Did you know that work is a form of energy?

C2.1 45 pound weight being lifted

You should recall from previous studies that force is a push or pull. Think about how much force you would have to exert to lift a 20 kilogram weight from the ground to above your head. How does force relate to work and energy? What if I told you that you would have to do no work to hold that weight above your head once it is there? Does that sound right?

By the end of this lesson, you will be able to

recall, from previous studies, that force is a push or pull and that work is energy used to increase the speed of an object or move an object against a force
calculate «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mi»W«/mi» «mo»=«/mo» «mi»F«/mi» «mi»d«/mi» «/math» and show that a change in energy is equal to work done on a system: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mo»§#8710;«/mo» «mi»E«/mi» «mo»=«/mo» «mi»W«/mi» «/math»
derive the «math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «mi»SI«/mi» «/math» unit of energy and work, the joule, from fundamental units and explain where the joule comes from

Gravity, Force, and Work © YouTube phoenixfilmandvideo

This video clip provides you with an overview of the concepts of gravity, force, and work. This will help get you in the right mindset for this lesson.

Force and work are related to one another, and it is important to understand each one.

C2.2 Baseball hit

Force

A force is defined as a push or pull on an object. Force is measured in the units of newtons (N).

An object at rest tends to stay at rest, unless acted upon by an outside force. What does this mean?

Think of a soccer player waiting to start a play by kicking a ball that is at rest into play. The ball is at rest because there are no unbalanced forces acting on it. When the player kicks the ball, an unbalanced force is applied to it over a distance, so it moves.

An unbalanced force is when the force acting in one direction is greater than the force acting in the opposite direction.

C2.3 Soccer ball at rest

C2.4 Gravel pathway

Now, think of the player walking home from soccer practice kicking the ball along the gravel pathway. When she kicks the soccer ball, why does it not just keep travelling forever on the pathway? Why does it slow down and stop every few metres until the player kicks it again?

An object in motion tends to stay in motion, moving along at a constant speed and in a straight line, unlesss acted upon by an outside force. How does this apply to the soccer ball on the gravel pathway?

The friction that occurs between the moving soccer ball and the uneven surface of the gravel pathway, slows the motion of the ball down. An unbalanced force (friction) is applied to the ball in the opposite direction to the ball’s movement, slowing the speed of the ball. Without the resistive force, the ball could keep moving.

When the ball is kicked from rest, energy from the soccer player’s movement is transferred to the ball, allowing it to move. When the soccer ball is travelling along the gravel pathway, energy from the ball is transferred to the ground through friction, preventing it from continuing to move.

Basically, if energy is used to apply a force to an object over a distance and the object then changes in some way, force and energy are related.

Work

C2.5 Children playing with a wagon

Work is done on an object whenever a force moves an object a distance and the distance is in the direction of the force.

Work is done on an object if three conditions are met:

There must be movement of the object.
There must be a force exerted on the object.
The force and the distance the object travels must be in the same direction.

When determining if work is done in a scenario, all three conditions must be met in order to say work has been done.

Please read pages 156 and 157 in your Science 10 textbook. Make sure you take notes on your readings to study from later. You should focus on what effect unbalanced forces can have on an object depending upon its initial conditions and what work is and how we determine if work is done. Remember, if you have any questions or do not understand something, ask your teacher!

Complete the following practice questions to check your understanding of the concept you just learned. Make sure you write complete answers to the practice questions in your notes. After you have checked your answers, make corrections to your responses (where necessary) to study from.

For each of the following scenarios, indicate whether unbalanced forces are present that will affect the movement of the object.

A book is shoved across a table and slows down.
A canoe is floating in a lake.
A child climbs onto one end of an unoccupied seesaw.

Check your work.

A book is shoved across a table and slows down. (unbalanced forces)
A canoe is floating in a lake. (balanced forces)
A child climbs onto one end of an unoccupied seesaw. (unbalanced forces)

For each of the following scenarios, indicate whether work is being done.

A caretaker pushes a mop across the floor.
A person in a wheelchair coasts down a ramp.
A horse pulls a carriage during a race.
A boy carries a book from his desk to the shelf.

Check your work.

A caretaker pushes a mop across the floor. (Work is done.)
A person in a wheelchair coasts down a ramp. (Work is not done by the person in the wheelchair—coasting does not require a force to be exerted.)
A horse pulls a carriage during a race. (Work is done on the carriage by the horse.)
A boy carries a book from his desk to the shelf. (Work is not done by the boy on the book—the force required for the book to be held and carried is up while the boy travels forward with the book. So the force acting on the book and the direction of movement are not in the same direction.)

How is the amount of work done in a system calculated?

C2.6 Calculator and pencil

Remember that work is done on an object whenever a force moves an object a distance and the distance is in the direction of the force.

\begin{array}{rcl} work & = & force \times distance the object travels \\ W & = & F d \end{array}

Work is a measurement of energy, so its units is the joule (J). It can also be expressed as a unit of newton × metre (N·m).

1 joule (J) = newton \times metre Note : 1 newton (N) = \frac{kg \cdot m}{s^{2}} So, 1 J = \frac{1 kg \cdot m}{s^{2}} \times m 1 J = 1 \frac{kg \cdot m^{2}}{s^{2}}

In previous science studies and in Unit B, you were taught about the importance of expressing your final answer in calculation questions to the correct number of significant digits.

Guidelines for Significant Digits, Manipulation of Data, and Rounding in Science

Significant Digits (measured values)

For all non-logarithmic values, regardless of decimal position, any of the digits 1 to 9 is a significant digit; 0 may be significant. For example:

123 0.123 0.002 30 2.30 × 10³ 2.03
All of these have three significant digits.
Leading zeros are not significant. For example:

0.12 and 0.012 each have two significant digits.
All trailing zeros are significant. For example:

200 has three significant digits.
0.123 00 and 20.000 each have five significant digits.

Manipulation of Data

When adding or subtracting measured quantities, the calculated answer should be rounded to the same degree of precision as that of the least precise number used in the computation if this is the only operation. For example in the following addition:

12.3 (least precise) 0.12 \frac{12.34}{24.76}

When multiplying or dividing measured quantities, the calculated answer should be rounded to the same number of significant digits as are contained in the quantity with the fewest number of significant digits if this is the only operation. For example:

(1.23)(54.321) = 66.814 83

The answer should be rounded to 66.8.
When a series of calculations is performed, each interim value should not be rounded before carrying out the next calculation. The final answer should then be rounded to the same number of significant digits as are contained in the quantity in the original data with the fewest number of significant digits. For example:

In determining the value of (1.23)(4.321) / (3.45 − 3.21), three calculations are required

3.45 − 3.21 = 0.24
(1.23)(4.321) = 5.314 83
5.314 83 / 0.24 = 22.145 125
[Not 5.31 / 0.24 = 22.125]

The value should be rounded to 22.1.

Note: In the example given, steps a and b yield intermediate values. These values should not be used in determining the number of significant digits.

When calculations involve exact numbers (counted and defined values), the calculated answer should be rounded based upon the precision of the measured value(s). For example:

12 eggs × 52.3 g/egg = 627.6 g
or
5 mol × 32.06 g/mol = 160.30 g
or
(1 mol)(–1 095.8 kJ/mol) + (2 mol)(40.8 kJ/mol) = –1 014.2 kJ

Rounding

When the first digit to be dropped is less than or equal to 4, the last digit retained should not be changed. For example:

1.234 5 rounded to three digits is 1.23.
When the first digit to be dropped is greater than or equal to 5, the last digit retained should be increased by one. For example:

12.25 rounded to three digits is 12.3.

Examples

Example 1

What work is done by a forklift raising a 5 720 N box 1.4 m?
- Step 1
- Step 2
- Step 3
- Step 4
Step 1: List the variables.

$\begin{array}{rcl} W & = & ? \\ F & = & 5 720 N \\ d & = & 1.4 m \end{array}$

Step 2: Identify the correct formula and rearrange if necessary.

W = Fd

Step 3: Substitute the values into the formula.

W = (5 720 N)(1.4 m)

Step 4: Calculate the answer.

W = 8 000 J

The answer must be rounded to two significant digits.

8 000 J cannot be rounded to 2 significant digits, so it must be put into scientific notation.
Move the decimal point to the left until your answer is between 1 and 10.
8 008: Move the decimal three places to the left to become $8.008$ .
Three decimals to the left is indicated by a 10³(“3” for moving three places to the left).
Round the value of 8.008 to two significant digits: 8.0.

The amount of work done by the forklift is 8.0 × 10³ J.

Example 2

A force of 825 N is needed to push a car across a lot. Two students push the car 32 m.

How much work is done?
- Step 1
- Step 2
- Step 3
- Step 4
Step 1: List the variables.

$\begin{array}{rcl} W & = & ? \\ F & = & 825 N \\ d & = & 32 m \end{array}$

Step 2: Identify the correct formula and rearrange if necessary.

W = Fd

Step 3: Substitute the values into the formula.

W = (825 N)(32 m)

Step 4: Calculate the answer.

W = 26 400 J

The answer must be rounded to two significant digits.

26 400 J cannot be rounded to two significant digits, so it must be put into scientific notation.
Move the decimal point to the left until your answer is between 1 and 10.
26 400: Move the decimal four places to the left to become 2.640 0.
Four decimals to the left is indicated by a 10⁴(“4” for moving four places to the left).
Round the value of 2.640 0 to two significant digits: 2.6.

The amount of work done by the two students is 2.6 × 10⁴ J.
After a rainstorm, the force needed to push the car doubled because the ground became softer. How does the amount of work done by the students change?
- Step 1
- Step 2
- Step 3
- Step 4
Step 1: List the variables.

$\begin{array}{rcl} W & = & ? \\ F & = & 825 N \times 2 \\ d & = & 32 m \end{array}$

Step 2: Identify the correct formula and rearrange if necessary.

W = Fd

Step 3: Substitute the values into the formula.

W = (825 N)(2)(32 m)

Step 4: Calculate the answer.

W = 52 800 J

The answer must be rounded to two significant digits.

52 800 J cannot be rounded to two significant digits, so it must be put into scientific notation.
Move the decimal point to the left until your answer is between 1 and 10.
52 800: Move the decimal four places to the left to become 5.280 0.
Four decimals to the left is indicated by a 10⁴(“4” for moving four places to the left).
Round the value of 5.280 0 to two significant digits: 5.3.

The amount of work done by the two students is 5.3 × 10⁴ J.

If the amount of force doubles, then the amount of work done also doubles.

Example 3

A delivery clerk must carry a 34 N package from the ground floor to the third floor of an apartment building. If it is determined that he did 306 J of work carrying the package, what height did he carry the package to?
- Step 1
- Step 2
- Step 3
- Step 4
Step 1: List the variables.

$\begin{array}{rcl} W & = & 306 J \\ F & = & 24 N \\ d & = & ? \end{array}$

Step 2: Identify the correct formula and rearrange if necessary.

W = Fd

To isolate d, you must divide each side by F. To move F to the other side, you must use the opposite operation. Division is opposite to multiplication.

$\frac{W}{F} = \frac{F d}{F}$

Now, cancel the like terms.

$\frac{W}{F} = d or d = \frac{W}{F}$

Step 3: Substitute the values into the formula

$d = \frac{306 J}{34 N}$

Step 4: Calculate the answer.

d = 9 m

The answer must be rounded to two significant digits.

The height that the delivery clerk carried the package was 9.0 m.

Example 4

How much energy must a person use to push a 25 N rock a distance of 1.72 m?

Work is a measurement of energy. So, the amount of work done to push the rock will be equal to the amount of energy the person must use.
- Step 1
- Step 2
- Step 3
- Step 4
Step 1: List the variables.

$\begin{array}{rcl} W & = & ? \\ F & = & 25 N \\ d & = & 1.72 m \end{array}$

Step 2: Identify the correct formula and rearrange if necessary.

W = Fd

Step 3: Substitute the values into the formula.

W = (25 N)(1.72 m)

Step 4: Calculate the answer.

W = 43 J

The answer must be rounded to two significant digits.
The amount of energy the person must use is 43 J.

Please read page 106 in your Science 10 textbook. Make sure you take notes on your readings to study from later. You should focus on how the amount of work can be calculated using the W = Fd formula. Remember, if you have any questions or do not understand something, ask your teacher!

Complete the following practice questions to check your understanding of the concept you just learned. Make sure you write complete answers to the practice questions in your notes. After you have checked your answers, make corrections to your responses (where necessary) to study from.

A student pushes a book 65 cm across a desk by applying a constant force of 27 N. How much work does the student do?

Check your work.

Step 1: List the variables.

\begin{array}{rcl} W & = & ? \\ F & = & 27 N \\ d & = & 65 cm = 0.65 m (65 cm \times \frac{1 m}{100 cm}) \end{array}

If you need to review how to do unit conversions, see this video.

Step 2: Identify the correct formula and rearrange if necessary.

W = Fd

Step 3: Substitute the values into the formula.

W = (27 N)(0.65 m)

Step 4: Calculate the answer.

W = 17.55 J

The answer must be rounded to two significant digits.
The amount of work the student does is 18 J.

Step 1: List the variables.

\begin{array}{rcl} W & = & ? \\ F & = & 27 N \\ d & = & 65 cm = 0.65 m (65 cm \times \frac{1 m}{100 cm}) \end{array}

If you need to review how to do unit conversions, see this video.

Step 2: Identify the correct formula and rearrange if necessary.

W = F d

Step 3: Substitute the values into the formula.

W = (27 N) (0.65 m)

Step 4: Calculate the answer.

W = 17.55 J

The answer must be rounded to two significant digits.
The amount of work the student does is

18 J .

A boy pulls a 12 kg box on a horizontal surface and uses 179 J of work to move the box 4.2 m. How much force did the boy exert on the box?

Check your work.

Step 1: List the variables.

\begin{array}{rcl} W & = & 179 J \\ F & = & ? \\ d & = & 4.2 m \end{array}

Step 2: Identify the correct formula and rearrange if necessary.

W = Fd

To isolate F, you must divide each side by d. To move d to the other side, you must use the opposite operation.

\frac{W}{d} = \frac{F d}{d}

Now, cancel the like terms.

\frac{W}{d} = F or F = \frac{W}{d}

Step 3: Substitute the values into the formula.

F = \frac{179 J}{4.2 m}

Step 4: Calculate the answer.

F = 42.619...N

The answer must be rounded to two significant digits.
The force the boy exerted on the box was 43 N.

Forces and Motion © 2017 PhET

This simulation activity has you investigate forces, both balanced forces and unbalanced forces. You will then relate this to work done.

You and some friends are at the park. You find some rope and decide you’d like to play a game of tug-of-war. Unfortunately, there are five people, so you can’t have an equal amount of people on each side. One of your friends suggests that the two biggest people should be on one side, while the three smaller people should be on the other side. Do you think this is a fair way to split up the teams? Why or why not?

Procedure
Analysis

Click on the play button to open the activity. This interactive can also be accessed at https://quick.adlc.ca/force Select the “Net Force” icon.

Task 1: Place two people that are the same size on opposite sides of the cart and the same distance away from the cart.

Make a prediction about the movement of the cart.

AFTER you have observed the actual movement, click on the sum of the forces box at the top right-hand corner of the simulation. Record the number in the data chart.

	Predicted Movement	Actual Movement (none, left, right)	Sum of Forces (0, x-left, x-right)
Same size, same placement on rope. C2.7 Same size, same placement on rope

Check your work.

	Predicted Movement	Actual Movement (none, left, right)	Sum of Forces (0, x-left, x-right)
Same size, same placement on rope. C2.7 Same size, same placement on rope		none	0

Task 2: Place two people that are the same size different distances away from the cart.

Make a prediction about the movement of the cart.

AFTER you have observed the actual movement, click on the sum of the forces box at the top right-hand corner of the simulation. Record the number in the data chart.

	Predicted Movement	Actual Movement (none, left, right)	Sum of Forces (0, x-left, x-right)
Same size, different placement on rope. C2.8 same size, different placement on rope

Check your work.

	Predicted Movement	Actual Movement (none, left, right)	Sum of Forces (0, x-left, x-right)
Same size, different placement on rope. C2.8 same size, different placement on rope		none	0

Task 3: Place two people that are different sizes the same distance away from the cart.

Make a prediction about the movement of the cart.

AFTER you have observed the actual movement, click on the sum of the forces box at the top right hand corner of the simulation. Record the number in the data chart.

	Predicted Movement	Actual Movement (none, left, right)	Sum of Forces (0, x-left, x-right)
Different size, same placement on rope. C2.8a different size, same placement on rope

Check your work.

	Predicted Movement	Actual Movement (none, left, right)	Sum of Forces (0, x-left, x-right)
Different size, same placement on rope. C2.8a different size, same placement on rope		left	x-left

Task 4: Place two people that are the different sizes different distances away from the cart.

Make a prediction about the movement of the cart.

AFTER you have observed the actual movement, click on the sum of the forces box at the top right-hand corner of the simulation. Record the number in the data chart.

	Predicted Movement	Actual Movement (none, left, right)	Sum of Forces (0, x-left, x-right)
Different size, different placement on rope. C2.9 different size, different placement on rope

Check your work.

	Predicted Movement	Actual Movement (none, left, right)	Sum of Forces (0, x-left, x-right)
Different size, different placement on rope. C2.9 different size, different placement on rope		left	x-left

Please return to the top of this page and click on analysis to complete the analysis questions.

Which of the tasks represented balanced forces? Which of the tasks represented unbalanced forces?

Check your work.

The balanced forces were seen in tasks 1 and 2; the unbalanced forces were seen in tasks 3 and 4.
Do balanced or unbalanced forces cause a change in motion? Explain.

Check your work.

Unbalanced forces cause a change in motion; when there are unbalanced forces, an object’s motion can be changed.
Now that you have had a chance to experiment with the simulation, go back to the question at the beginning of the investigation. What do you think would be the best way to divide up your friends for the game of tug-of-war? Explain your reasoning.

Check your work.

Use this answer for question 8 in Assignment C1.
In which of the tasks was work done by the people on the cart? Explain.

Check your work.

Use this answer for question 9 in Assignment C1.

The relationship between force and work is an important one to understand.

C2.9 Boy playing tug-of war with dog

Knowing that force is a push or pull on an object, you can predict if the forces are unbalanced or balanced and how that will affect an object. At the start of the lesson, this question was posed: What if I told you that you would have to do no work to hold that weight above your head once it is there? You now know that this is indeed true, because in order for work to be done on the weight, it needs to be moving a distance.

In this Interactive, you will analyze the motion of a cart being pulled up an inclined plane at a constant speed. The angle of the incline will be modified by 10° increments. In each simulation, the cart is pulled to the same height: 1.0 metre above the original starting position.

To determine the effect of the angle of an inclined plane upon the amount of force and the amount of work done when pulling a cart up an inclined plane at a constant speed and to the same height.

Please click on the procedure tab to continue.

Click on the play button to open the Interactive. This interactive can also be accessed at https://quick.adlc.ca/uphill (There is a small hot spot in the top left corner. Clicking/tapping the hot spot opens the Interactive in full-screen mode. (Use the “Esc” key on a keyboard (or comparable method) to exit from full-screen mode.)
Select the 4.0 kg mass choice. Choose the angle of 30.0°.
Tap the “Run Trial” button. The force required to pull the cart at a constant speed is displayed on the screen; record this in the Data Table.
The displacement (distance) from the starting position to the final position can be measured using the cm scale; record this in the Data Table. (Note that the table lists metres as the unit; 100 cm = 1.00 m.)

To convert from centimetres to metres, divide the centimetre value by 100.

For example:

«math»«mtable columnspacing=¨0px¨ columnalign=¨right center left¨»«mtr»«mtd»«mn»45«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»cm«/mi»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mo»?«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»45«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»cm«/mi»«mo»§#215;«/mo»«mfenced»«mfrac»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mrow»«mrow»«mn»100«/mn»«mo»§#160;«/mo»«mi»cm«/mi»«/mrow»«/mfrac»«/mfenced»«/mtd»«mtd»«mo»=«/mo»«/mtd»«mtd»«mn»0«/mn»«mo».«/mo»«mn»45«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mtd»«/mtr»«/mtable»«/math»
The force and the displacement directions are both going parallel to the inclined plane. Use the force and displacement to calculate the work done. Remember that W = Fd.
Repeat the procedure for all angles.
Please click on the observations tab to continue.

Angle (°)	Force (N)	Displacement (m)	Work (J)
30.0
40.0
40.0
60.0
70.0
80.0
90.0

Check your work.

Angle (°)	Force (N)	Displacement (m)	Work (J)
30.0	19.6	2.0	39.2
40.0	25.2	1.5	37.8
50.0	30.0	1.3	39.0
60.0	33.9	1.1	37.3
70.0	36.8	1.0	36.8
80.0	38.6	1.0	38.6
90.0	39.2	1.0	39.2

Sample calculation for an angle of 30.0°:

«math»«mn»200«/mn»«mo»§#160;«/mo»«mi»cm«/mi»«mo»§#215;«/mo»«mfenced»«mfrac»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»m«/mi»«/mrow»«mrow»«mn»100«/mn»«mo»§#160;«/mo»«mi»cm«/mi»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mn»2«/mn»«mo».«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»m«/mi»«/math»

W = Fd = (19.6N)(2.0 m) = 39.2 J

Please click on the analysis tab to complete the analysis questions.

Describe how varying the incline angle affects the force.

Check your work.

As the incline angle increases, the amount of force increases.
Describe how varying the incline angle affects the work.

Check your work.

The incline angle does not seem to have a noticeable effect on the work value.
When a force does work, the object’s energy will change. In this interactive, does the work cause a kinetic energy change or a potential energy change?

Check your work.

Use this answer for question 10 in Assignment C1.

Crossword Puzzle

Download the PDF version and complete the crossword. This crossword will give you practice with the different forms of energy, scientists, and terminology.

Check your work.

Unit 3 Assignment Lessons 2-4

It is now time to complete the Lesson 3 portion of 3.2 Assignment. This assignment has two parts.

Part 1 Written Portion: Select the preferred document type from the options below. Download and save the assignment on your desktop (or documents folder).

PDF Document
Open and print this saved document.
Record your responses in the appropriate textboxes.
When you have completed the assignment, scan it and save it on your desktop (or documents folder).
Once you have completed the written portion of your assignment, click on the button below to go to the submission page.

Written Portion Submission Page
Part 2 Online Portion: It is now time to complete the online portion of this assignment. Click on the button below to go to the online questions of this assignment.

Online Questions

This assignment is worth ___% of your final grade.

Site:	MoodleHUB.ca 🍁
Course:	Science 10 [5 cr] - AB Ed copy 1
Book:	Lesson 2 Work and Energy

Printed by:	Guest user
Date:	Sunday, 7 September 2025, 6:43 PM

Lesson 2 Work and Energy

Table of contents

Introduction

Did you know that work is a form of energy?

Did you know that work is a form of energy?

Targets

Watch This

Gravity, Force, and Work © YouTube phoenixfilmandvideo

Operational Definitions of Work and Force

Force and work are related to one another, and it is important to understand each one.

Force and work are related to one another, and it is important to understand each one.

Read This

Practice Questions

Calculation of Work

How is the amount of work done in a system calculated?