Because the balls are identical, both experience identical gravitational forces. We know that the first ball will fall to the ground because of its weight, like we discussed before. The second ball, however, won’t move, because the table is in the way. Even though this ball isn’t moving, it still has a weight, just like the other ball.

Remember that weight is a force. The table is stopping the ball from falling to the ground. So the ball exerts the force of its weight on the table. There is a formula we can use to calculate the value of an object’s weight. The weight of the object is equal to the mass of the object multiplied by the acceleration due to gravity. We can write this in a shorter way as 𝑊 equals 𝑚𝑔, where 𝑊 is the weight, 𝑚 is mass, and 𝑔 is the acceleration due to gravity.

Weight is a force and can be measured in units of newtons. When we use this formula, to make sure we get the right value and the right units, we should use a mass in units of kilograms and acceleration due to gravity in units of meters per second squared. Let’s try using this formula to calculate the weight of these balls.

Let’s say that each ball has a mass of 0.5 kilograms. Earlier, we said that near Earth’s surface, acceleration due to gravity has a value of 9.8 meters per second squared. If we substitute these values into the formula, we find that the weight of each ball is equal to 0.5 kilograms multiplied by 9.8 meters per second squared. This gives us a weight of 4.9 newtons.

Notice that we didn’t need to include anything about where the ball was or whether it was moving. When the ball on the left is held in the air, its weight is 4.9 newtons. Its weight is still 4.9 newtons when it’s moving towards the ground. And it’s still 4.9 newtons after it’s hit the ground and is stationary on the floor. The ball that is resting on the table also has a weight of 4.9 newtons the whole time.

We can also note that this formula does involve the object’s mass. Just like we said before, mass and weight are related. A greater mass means the object has a greater weight. But weight is a force and mass is not. And weight also depends on the value of the acceleration due to gravity.

Now we’ve learned all about weight, let’s take a look at some example questions.

The diagram shows two objects at different positions around Earth. The force of gravity acts on the black object in the direction of the black arrow. Which color arrow correctly shows the direction in which the force of gravity acts on the green object?

This question is asking us to compare the direction of the gravitational forces acting on two objects at different points around Earth. We can recall that the gravitational force acting on an object is also known as its weight.

When we pick up an object, we can feel its weight. The force pulls the object downwards, towards the ground. We can also recall that the gravitational force pulls objects towards the center of the Earth. This is why we always feel weight acting downwards. When we’re standing on Earth’s surface, the center of the Earth is always below us.

Let’s take a look at the diagram we’ve been given in this question. We’re told that the gravitational force on the black object acts in the direction of the black arrow. This arrow is pointing towards the center of Earth. Because of where the black object is located, the arrow also happens to be pointing downwards on our screen. But the fact that it’s pointing towards the center of the Earth is the most important thing.

Now let’s look at the green object. We need to work out the direction in which the gravitational force acts on this object. And we’ve been given two options. We have the red arrow, which is pointing to the left on our screen, and the blue arrow, which is pointing downwards. We might be tempted to pick the blue arrow, because we always experience weight to be acting downwards. But we need to remember that weight is really acting towards the center of Earth.

When we’re standing on Earth’s surface, this is always below us. And so weight always acts downwards. But when we look at Earth from a zoomed-out perspective, we’ll realize that weight actually acts towards the center of Earth. In the diagram we’ve been given, we can see that the arrow pointing downwards does not point towards the center of Earth. So the blue arrow is not the correct answer.

This leaves us with the red arrow. We can see that this arrow is pointing towards the center of Earth. So the red arrow correctly shows the direction of the gravitational force on the green object. The answer to this question is “red.”

Now let’s look at another example.

Two boxes have the same mass. One box falls toward the ground from a point near the ground. The other box is at rest on the ground. In which of the following ways do the weights of the boxes compare? (A) The falling box has greater weight. (B) The falling box has less weight. Or (C) both boxes have the same weight.

In this question, we are shown two boxes. One box is at rest on the ground. The other is allowed to freely fall from a point near the ground. Recall that the weight of an object only depends on the object’s mass and the Earth, which it is attracted to. It does not depend on how it is moving.

We might recall that the strength of the gravitational force acting on an object is indicated by a quantity called acceleration due to gravity. But it’s important to remember that this is a property of Earth’s gravitational force and not a measure of the object’s motion. Since the weight of an object doesn’t depend on its motion, it doesn’t matter that one box is falling and the other is at rest. We only need to look at the mass of the objects.

The question states that both objects have the same mass. And therefore they must have the same weight. So the correct answer is option (C). Both boxes have the same weight.

Now let’s look at one final example.

An object accelerates by 9.8 meters per second squared due to gravity. The object has a mass of two kilograms. What is the weight of the object?

Recall that the weight of an object is equal to its mass multiplied by the acceleration due to gravity it is experiencing. In this question, we are told the object has a mass of two kilograms. We also know that the object accelerates by 9.8 meters per second squared due to gravity. Substituting these into our equation gives us weight equals two kilograms times 9.8 meters per second squared. This simplifies to 19.6 newtons. So the weight of the object is equal to 19.6 newtons.

Let’s finish up this video by summarizing some key points. Weight is a gravitational force acting on an object, pulling it toward the center of Earth. Since weight is a force, it can be measured in units of newtons. The weight of an object does not depend on its motion. Weight causes objects to accelerate towards the ground, unless there is something to slow or stop the object. The weight of an object is equal to its mass multiplied by the acceleration due to gravity that it experiences. The acceleration due to gravity, denoted by a lowercase 𝑔, is equal to 9.8 meters per second squared near Earth’s surface.