*Contributor: Jay Gregorio. Lesson ID: 13255*

Put in the work learning what work really means in physics. Spoiler alert: It is not the same as the everyday definition! Discover the differences and how to calculate things like force and weight!

categories

subject

Science

learning style

Kinesthetic, Visual

personality style

Beaver

Grade Level

Middle School (6-8), High School (9-12)

Lesson Type

Dig Deeper

Take a look at the picture above.

- If you are holding a book with your hand, are you doing work?

You probably think that holding a book requires effort because you have to support its weight. Therefore, you are tempted to answer yes.

Surprisingly, that is not the case when we describe *work* in physics. Regardless of how long you hold the book with your hand, you are never doing work.

- Why is that?
- How does physics define work?

Let's find out!

The term *work* is used a lot in our everyday language.

When you spend hours on a school project, it is hard work. When you complete a task and do a good job, you are described as hardworking.

In short, the word *work* is used whenever there is a physical effort. Physics, however, thinks about work in a different way.

**What Is Work in Physics?**

Let us go back to the example of holding a book. In physics, this situation has no work done. Let's explain why.

Physics defines work as *a product of force and displacement along the direction of the force*.

Mathematically, it is expressed as:

In symbols:

Based on this formula, for work to be done, there must be a force involved, and this force must move the object along its direction causing displacement.

These are the two requirements to conclude that work is done.

- When you use your palm to support the weight of the book, is there force?

The answer is yes. The direction of the force is upward. Since there is force, we satisfy the first requirement for work done.

- Did the object move along the direction of the force and have a displacement?

The answer is no. Therefore, you are unable to satisfy both requirements for work to be done. So, work done is zero.

Now, let's consider a situation where you lift a book from a tabletop:

- When you lift the book, is there force?

The answer is yes. The direction of the force is upward.

- Did the object move along the direction of force causing displacement?

The answer is yes. When you lift a book, the force you apply is upward and the book will move from the tabletop up to a certain height.

In this case, we are able to satisfy both requirements. Therefore, work is done!

It important to note here that displacement is not the same as distance. Look at the diagram below:

The first man walked 3m in a circle, so there was no displacement. The second man walked 3m in a straight line, so the distance and the displacement are both 3 m.

**Calculating Work Done**

Now that you know the requirements for work to be done on an object, let's talk about calculating work.

In the formula W = F * d:

- the force (F) is measured in the unit Newton (N)
- and displacement (d) is measured in the unit meter (m)

Both Newton (N) and meter (m) are examples of the SI unit of measure, or international system of measurement.

If you multiply these two quantities, the resulting unit would be a Newton-meter (Nm). This combined unit is equivalent to a unit called joule (J), which is a measure of energy.

Yes, work done on an object is an example of energy transfer!

Let's look at our example.

If the amount of force needed to lift the book from the tabletop is 10 N, and this force resulted in an upward displacement of 0.5 m:

W = F * d

W = 10 N * 0.5 m

W = 5 Nm or 5J

This means that it would require 5J of energy to lift the book 0.5 m from the tabletop.

You may encounter problems where the work done is given, and you are asked to determine the amount of force or the displacement of the object.

For these situations, all you have to do is rearrange your equation:

- you can find force using F = W ÷ d
- you can find the displacement using d = W ÷ F

These rearrangements are illustrated in the work formula triangle below. Note that this triangle can only be used if the equation involves three quantities only.

If you want to learn more about work done on objects, explore the **Additional Resources** found in the right-hand sidebar.

It is important to note that there are different kinds of force that may result in displacement. In fact, your own weight is a force; so when you move up or down a flight of steps, you are doing work yourself!

- How is that possible?

First, you have to understand how you can calculate your weight in physics. Just like work, weight has a different meaning here.

**Calculating Your Weight**

When you step on a bathroom scale, you see a measurement of your mass. (In America, this is generally in pounds. In physics, we use kilograms. One kilogram equals 2.20462 pounds.)

In physics, your weight (W) is a force that you exert downward toward the earth because of gravity's effect (g) on your mass (m).

- How do you know your weight (W)?

You step on your scale to find your mass (m) in kilograms (kg). This number in kilograms (kg) must then be multiplied by 9.8 meters per square seconds (m/s^{2}), which is the gravitational constant (g) on earth. And because weight is a force, it is measured in Newtons (N).

To explain this further, let's do a simple math example!

Frank steps on his bathroom scale, and the reading says that his mass (m) is 80.0 kg. To get Frank's weight (W), we must multiply this reading with the gravitational constant (g) of 9.8 m/s^{2}.

Weight (W) = mass (m) * gravitational constant (g)

W = m * g

W = 80.0 kg * 9.8 m/s^{2}

W = 784.0 kg m/s^{2} or 784.0 N

In this example, the weight of 784.0 N is the amount of force Frank exerts downward onto the earth!

Your weight is useful information if you want to know how much work you can do.

If you are playing basketball and jump to shoot the ball into the basket, the height of your jump can be used as a displacement. Remember that you only need force (your weight) and a displacement (height of your jump) to calculate work done!

If you want to learn more about weight in physics, explore the **Additional Resource** found in the right-hand sidebar.

In the *Got It?* section, you will review these concepts and determine how much you've learned! Move on whenever you're ready.