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2.3. Work, Energy and Power

You were probably introduced to the idea of energy pretty early on in your Physics education, by looking at types of energy and energy transfers. You will have heard of the Conservation of Energy - the idea that energy can never be created or destroyed, only transferred. This idea fundamentally underpins our understanding in Physics. But what exactly is energy? Look up online and most sources will tell you that energy is the 'ability to do work'. However, the logic is somewhat circular, as if you search for 'work' it will tell you that is energy transferred. In practice, energy is an extremely useful quantitative property that allows is given tomeaning through its use in calculations 

Take a look at the Crash Course Physics video below which introduces some of these key ideas.

The section is broken up as follows:

 

Conservation of Energy

To begin this study into ideas to do with energy, let's look at something called a perpetual motion machine. Perpetual motion machines are a hypothetical device that producing motion that can do work indefinitely (i.e. keep moving) without an energy source. A machine of this kind is impossible in practice, as it violates one of the fundamental physical laws of the universe - the Conservation of Energy. Energy will always be lost to the surroundings, so eventually the kinetic energy will decrease until the machine grinds to a halt.

​There a number of different types of energy that we have previously considered at GCSE. Energy can be transferred from one for to another, between these different types.

  • chemical - energy stored between chemical bonds

  • heat - energy in warm objects, stored as the kinetic and potential energy of vibrating molecules

  • electrical - energy transfer through moving charges

  • magnetic - energy stored when magnetic poles are pushed together or moved apart

  • sound - the energy in vibrating molecules

  • light - energy transferred through light waves

  • elastic potential - energy stored when a material is stretched/ squashed 

  • kinetic - energy stored in a moving mass

  • gravitational potential - energy stored by an object at height

  • nuclear - potential energy in the binding forces of the nucleus

 

Energy is an example of a scalar quantity, which means these quantities have magnitude only.

The Conservation of Energy states that:

"In a closed system, the total amount of energy must remain constant"

or in other words:

"Energy can never be created or destroyed, only transferred from one form to another"

Going back to the perpetual motion machine example at the beginning - a perpetual motion machine does work as it moves (i.e. transfers energy to something, such as turning an axle, or creating friction), which means energy is lost gradually from the system ('the system' is a general term used to describe whatever object we are considering). Without any external input of energy, the total amount of energy in the system will decrease, causing it to slow down and eventually stop.

Video Lessons

Chris Doner
Conservation of Energy
IB Specific
Khan Academy
Conservation of Energy
Physics Online
Conservation of Energy

Resources

IB Physics
Topic 2 Notes
IB-Physics.net
Chapter 2 Summary
IB Revision Notes
Isaac Physics
Conservation of Energy
Level 5/6 Beyond IB
Mr. G
2.3 Teaching Notes
2.3 Student Notes
Physics and Maths Tutor
Motion Definitions
Motion Key Notes
Motion Detailed Notes
Mechanics Flashcards
A Level Resources - content slightly different

Questions

 

Doing Work

The word 'work' in Physics means the mechanical transfer of energy; that is basically energy transfer that is not thermal. Or in other words, 'doing work' means moving stuff.

The equation for work done is:

Work done (J) = Force applied (N) × distance moved in the direction of the force (m)

In fact, it is through this equation that the Joule, the unit of energy, is defined:

The work done by a force of one Newton acting through one metre

So 1 Joule is equivalent to 1 Newton metre.

The applied force will not always be acting in the same direction as the direction of movement. If there is an angle of θ between the applied force and direction of movement, then this equation can be rewritten as:

W=  Fscosθ

In this example, a skier of weight 800 N and travels a distance of 200 m down the slope (at 30° to the horizontal). In order to calculate the work done by gravity, we need to work out the distance travelled vertically (i.e. in the direction of the weight force).

W =  F s cosθ 

     = 800 × 200 × cos(60)

     = 80 000 J

workdoneskier.png
geogebra_logo.png

This Geogebra simulation allows you to play around with each of these variable, changing the force, the distance travelled and the angle between the force and motion to determine the magnitude of the work done.

Worked Example - Resistive forces on a car

This idea of work done can be very useful in solving problems. We will talk through two ways of solving the same problem - one using Newton's laws and the other using energy conservation ideas. 

 

Q. The highway code states that a car travelling at 40 mph (about 18 msˉ¹) comes to a stop in 24 m after applying the brakes. If we have a car of mass 1500 kg, calculate the average resistive force decelerating the car.

Resistiveforcesoncar.png

Using Forces and Motion

In the previous sections we have looked at ideas about Forces and Motion that we can use to solve this problem. We can use our SUVAT equations to work out the deceleration of the car, then use Newton's Second Law (F=ma) to calculate the average decelerating force acting.

 

v² = u² + 2as

0 = 18² + (2 × 24 × a)

a = (-) 6.75 msˉ²

F = ma

   = 1500 × 6.75

∴ F= 10 125 N

Using Energy and Work Done

We know that the car initially has kinetic energy (which we can calculate using EK = ½mv². When the brakes are applied, work is done by the frictional forces of the brakes on the car, which acts over a certain distance. We can therefore calculate the average size of these forces.

 

EK = ½mv²

     = ½ × 1500 × 18²

     = 243 000 J

W = Fd

243 000  = F × 24

∴ F = 10 125 N

Force-Distance Graphs

We can represent the force applied with distance graphically as shown below. We know that work done = force x distance.

Graphically, this means that the area under our force-distance graph will give us the work done, or energy transferred. Depending on the context of the question, this work done could be as energy transferred to the kinetic energy gained by an object moving through a distance, or could be stored as potential energy as an object moves within a field.

Fdgraph.png

Video Lessons

Resources

IB Physics
Topic 2 Notes
IB-Physics.net
Chapter 2 Summary
IB Revision Notes
Isaac Physics
Work
Mr. G
2.3 Teaching Notes
2.3 Student Notes
Physics and Maths Tutor
Motion Definitions
Motion Key Notes
Motion Detailed Notes
Mechanics Flashcards
A Level Resources - content slightly different

Questions

Cambridge University Press
Topic 2: Add Qs
Topic 2: Add Qs MS
Topic 2: MCQs
CUP Website Link
Freely available online
Dr French's Eclecticon
Work and Power
Work and Power Solutions
Link to Dr French's Site
Extension: Pre-University Material
Grade Gorilla
2.3 (Energy & Power) MCQ
Topic 2 (Mechanics B) End Quiz
Quick IB Specific Mixed MCQs
Isaac Physics
Work, Energy, Power
Mixed Questions
Mr. G
2.3 Formative Assessment
Topic 2 Summary Qs
IB Specific Questions
Physics and Maths Tutor
Work, Energy, Power (AQA 2)
Work, Energy, Power MS (AQA 2)
Work, Energy, Power (AQA 1)
Work, Energy, Power MS (AQA 1)
A-Level Qs: overlapping content
Physics and Maths Tutor
Work & Energy (OCR)
Work & Energy MS (OCR)
Energy, Work, Power (Edexcel 1)
Energy, Work, Power MS (Edexcel 1)
A-Level Qs: overlapping content
 

GPE and KE

Gravitational potential energy is the energy stored within a gravitational field. If work is done against gravity (to lift it up), then that energy is transferred into GPE.

If we assume a uniform gravitational field (which is valid for most contexts on the surface of Earth - though we explore these ideas further in Chapter 10), then our gravitational potential energy is given by:

Gravitational Potential Energy (J) = mass (kg) × gravitational field strength (Nkgˉ¹) × change in height (m)

ΔEP = mgΔh

Kinetic energy is the energy stored in a mass in motion. Our equation for kinetic energy is given by:

Kinetic Energy (J) = ½ × mass (kg) × velocity² (msˉ¹)

ΔEK = ½mv²

 

We are (hopefully) already familiar with these two equations from GCSE. When an object moves within a gravitational field (e.g. a cup falling off a table), energy is transferred between EP and EK. We can use our ideas of conservation of energy to make some predictions about the movement of the object.  

phet-logo-trademarked.png

PHET's Skatepark simulation allows you to visualise the transfer of energy between kinetic and gravitational potential energy of a skater in the half pipe.

Look at how the energy transfers change when:

  • Mass is increased

  • Initial height is increased

  • Friction is added

Walter Lewin (an MIT professor) has a wonderful demonstration of conservation of energy (as well as some other great YouTube videos), take a look.

We can use our EK and EP equations, with our conservation of energy in our calculations.

 

As an example, I drop a 2 kg ball from a height of 4 m. What is the speed when the ball hits the floor?

Yes, we could solve this using our SUVAT equations, but we can also use the conseration of energy. 

Start by thinking about energy transfers - it starts with Gravitational Potential Energy, which gets transferred to Kinetic Energy as it accelerates. If we assume no air resistance there is no thermal energy lost, so GPE at start = KE at end.

EP = EK

mgh = ½mv²

v = √(2gh)

         = √(2× 9.81 × 4)

= 8.9 msˉ¹

The equation v = √(2gh) is a useful shortcut in calculating velocity after an object falls through a certain height. Notice that the final velocity is independent of the object's mass (as we saw in the previous sections).

 

 Isaac Physics also have some nice online lessons looking at conservation of energy, take a look

Video Lessons

Resources

IB Physics
Topic 2 Notes
IB-Physics.net
Chapter 2 Summary
IB Revision Notes
Isaac Physics
Linear Kinetic Energy
Gravitational Potential Energy
Conserving GPE & KE
Level 5/6 Beyond IB
Isaac Physics
Conserving GPE & KE
Level 5/6 Beyond IB
Mr. G
2.3 Teaching Notes
2.3 Student Notes
Physics and Maths Tutor
Motion Definitions
Motion Key Notes
Motion Detailed Notes
Mechanics Flashcards
A Level Resources - content slightly different

Questions

Cambridge University Press
Topic 2: Add Qs
Topic 2: Add Qs MS
Topic 2: MCQs
CUP Website Link
Freely available online
Grade Gorilla
2.3 (Energy & Power) MCQ
Topic 2 (Mechanics B) End Quiz
Quick IB Specific Mixed MCQs
Isaac Physics
Work, Energy, Power
Mixed Questions
Mr. G
2.3 Formative Assessment
Topic 2 Summary Qs
IB Specific Questions
Physics and Maths Tutor
Conservation of Energy (AQA 2)
Conservation of Energy MS (AQA 2)
A-Level Qs: overlapping content
 

Power and Efficiency

 Power is defined as:

The rate at which energy is transferred

As an equation this becomes:

power.png

This shows us that 1 Watt is equivalent to 1 Joule per second. We can use this idea of power for a number of applications, such as the power of a kettle being used to heat up water.

 

We can also come up with an alternative equation for power using our original work done equation and dividing both sides by time:

power2.png

Lastly, we have an equation for efficiency of a machine. This is the ratio of useful energy output and total energy input, usually expressed as a fraction or percentage. We can alternatively use our values for power.

efficiency.png

Video Lessons

Chris Doner
Power and Efficiency
IB Specific
Khan Academy
Power
Physics Online
Power
Efficiency
Physics Online
Power
Study Nova
Work, Energy and Power
Power (Lecture)

Resources

IB Physics
Topic 2 Notes
IB-Physics.net
Chapter 2 Summary
IB Revision Notes
Isaac Physics
Mechanical Power
Mr. G
2.3 Teaching Notes
2.3 Student Notes
Physics and Maths Tutor
Motion Definitions
Motion Key Notes
Motion Detailed Notes
Mechanics Flashcards
A Level Resources - content slightly different

Questions

Cambridge University Press
Topic 2: Add Qs
Topic 2: Add Qs MS
Topic 2: MCQs
CUP Website Link
Freely available online
Dr French's Eclecticon
Work and Power
Work and Power Solutions
Link to Dr French's Site
Extension: Pre-University Material
Grade Gorilla
2.3 (Energy & Power) MCQ
Topic 2 (Mechanics B) End Quiz
Quick IB Specific Mixed MCQs
Isaac Physics
Work, Energy, Power
Mixed Questions
Mr. G
2.3 Formative Assessment
Topic 2 Summary Qs
IB Specific Questions
Physics and Maths Tutor
Work, Energy, Power (AQA 2)
Work, Energy, Power MS (AQA 2)
Work, Energy, Power (AQA 1)
Work, Energy, Power MS (AQA 1)
A-Level Qs: overlapping content
Physics and Maths Tutor
Work & Energy (OCR)
Work & Energy MS (OCR)
Energy, Work, Power (Edexcel 1)
Energy, Work, Power MS (Edexcel 1)
A-Level Qs: overlapping content
 

Hooke's Law

Hooke's Law describes how an object behaves when it is stretched by a tension force. You may be familiar with the classic experiment of a string being stretched by adding masses. If not take a little look at the below video by A Level Physics Online.

Hooke's Law states that the extension of a spring is proportional to the force applied (i.e. F ∝ x). As an equation this becomes:

F = kx

Here, k is a constant of proportionality called the spring constant. The higher the value for k, the stiffer the spring. Typically, we plot force against extension, and obtain the relationship shown below. Notice that the graph is only proportional up to a point. Beyond this 'limit of proportionality', Hooke's Law is no longer obeyed and the spring becomes plastically deformed.

Hooke.png
phet-logo-trademarked.png

PHET's Hooke's Law simulation illustrates some of the key ideas quite nicely. 

  • First, try the first tab, 'Intro', and see how displacement changes with force applied. Compare the spring force and applied force values.

  • Next, look at the second tab, 'Systems', and compare the spring constant with springs in series and in parallel.

  • Finally, take a look at the third tab, 'Energy', and compare the energy and force plots.

Energy Changes and Hooke's law

If we  look at the force-extension graph characteristic of Hooke's Law, this is very similar to our Force-Distance graph we looked at previously. In that instance, the work area under showed us the work done. Now, in the context of this example, that work done is in the form of energy transferred into elastic potential energy. Therefore, for our Force-extension graph, the area tells us the elastic potential energy stored in the spring. We can work out an equation using the area of our graph as shown below:

Fdgraph2.png
energyspring.png

Elastic bands have non-linear Force-extension graph. The loading curve (when weight is added), appears different to the unloading curve (when weight is removed). This asymmetric behaviour is called a hysteresis loop. We saw before that the energy under the curve shows the energy stored in the rubber band at each point. This shape means that we have a different energy beforehand and afterwards. This energy has gone into heating up the elastic material. 

elastic.png

Video Lessons

Resources

IB Physics
Topic 2 Notes
IB-Physics.net
Chapter 2 Summary
IB Revision Notes
Isaac Physics
Hooke's Law
Mr. G
2.3 Teaching Notes
2.3 Student Notes
Physics and Maths Tutor
Motion Definitions
Motion Key Notes
Motion Detailed Notes
Materials Flashcards
A Level Resources - content slightly different

Questions

Cambridge University Press
Topic 2: Add Qs
Topic 2: Add Qs MS
Topic 2: MCQs
CUP Website Link
Freely available online
Grade Gorilla
2.3 (Energy & Power) MCQ
Topic 2 (Mechanics B) End Quiz
Quick IB Specific Mixed MCQs
Isaac Physics
Springs
Energy, Springs, Materials
Materials questions not relevant
Mr. G
2.3 Formative Assessment
Topic 2 Summary Qs
IB Specific Questions
Physics and Maths Tutor
Materials (AQA 1)
Materials MS (AQA 1)
MCQ Materials (AQA 2)
MCQ Materials MS (AQA 2)
A-Level Qs: overlapping content
Physics and Maths Tutor
Bulk Properties (AQA 2)
Bulk Properties MS (AQA 2)
Materials (Edexcel 2)
Materials MS (Edexcel 2)
A-Level Qs: overlapping content

Additional Resources

 
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Definitions and Key Words : Chapter 2

A set of Quizlet flashcards of the key words and definitions for this chapter is provided here. 

IB Questions

A question by question breakdown of the IB papers by year is shown below to allow you to filter questions by topic. Hopefully you have access to many of these papers through your school. If available, there may be some links to online sources of questions, though please be patient if the links are broken! (DrR: If you do find some broken links, please contact me through the site)

 

Questions on this topic (Section 2) are shown in red.