Physics

Law of Inertia: Hands-free driving

The everyday use of self-driving cars may still be science fiction but the basic laws of motion that describe how cars change speed and direction while avoiding – or colliding with – obstacles, have been known for over 300 years.

In this lesson you will investigate the following:

• Newton’s first law of motion – the law of inertia – and how inertia relates to car safety.

• How to draw free body diagrams and why they are used to analyze forces.

• Common misconceptions about the law of inertia and how they can be corrected by clear science communication.

Buckle up as we take a high-impact ride from 1687 to the future!

This is a print version of an interactive online lesson. To sign up for the real thing or for curriculum details about the lesson go to www.cosmosforschools.com

Introduction: Law of inertia

Google has come a long way from being just a search engine. Its new self-driving car can do pretty much everything a humandriver can, from calculating routes to reading road signs – a true “automobile” in every sense of the word.

Using feedback from sophisticated sensors, the car cleverly adjusts its speed and deftly navigates through traffic. Infrared laserbeams construct a virtual 360 degree view of the world around it, and multiple radars and sensors keep the car moving safely to itsdestination. There are even plans to develop systems that enable the car to “talk” to traffic light systems and other cars!

A car that is constantly aware of its surroundings is particularly useful for avoiding collisions. Because of inertia – the naturaltendency of an object to resist any change in its motion – it’s not easy to bring a car to a stop, especially when travelling at highspeed. A significant number of car crashes are due to drivers being unable to brake in time – something a smart car can avoid. Infact, experts have predicted that replacing half the cars on US roads with self-driving cars would prevent 1.8 million car crashes andsave 10,000 lives each year.

It may be several more years before you see a self-driving car cruising down the street, but as Google and other companies work onmaking it a reality you can be sure that cars will continue to become even smarter and safer.

 

Read or listen to the full Cosmos magazine article here.

Question 1

Compare: Cosmos magazine and Al Gore’s An Inconvenient Truth – a popular account of the scientific evidence for human-inducedclimate change – are two contemporary examples of effective science communication to a broad audience. Isaac Newton’s Principia

Mathematica was published in Latin in 1687 and laid down the three fundamental laws of motion. It's a dense scholarly work thatwas clearly intended for the educated elite, at a time when the scientific revolution was still taking off.

The Cosmos magazine article about the Google car is interspersed with fragments of a fictional futuristic story about a family whouses a self-driving car.

Use the table below to list the advantages and disadvantages of story telling to communicate scientific discoveries. How might ithelp or hinder our understanding?

Advantages Disadvantages

Gather: Law of inertia

All objects have inertia – a natural tendency to maintain their state of motion. An object at rest "wants" to stay at rest and a movingobject "wants" to keep moving with the same speed in the same direction.

This universal property of bodies depends only on their mass, or the amount of matter they contain. A stationary car is harder topush into motion than a bicycle because the car has more mass and so more inertia.

Inertia is one of the basic concepts needed to understand car crashes and develop safer cars.

Inertia

3:43

Question 1

Recall: All objects at rest "want" to stay at rest. Give twoexamples of this principle that are mentioned in the video.

Question 2

Select: As shown in the video, a driver who is involved in ahead-on collision while not wearing a seatbelt will keep movingforward at their original speed – until stopped by the steeringwheel and windshield.

This is because every moving object has a natural tendency tomaintain its state of motion.

True

False

moving with the same speed in different directions have different velocities.

An object's acceleration is the rate at which its velocity is changing. So an object at rest and an object moving at a constantvelocity both have zero acceleration.

We can now say that inertia is an object's tendency to maintain a constant velocity, or zero acceleration.

So what causes an object to change velocity, or accelerate? Newton's first law of motion – the law of inertia – states that anychange in velocity must be caused by an unbalanced force.

We can understand the distinction between balanced and unbalanced forces by considering an example.

Imagine that you're standing motionless on a diving board.The force of gravity is obviously pulling you downward, but youaren't accelerating – you're not moving at all!

For the law of inertia to be correct, the gravitational force mustbe balanced by an equal and opposite force pushing up on youfrom the board. This sort of force – which can be provided bythe ground, chairs, walls or any rigid support – is known asa normal force. For a scientist, "normal" means perpendicularand normal forces always act at right angles to the supportingsurface.

When you leap from the diving board, the normal force that hadbeen supporting you is removed and the unbalanced force ofgravity causes you to fall into the pool below.

Question 3

Explain: When we say that a car is accelerating we usually meanthat it's speeding up.

Explain why braking and steering also qualify as accelerating inthe scientific sense.

Question 4

Think: The Voyager 1 space probe was launched by NASA in1977 and is now the most distant spacecraft from Earth as ithurtles into interstellar space at over 60,000 km/h.

So long as no unbalanced forces act on Voyager 1, it willcontinue moving with the same speed and direction forever.

True

False

The law of inertiaScientists describe the motion of objects using the concepts of velocity and acceleration.

An object's velocity is a combination of its speed and direction of motion. Velocity is distinct from speed alone: two objects

Question 5

Complete: A tennis ball is moving from left to right as shown in the left hand column below. The next column shows its state ofmotion a short time later in four different possible scenarios.

1. Decide whether the velocity of the tennis ball has changed from its starting velocity in each of the four cases.

2. Using your understanding of the law of inertia, decide whether the forces acting on the ball must have been balanced orunbalanced.

3. Indicate the direction of any unbalanced force by drawing an arrow (up, down, left or right) or – if the forces were balanced –type "none".

The Google car relies on the fact that moving objectsfollow Newton's laws, so their movements can often bepredicted. Human drivers predict the motion of other cars,pedestrians and obstacles – self-driving cars need to make thesame predictions using sensors and high-tech computers.

The first step in predicting changes in the motion of an object isto identify the forces acting on it. These can be divided into twotypes depending on whether or not contact is required.

The most obvious example of a non-contact force – or action ata distance – is gravity.

Types of force

An example of obstacle-avoidance technology beingdeveloped by Ford. Radars, ultrasonic sensors and a

camera scan the road ahead for obstacles and warn thedriver. If the driver doesn't act in time the computer will.

Question 6

Match: The following diagram lists the major types of force on the left hand side, separated into contact and non-contact. Drawlines to match each type of force to its description – one has already been done for you.

Note the abbreviations, e.g. F , which you will use to label forces in later questions.

app

Question 7

Analyze: Examine the situations illustrated in the sketchpad.

1. Decide whether the forces acting on the glass, apple, nail and planet are balanced or unbalanced and type your answer in thespace provided.

2. If the forces are balanced type "none" in the second space. Otherwise identify the unbalanced force:

gravity   |   magnetism   |   friction

1:06

Question 8

Explain: Use what you have learned about Newton's first law to explain the principle behind this spectacular feat. Do you think thatit's real or staged? Why?

Process: Law of inertia

Question 1

Reflect: The inertia of an object depends only on its mass: thegreater the mass, the greater the inertia.

Which of the following has the greatest inertia?

A downhill skier making a descent at 150 km/h

A baby sleeping in a cot

An elephant walking at a speed of 5 km/h

A bullet traveling at 2000 km/h

Question 2

Identify: The law of inertia implies that a moving object willcontinue moving forever unless acted on by an unbalancedforce.

Identify the unbalanced force that causes a skier to come to restat the bottom of a ski slope.

Gravity

Friction and air resistance

Spring force

Normal force

Question 3

Summarize: What an object will do depends on its velocity and the combination of forces acting on it. Complete the following tableto indicate in which circumstances an object will:

start moving   |   stay moving with constant velocity   |   stay at rest   |   stop, or stay moving with new velocity

No forces or balanced forces Unbalanced force

An object at rest will:

A moving object will:

concept of inertia. A number of round wooden blocks arestacked in the form of a bearded man called Daruma – thefounder of Zen buddhism.

Players strike one block at a time with a small hammer, startingat the bottom, and hope that Daruma doesn't collapse in aheap.

The trick is to apply the horizontal force only to a single block.When you strike hard enough the applied force is nottransferred to the overlying block by friction. Then the inertia ofthe upper blocks means that they simply drop straight down.

We can represent the forces acting on an object as arrows, with the length of the arrow indicating the strength of the force. Likevelocity, force has a direction component so the direction of the force is indicated by the direction of the arrow. We can drawcontact forces – such as normal forces – at the point of contact and non-contact forces – such as gravity – through an object's centre

of mass.

Drawing forces

Did you know?

The traditional Japanese game daruma otoshi illustrates the

Question 4

Draw: Identify all of the forces acting on the dummy:

1. as it sits on the stationary truck,

2. as the truck is accelerating and the dummy is sliding off the back, and

3. at the moment it slides off completely.

Draw:

contact forces as blue arrows starting from the point of contact – indicated by the blue circle,

non-contact forces as red arrows starting from the dummy's centre of mass – indicated by the red circle.

The length of the arrows should roughly indicate the size of the forces. Identify the type of each force using a label such as F  forgravity, F  for normal force or F for friction.

Hint: you can ignore air resistance but don't forget about other types of friction!

grav

norm frict 

Force diagrams like those above can get messy. We can often get a better understanding by constructing free body diagrams. Theserepresent objects as simple squares and the forces acting on them as arrows radiating from the squares.

Free body diagrams ignore the distinction between contact and non-contact forces and we think of the objects isolatedfrom their contexts. They are especially useful for engineers to figure out the forces applying to structures, such as bridge pylons.

Three examples of free body diagrams are shown below.

Free body diagrams

Free body diagrams for the abseiler, ice skater and car shown. Abbreviations for the types of force include: tens –tension, grav – gravity, norm – normal, frict – friction, app – applied and air – air resistance.

Question 5

Imagine: The free body diagram for the abseiler shows that theforce of gravity is balanced by the tension force in the rope.

If the tension force arrow was longer than the gravitational forcearrow then what would be happening to the abseiler?

Question 6

Select: Suppose the ice skater glides effortlessly across thefrozen lake in a straight line and slowly comes to a stop. Decidewhich of the following statements are true.

No force is required to bring the skater to a stop.

The vertical forces acting on the skater are

balanced.

The skater slows down because the friction and

air resistance acting on her are unbalanced

forces.

The inertia of the skater gradually decreases as

she slows down.

Question 7

Draw: Draw free body diagrams for the two objects pictured below.

1. A car accelerating forwards. Hint: In the car example above the forces are balanced, so the car must be travelling at a constant

velocity.

2. A skydiver falling at terminal velocity. This is the constant velocity that a body in free fall reaches when the forces acting on itbalance each other out.

When a driver suddenly hits the brakes to avoid a collision they are effectively applying an additional friction force to the carthrough the brake pads. Braking distance – the distance travelled by a braking car before it stops – increases with speed and this isthe main reason why speeding is so dangerous.

The stopping distance of a car consists of the braking distance plus the so-called thinking distance – the distance travelled by the carbefore the driver applies the brakes. Human drivers always take some time to notice and react to potential dangers, while their carscontinue moving forward at the same speed due to inertia. One of the main advantages of self-driving cars is that they can respondmore quickly and are not affected by distraction, panic, alcohol or drugs.

Extension: Stopping distance

Question 8

Draw: Imagine you're a passenger in a self-driving car of the future, cruising at a constant speed. Free body diagrams for your carand you are shown in the sketchpad below.

The car's sensors detect a small child on the road ahead. Its central computer quickly calculates the braking force required to avoidhitting the child, and the car begins to brake smoothly. Draw two more free body diagrams to represent this scenario:

1. one for the braking car, and

2. one for your own body. For the purposes of this question assume that you're not wearing a seatbelt or other restraint but arestill seated and have no frictional forces acting on you. This could quickly change as the car continues to brake.

Hint: Remember to indicate the relative strength of the forces by the length of the arrows, and to label all forces.

Question 9

Explain: Would you still need to wear a seatbelt as a passenger in a self-driving car? Use the free body diagrams you have drawn toexplain why or why not.

Apply: Law of inertia

Make a video to explain the law of inertia

The Cosmos magazine article about the Google car used a science fiction story to communicate science effectively. Now it's yourturn to investigate common misunderstandings of the law of inertia and put your science communication skills to the test!

2:28

Question 1

Recall: Derek's first incorrect law of motion states that a moving object with no unbalanced forces acting on it will naturally come torest. What would a moving object with no unbalanced forces on it really do, and why?

Question 2

Reflect: Before we can correct a misconception we need to understand how it comes about. Until the scientific revolution, it wasgenerally believed that the natural state of an object is rest. According to that theory an unbalanced force must continually act onan object just to keep it moving at a constant velocity – as expressed in Derek's second incorrect law.

Think about pushing a table across a room, dragging a sled by a rope or spinning a roundabout in a playground. Why do you needto apply a continual force just to keep these objects moving at a constant rate? Why do you think it's counter-intuitive that an objectwill keep moving at constant velocity without an unbalanced force?

Your task is to collect evidence that ordinary people misunderstand the law of inertia and then create a video that provides acorrect explanation of the law. The evidence you collect will take the form of short interviews with other students at your school.

You can use the following video for inspiration!

2:51

Question 3

Plan: Describe the situation – real or imagined – that you plan to present to your interviewees and write down your interviewquestions in point form. Also indicate whether you would use any props or diagrams in your interviews.

Question 4

Record: Taking your prepared questions and any props you might need, carry out interviews with about five people. If you decideto record the interviews on video, you must ask your interviewees for permission first. Otherwise you can present the questions asa written survey and ask them to fill it in. If you are unable to carry out the interviews at school, predict what the answers to yourquestions would be and perhaps use members of your group as actors.

Once you have recorded your interviews in video or written format, upload them in the project space below.

Question 5

Create: Think of various ways you could communicate the key idea of the law of inertia in a video so that non-scientists wouldunderstand it. Be as creative as you can! For example, you might speak directly to the camera, draw diagrams, use props oranimation apps, or even perform an experiment.

Once you've planned, filmed and edited your video upload it below. If you're unable to make the video itself then upload a script ofthe video you would want to make and any visual aids you would use to make it.

Career: Law of inertia

2:20

Question 1

Reflect: Think of a high-tech device or medical treatment that you would like to see invented. What sorts of scientific knowledgewould be needed to make it a reality? In the long process of developing the product – from making scientific discoveries anddesigning new technologies to safety testing and marketing – which role would you prefer to play, and why?

Cosmos Lessons team

Lesson authors: Kathryn Grainger and Campbell EdgarIntroduction author: Yi-Di NgEditor: Jim RountreeArt director: Wendy JohnsEducation director: Daniel Pikler

Image credits: iStock, Shutterstock, Ford, Mountain FolkcraftVideo credits: Griff Jones/IIHS, BMW/motoroidsmag, DerekMuller/Veritasium, Google Self Driving Car Project on YouTube