Energy
Canada Grade 11 Physics Revision Notes
Energy is one of the most important ideas in physics. It helps us understand how objects move, how machines operate, how vehicles use fuel, how hydroelectric systems generate electricity, and how energy changes from one form to another.
In Grade 11 Physics, you will work with kinetic energy, gravitational potential energy, work, conservation of mechanical energy, power and efficiency. These concepts are connected, so understanding their relationships is much more useful than simply memorizing formulas.
These notes are designed for Canadian Grade 11 Physics students, with a focus on the problem-solving approach used in Ontario Grade 11 Physics and applications relevant to Canadian learners.
1. What Is Energy?
Energy is the ability of a system to cause change or do work. Energy can exist in many different forms and can be transferred or transformed from one form to another.
In physics, energy is measured in joules (J).
Some common forms of energy include:
- Kinetic energy
- Gravitational potential energy
- Elastic potential energy
- Thermal energy
- Chemical energy
- Electrical energy
- Nuclear energy
- Radiant energy
In this Grade 11 unit, the main focus is on mechanical energy and its relationship with work, power and efficiency.
Rahul Sir's Key Idea: Energy is not simply "used up." It is transferred from one object or system to another or transformed into different forms.
2. Kinetic Energy
Kinetic energy is the energy an object possesses because of its motion.
The kinetic energy of an object is:
\[ E_k=\frac{1}{2}mv^2 \]
where:
- Ek = kinetic energy in joules (J)
- m = mass in kilograms (kg)
- v = speed in metres per second (m/s)
Notice that velocity is squared in the equation. This means that doubling the speed does not simply double the kinetic energy.
If speed doubles:
\[ E_k\propto v^2 \]
Therefore, doubling the speed makes the kinetic energy four times larger.
Example
A 4 kg object moves at 5 m/s.
\[ E_k=\frac{1}{2}(4)(5^2) \]
\[ E_k=2(25) \]
\[ \boxed{E_k=50\,J} \]
3. Gravitational Potential Energy
Gravitational potential energy is energy associated with an object's position in a gravitational field.
Near Earth's surface, gravitational potential energy can be calculated using:
\[ E_g=mgh \]
where:
- Eg = gravitational potential energy
- m = mass in kilograms
- g = gravitational acceleration
- h = height above the chosen reference level
Near Earth's surface:
\[ g\approx9.8\,m/s^2 \]
The choice of zero height is a reference choice. What matters in most problems is the change in gravitational potential energy.
Important: A higher object generally has greater gravitational potential energy relative to the same reference level.
4. Kinetic Energy and Potential Energy Together
Mechanical energy is often described using two major forms:
- Kinetic energy — energy of motion
- Potential energy — stored energy associated with position or configuration
Mechanical energy can therefore be written as:
\[ E_{\text{mech}}=E_k+E_p \]
For gravitational potential energy:
\[ E_{\text{mech}} = \frac{1}{2}mv^2+mgh \]
A useful way to think about this is that energy can move between kinetic and potential forms.
For example, when a ball falls:
- Gravitational potential energy decreases.
- Kinetic energy increases.
- The total mechanical energy can remain constant if energy losses are negligible.
Potential energy can transform into kinetic energy, and kinetic energy can transform into potential energy.
5. Conservation of Mechanical Energy
When only conservative forces are doing work, the total mechanical energy of a system remains constant.
Therefore:
\[ E_{\text{mech},i}=E_{\text{mech},f} \]
For a system involving kinetic and gravitational potential energy:
\[ E_{k,i}+E_{g,i} = E_{k,f}+E_{g,f} \]
Expanding the equation:
\[ \frac{1}{2}mv_i^2+mgh_i = \frac{1}{2}mv_f^2+mgh_f \]
This equation is extremely useful for objects moving under gravity when friction and other energy losses can be ignored.
Exam Tip: Before using conservation of mechanical energy, ask whether friction or another non-conservative force is doing significant work.
6. Understanding Energy Transformation
Consider a ball held at the top of a hill.
At the starting point, the ball may have high gravitational potential energy and little or no kinetic energy.
As the ball moves downward:
\[ E_g\rightarrow E_k \]
At the bottom, much of the original gravitational potential energy may have been transformed into kinetic energy.
If friction is present, some energy is also transformed into thermal energy.
Total energy is conserved, but mechanical energy may decrease when energy is transferred into thermal, sound or other forms.
7. Worked Example: Conservation of Energy
A 2 kg object is released from rest at a height of 5 m. Ignore air resistance. Find its speed just before reaching the ground.
Step 1: Identify the initial energy
The object starts from rest, so:
\[ v_i=0 \]
Therefore, its initial kinetic energy is zero.
Initial gravitational potential energy is:
\[ E_{g,i}=mgh \]
Step 2: Apply conservation of mechanical energy
\[ E_{g,i}=E_{k,f} \]
\[ mgh=\frac{1}{2}mv_f^2 \]
Notice that mass cancels:
\[ gh=\frac{1}{2}v_f^2 \]
Therefore:
\[ v_f=\sqrt{2gh} \]
\[ v_f=\sqrt{2(9.8)(5)} \]
\[ v_f\approx9.9\,m/s \]
The object's speed just before reaching the ground is approximately 9.9 m/s, assuming negligible air resistance.
8. Work in Physics
In physics, work is done when a force causes a displacement.
If a constant force acts at an angle \( \theta \) to the displacement:
\[ W=Fd\cos\theta \]
where:
- W = work in joules
- F = force in newtons
- d = displacement in metres
- θ = angle between force and displacement
The SI unit of work is the joule (J).
Force in the Same Direction
If force and displacement point in the same direction:
\[ \theta=0^\circ \]
Therefore:
\[ W=Fd \]
Force Opposite to Displacement
If the force acts opposite to the displacement:
\[ \theta=180^\circ \]
Therefore:
\[ W=-Fd \]
Friction commonly does negative work on a moving object.
Force Perpendicular to Displacement
If:
\[ \theta=90^\circ \]
then:
\[ W=0 \]
9. Work-Energy Relationship
Work provides a direct connection between force and energy.
The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.
\[ W_{\text{net}}=\Delta E_k \]
Since:
\[ \Delta E_k=E_{k,f}-E_{k,i} \]
we can write:
\[ W_{\text{net}} = E_{k,f}-E_{k,i} \]
Therefore:
- Positive net work → kinetic energy increases.
- Negative net work → kinetic energy decreases.
- Zero net work → kinetic energy remains unchanged.
10. Work and Force
Work and force are related, but they are not the same thing.
A force can act on an object without doing work if there is no displacement in the direction of that force.
For example, imagine holding a heavy object stationary. You may exert an upward force, but if the object does not move, the displacement is zero.
\[ W=Fd \]
Since:
\[ d=0 \]
the work done by that force is:
\[ W=0 \]
Exam Tip: Do not assume that a large force automatically means large work. Displacement and the direction of the force also matter.
11. Power
Power describes how quickly work is done or energy is transferred.
Average power is:
\[ P=\frac{W}{t} \]
where:
- P = power
- W = work
- t = time
The SI unit of power is the watt (W).
\[ 1\,W=1\,J/s \]
A machine that performs the same amount of work in less time has a greater power output.
Power from Force and Velocity
When a force acts in the direction of motion:
\[ P=Fv \]
More generally:
\[ P=Fv\cos\theta \]
12. Worked Example: Power
A machine performs 6000 J of work in 20 seconds. Find its average power output.
Step 1: Identify the values
\[ W=6000\,J \]
\[ t=20\,s \]
Step 2: Use the power equation
\[ P=\frac{W}{t} \]
Step 3: Substitute
\[ P=\frac{6000}{20} \]
\[ \boxed{P=300\,W} \]
The machine has an average power output of 300 W.
13. Efficiency
No real machine converts all of its input energy into useful output energy. Some energy is transferred into unwanted or less useful forms, such as thermal energy or sound.
Efficiency compares useful output energy with the total input energy.
\[ \text{Efficiency} = \frac{\text{Useful Output Energy}} {\text{Total Input Energy}} \times100\% \]
Efficiency can also be expressed using power:
\[ \text{Efficiency} = \frac{\text{Useful Output Power}} {\text{Total Input Power}} \times100\% \]
An ideal machine would have:
\[ \text{Efficiency}=100\% \]
Real machines generally have efficiencies below 100%.
14. Worked Example: Efficiency
A machine receives 5000 J of energy and produces 3500 J of useful output energy. Calculate its efficiency.
Step 1: Use the efficiency equation
\[ \text{Efficiency} = \frac{E_{\text{useful}}} {E_{\text{input}}} \times100\% \]
Step 2: Substitute
\[ \text{Efficiency} = \frac{3500}{5000} \times100\% \]
\[ \text{Efficiency}=70\% \]
Therefore, the machine has an efficiency of 70%.
The remaining energy has been transferred into other forms.
15. Efficiency in Real-World Systems
Efficiency is important when studying real technologies and energy systems.
For example, engineers may compare the efficiency of:
- Electric motors
- Hydroelectric systems
- Wind turbines
- Solar energy systems
- Transportation systems
- Heating and cooling systems
Canadian students may encounter energy-efficiency examples involving transportation, buildings, electrical systems and renewable energy.
Improving efficiency means obtaining more useful output for the same amount of input energy.
16. Work, Energy and Power: The Difference
These three terms are related but should not be confused.
| Quantity | Meaning | Formula | SI Unit |
|---|---|---|---|
| Energy | Ability to cause change or do work | Depends on the type | J |
| Work | Energy transferred by a force through displacement | \(W=Fd\cos\theta\) | J |
| Power | Rate of energy transfer or work done | \(P=W/t\) | W |
Memory Trick:
Energy → how much.
Work → energy transferred.
Power → how quickly.
17. Energy Conservation with Friction
Students often make the mistake of saying that energy is not conserved when friction is present.
Energy is still conserved. However, mechanical energy is transferred into other forms.
For example, when a sled moves across snow:
\[ E_{\text{mechanical}} \rightarrow E_{\text{thermal}} \]
Therefore, if friction acts:
\[ E_{\text{mech},i} \neq E_{\text{mech},f} \]
But total energy remains conserved when all relevant forms of energy are included.
Important: "Mechanical energy is not conserved" does not mean "energy is not conserved."
18. Common Energy Mistakes
Mistake 1: Confusing Energy and Power
Energy is measured in joules. Power is measured in watts.
Mistake 2: Forgetting the Square in Kinetic Energy
\[ E_k=\frac{1}{2}mv^2 \]
Velocity or speed must be squared.
Mistake 3: Using \(mgh\) Without Thinking About the Reference Level
Potential energy depends on the chosen reference height. Energy differences are often more important than the absolute value.
Mistake 4: Assuming Mechanical Energy Is Always Conserved
Friction and other non-conservative forces can transfer mechanical energy into other forms.
Mistake 5: Confusing Work with Force
A force does not necessarily do work. Displacement and the direction of the force must also be considered.
Mistake 6: Forgetting the Percentage in Efficiency
If the efficiency equation gives a decimal such as 0.75, multiply by 100 to express it as 75%.
19. A Reliable Energy Problem-Solving Method
\[ E_k=\frac{1}{2}mv^2 \]
\[ E_g=mgh \]
\[ W=Fd\cos\theta \]
\[ P=\frac{W}{t} \]
- Identify the system. Decide which objects and forms of energy are relevant.
- List the initial and final conditions. Look for speed, height, mass and other relevant information.
- Identify the energy forms. Ask whether you have kinetic energy, gravitational potential energy, work, thermal energy or another form.
- Check for energy losses. Determine whether friction or another non-conservative force is involved.
- Choose the appropriate equation.
- Substitute values with correct units.
- Check your answer. Ask whether the result makes physical sense.
20. Grade 11 Energy Formula Sheet
Kinetic Energy
\[ E_k=\frac{1}{2}mv^2 \]
Gravitational Potential Energy
\[ E_g=mgh \]
Mechanical Energy
\[ E_{\text{mech}}=E_k+E_p \]
Conservation of Mechanical Energy
\[ E_{k,i}+E_{p,i} = E_{k,f}+E_{p,f} \]
Work
\[ W=Fd\cos\theta \]
Work-Energy Theorem
\[ W_{\text{net}}=\Delta E_k \]
Power
\[ P=\frac{W}{t} \]
Power from Force and Velocity
\[ P=Fv\cos\theta \]
Efficiency
\[ \text{Efficiency} = \frac{\text{Useful Output Energy}} {\text{Input Energy}} \times100\% \]
Gravitational Acceleration
\[ g\approx9.8\,m/s^2 \]
21. Quick Revision Checklist
Before your Grade 11 Physics assessment, make sure you can:
- Define energy.
- Calculate kinetic energy.
- Explain how mass affects kinetic energy.
- Explain how speed affects kinetic energy.
- Calculate gravitational potential energy.
- Explain the importance of a reference level.
- Distinguish kinetic and potential energy.
- Apply conservation of mechanical energy.
- Recognize when friction affects mechanical energy.
- Calculate work done by a constant force.
- Determine whether work is positive, negative or zero.
- Apply the work-energy theorem.
- Calculate power.
- Explain the difference between energy and power.
- Calculate efficiency.
- Interpret energy transformations.
- Use correct SI units.
- Check whether an answer is physically reasonable.
22. Rahul Sir's Final Revision Tip
Energy problems become much easier when you stop looking at them as separate formulas and start thinking about energy transformations.
Ask yourself:
Where is the energy at the beginning?
Where does it go?
Where is the energy at the end?
If an object is moving, think about kinetic energy:
\[ E_k=\frac{1}{2}mv^2 \]
If an object is at a height, think about gravitational potential energy:
\[ E_g=mgh \]
If a force moves an object through a distance, think about work:
\[ W=Fd\cos\theta \]
If the question asks how quickly energy is transferred, think about power:
\[ P=\frac{W}{t} \]
And if you are comparing useful output with the energy supplied, think about efficiency:
\[ \text{Efficiency} = \frac{\text{Useful Output}} {\text{Input}} \times100\% \]
The most important relationship to remember is:
Energy can be transferred and transformed, but the total energy of an isolated system is conserved.
For Grade 11 Physics, focus on understanding the difference between kinetic energy, potential energy, work, power and efficiency. Once you understand what each quantity represents, choosing the correct equation becomes much easier.
Remember:
Energy → how much.
Work → energy transferred.
Power → how quickly.
Efficiency → how much useful output you get from the input.
Keep practising numerical problems, write down your known quantities, use SI units, and always ask yourself where the energy is going.
Understand the energy transformation first. The formula will follow.
— Rahul Sir | ODTutor Canada
