Chapter 4     The Science of Driving

Suppose you would like to buy a car for daily use. To decide which car to buy, you read many leaflets about different brands of car, like the one shown on the right. However, you probably get frustrated with those keywords like horsepower, displacement, V-6 engine, ABS system, ... etc. You don't know which car is the right choice for yourself!

In fact, car and driving has a close relationship with science especially physics. For example, when people talk about time of "zero to sixty" of a car, they are actually considering the time for the car to accelerate from rest up to the speed of 60 miles per hour. In this chapter, let us study about car and driving by scientific analysis.

Basic Physics of Driving

Mechanics, the branch of physics investigating motion, plays an important role in understanding about the motion of car. Thus we can use the concepts and tools developed in mechanics to investigate the motion of car. In fact, physics can tell us how cars react with different types of forces and thus we can make predictions about the motion of a car. For example, we can study whether a car would turn over if it moves on a circular track with certain radius. Physics is also useful for the investigation of the cause of many car accidents. Therefore, physics is indispensable in the study of motion of cars.

Preliminary knowledge
  • Keywords describing the motion of a car

    Typical Values of Acceleration [i]
    Objects/Events Acceleration
    Elevator (fast service) 2.9 m/s2
    Space Shuttle (take off) 29 m/s2
    Football tackle 390 m/s2
    Jumping flea 1960 m/s2
    High speed car crash 6860 m/s2

    In the terminology of mechanics, a car moves with certain velocity when it is moving on the road. You may think that velocity simply means the speed of the car. Indeed, velocity does not only tell us the speed of the car. By definition, velocity refers to how fast a car moves towards a particular direction. So, if two cars move with the same speed towards different direction, they are moving with different velocities.

    To change the speed of a car, you push the accelerator of the car. In other words, the car accelerates if you push the accelerator. In fact, a car accelerates whenever its velocity is changed by either changing the speed or the direction of the car's motion. So, even if you are driving your car at a constant speed while turning around a corner, you are still accelerating. The acceleration of a car is a measure of how fast the velocity of the car changes in a given time interval.

    When we speak of the velocity and acceleration, we usually refer to the instantaneous velocity and instantaneous acceleration. For example, the speedometer of a car tells us the instantaneous velocity of the car; that is, it shows the velocity at that instant of time. If you inspect the readings of the speedometer at regular time intervals, you probably notice that it changes often.

    The instantaneous velocity of a car often changes! [ii]

    By definition, velocity refers to the distance traveled in a certain time period while acceleration is the change in velocity in a certain time period. If we calculate the velocity and acceleration over a very short period of time, we will obtain the instantaneous velocity and instantaneous acceleration. However, if we calculate these quantities over a very long time interval, then we will find the average velocity and average acceleration.

    (Courtesy: PhysicsNet)

  • Accelerations

    The units of velocity and acceleration: Velocity is usually given in terms of kilometers per hour (km/hr), miles per hour (mph) or meters per second (m/s). Since acceleration is equal to the change in velocity per unit time, acceleration is usually given in units of km/hr2 or m/s2. Another unit of acceleration that is commonly used is "gee's" or simply "g's". You probably have heard about this unit in the discussion about space travel, combat aircraft or racing car. For example, the maximum acceleration of a combat aircraft is typically around 9.5 gee's. One "g" is 9.8 m/s2 and it's the maximum acceleration that your tires can withstand.

    The ability to accelerate, especially the ability to accelerate from 0 to 60 mph, is one of the typical measure of the power of a car. The table below shows the times taken for several 2002 cars to accelerate from 0 to 60 mph.

    Time from 0 to 60 in seconds for several models of 2002 cars [iii]
    Types of Vehicles Model 0 to 60 (sec)
    Family sedans Ford Focus ZTS 9.6
    Hyundai XG300 8.9
    Honda Accord EX V-6 7.6
    Sport sedans Ford Thunderbird 7.0
    Porsche 911 GT2 4.1
    Mercedes-Benz E430 6.3
    SUVs Ford Explorer 8.0
    Jeep Liberty 10.0
    Toyota Highlander 8.3

Newton's Laws of Motion

You have to push or pull a car in order to accelerate it. Scientists call this pull or push to be a force and the force is supplied by the car's engine. The term "force" was defined by the genius physicists Isaac Newton more than three hundred years ago. He formulated three laws of motion based on his findings about the properties of force. Newton's laws of motion is able to explain and predict how a car moves in different circumstances. Let us review the Newton's laws of motion one by one. There are three laws of motion due to Sir Isaac Newton.

Sir Isaac Newton [iv]

  1. Newton's first law of motion

    Newton's first law of motion states as follows.

    An object continues in a state of rest or uniform motion in a straight line, unless a net force acts upon it.

    In other words, all objects tend to "keep on doing what they're doing" unless acted upon by a net force. What does the term net force (also called unbalanced force) really mean? Let us consider the following example:

    Since the two forces acting on the book are of equal magnitude and in opposite directions, they balance with each other. The book is said to be at equilibrium. No net force is applied on the book and thus the book maintains its state of motion. When all the forces acting upon an object balance each other (i.e. no net force), the object will not accelerate.

    If an object is at rest, they will continue in the motionless state. If it moves with velocity of 10 m/s towards South with no net force acted on it, it will continue in this state of motion (10 m/s, South). If it moves with velocity of 20 m/s towards right with no net force acted on it, it will continue in this state of motion (20 m/s, right). The state of motion of an object will not be changed as long as no net force is applied on the object. All objects resist changes in their state of motion --- they tend to "keep on doing what they're doing". Such resistance to change in state of motion is called inertia.

    At the first sight, it might seem that the first law of motion is contradictory to our common sense. According to the first law of motion, a force is not needed to keep an object in motion. However, we may observe that a moving object will eventually come to a stop even there is "no force" (really?) acting on it. In fact, the object is slowed down by a net force named "friction". In the absence of frictional force, the object would continue to move with the same velocity on and on! That is to say, force is not required to keep a moving object in motion; indeed, a force is needed to bring that object to rest.

    (Courtesy: The Physics Classroom)

    Newton's first law of motion tells us that all objects resist changes in their state of motion. All objects have this tendency --- they have inertia. Is there any object having more inertia than others? Yes, of course! Mass is a measure of the inertia of a body. Roughly speaking, mass is the amount of material in a body. A body with larger mass has more inertia and thus it has larger tendency to resist changes in its state of motion. The mass of an object is usually given in unit of g (gram) or kg (kilogram).

    • Daily examples of Newton's first law of motion

      • You probably have experienced inertia in an automobile when it is braking to stop. Although a net force is exerted on the car to change its state of motion, no force is applied to change the state of motion of the passenger. Thus, if you are sitting on a braking car, you will keep on moving and slide out of the seat provided no net force is exerted to resist your motion due to the inertia. Seat belts are car's safety accessories that prevent passengers to follow such kind of motion of inertia and thereby protect passengers from flying out of the seat during car accidents. You could imagine how dangerous it is if you don't fasten your seat belt.

        That's what may happen to a passenger with no seat belt during an accident! [ii]

      • When a car accelerates, the driver would feel being pushed back to the seat due to his/her body's inertia. Besides, when a car is turning on a circular track, the driver would feel being throw away to the outside of the track. Is it also related to the inertia? Yes, it is. We should note that the direction of motion of a car would be changed if the car turns. However, according to the Newton's first law, a moving object would continue to move in a straight line provided that no net force acted on it. As a result, force must be applied to a car so that it can move along a circular track. Such force is called the centripetal force and it was shown that this force must be pointing towards the center of the circular path that the object is moved on. Thus the driver would feel being thrown outwards as the car turns.

        The centripetal force arises whenever the car turns! [iv]

  1. Newton's second law of motion

    How about the case that a net force is applied to change the motion of a body moving at constant velocity (or at rest, that is velocity = 0 m/s)? What will be the resulted acceleration of this body? The answer is given by the Newton's second law.

    Newton's second law of motion states as follows.

    An object being acted by a net force will undergo an acceleration that is directly proportional to the magnitude of the force, in the same direction as the net force, and inversely proportional to its mass.

    Newton's second law of motion describes the behavior of objects being acted upon by a net force. This law states that the acceleration of an object depends on two variables, namely the net force acting upon the object and the mass of the object itself. Moreover, if the net force increases, the object's acceleration will also increase. Nevertheless, if the mass of the object increases, its acceleration will decrease. Thus we know that a car will accelerate at a faster rate if a greater force is applied on it. Moreover, we know that a greater force should be applied on a heavy truck so that it accelerates at the same rate as a lightweight car.

    The acceleration of an object is directly proportional to the net force applied on it.

    According to the second law of motion, the acceleration of an object is directly proportional to the net force acting upon the object. In other words, for a constant mass object, doubling the net force results in a doubling of the acceleration. If the net force is halved instead, the acceleration will be halved.

    The acceleration of an object is inversely proportional to the mass of the object.

    Newton's second law of motion also states that the acceleration of an object is inversely proportional to the mass of the object. That is to say, if the net force is held constant, the acceleration of an object will be halved by doubling the mass of the object. Similarly, "halving" the mass leads to a doubling of the acceleration if the net force is held constant again.

    Note that the net force imparted on an object is a quantity acting in the same direction as its acceleration. As a result, Newton's second law of motion can be written in formula as:

    By making use of this formula, we can calculate the acceleration of any object being acted by a force. For example, we can find the weight of an object that tells us how large is the force of gravity acting on the object. Besides, we can calculate the braking distance of a car using the second law of motion.

    Calculating the braking distance of car by the Newton's 2nd law [v]

    In standard metric units, the unit of force is Newton (N). The above formula also indicates that the unit of force is given by the unit of mass multiplied by the unit of acceleration. If fact, one Newton is defined as the amount of force required for a 1-kg mass to have an acceleration of 1 m/s2.

  1. Newton's third law of motion

    When you push on an object, you exert a force on it. You would expect that there is nothing else involved in this event. However, Newton predicted that there would be an equal magnitude force pushing back in an opposite direction, i.e. from the object on you. The principle behind this prediction was stated in the Newton's third law.

    Newton's third law of motion states as follows.

    For every action, there is an equal and opposite reaction.

    Here, the terms "action" and "reaction" refer to the action force and reaction force. In addition, the term "equal" means equal in magnitude and the term "opposite" means opposite directions.
    Action-reaction force must occur in pairs!

    Newton's third law of motion tells us what will happen between two interacting objects if one of them exerts force on the other. According to this law, there would be a pair of forces called the action and reaction force acting on the two interacting objects. Moreover, the action and reaction force have equal magnitude while the two forces are acting in opposite directions, one pushing the first object by the second object and one pushing the second object by the first object. Thus Newton's third law implies that forces must occur in pairs --- equal and opposite action-reaction force pairs.

    You may wonder that if the action and reaction forces are really equal in magnitude but opposite in direction, why don't they cancel out with each other? In fact, this is a common misconception. The key to the answer is that action-reaction forces always act on different objects. We should note that only the forces acting on the same object could cancel each other. Therefore, forces acting on different objects don't cancel! (You could imagine it is impossible for these forces to cancel since they affect the motion of different objects.) Newton's Third Law state that an equal and opposite reaction force would arise if an object apply an action force to the other. However, we should bear in mind that these forces DO NOT CANCEL since they affect the motion of different objects.

    Newton's third law of motion is closely related to the motion of a car. Assuming you are driving a car on the road, consider the motion of the car. As the wheels of the car spin backwards, they push the road backwards. In consequence, the road must push the wheels forward according to the third law of motion. It is this reaction force acting on the wheels causes the car to move forward. Note that the magnitude of the force on the road is the same as that on the wheels while the direction of the force on the road (backward) is opposite to that on the wheels (forward). Action-reaction force pairs make it possible for cars to move.

    The ideas of the Newton's third law of motion can be clearly illustrated by simple experiments. The so-called "rollaway players experiment", on the right, (Courtesy: Cislunar Aerospace, Inc) is one of them. Can you explain the result of this experiment?


Horsepower, work and power
  • Let us first take a look at two closely related concepts called "work" and "power". Note that the terms "work" mentioned here is not the one that we are talking about in our daily life; it refers to that defined by the physicist. Physicist stated that work is done whenever a force is exerted on an object so that it moves over a non-zero distance in the same direction as the applied force. So if the applied force is perpendicular to the direction of the resultant object's motion, no work will be done. In our everyday life, there are many examples of work done: a horse pulls a plow through the fields, a weightlifter lifts a barbell above her head, a car is crashed into a tree leading to the deformation of the car, etc. A car also does work when it is moving. Whenever a car moves, it has to apply a force to overcome the frictional forces and air resistance that resists the motion of the car. Thus work must be done in order to keep the car moving.

    (Courtesy of Quiet Valley Historical Farm)
    Work must be done for either the car to move or pulling an ice block.

  • The standard metric unit of work (and also energy) is the Joule (abbreviated "J"). One Joule is equivalent to one Newton of force causing an object to move along the direction of the force with a distance of 1m.

  • The work done on an object can tell us how much force causes the object to move a certain distance. But it does not give us any information about how long does this force act on the object to cause the motion. In fact, we can perform the same amount of work over different time intervals. For example, a sport car takes a very short time to move from one city to another city. On the other hand, a family car takes a much longer time to complete the same journey. These two cars might do the same amount of work; however, the sport car does the work in a much shorter time than the family car. The quantity related with the rate at which a certain amount of work is done is called the power that is defined as follows:

    So we can say the sport car has a greater power than the family car.

  • Many machines are described by a power rating which indicates the rate at which that machine can do work upon other objects. One typical example is the car engine with the power rating usually stated in units of horsepower. The power rating of a car tells us how rapidly the car can accelerate. Suppose that a 60-horsepower engine could accelerate the car from "zero to sixty" (i.e. zero miles per hour to 60 miles per hour) in 18 seconds. If it is true, then a car with two times the horsepower could do the same amount of work in one-half of the time. That is, a 120-horsepower engine could accelerate the same car from "zero to sixty" in only 9 seconds. Some people think that it's cool to drive a car with short "zero to sixty" time and thus they want to buy a car with a higher power rating. Of course, cars with higher power rating are usually expensive as shown in the below table.

    Power ratings and prices of several models of cars [viii]
    Model Horsepower Price (US$)
    Dodge Viper 450 $66,000
    Ferrari 355 F1 375 $134,000
    Shelby Series 1 320 $108,000
    Lotus Esprit V8 350 $83,000
    Chevrolet Corvette 345 $42,000
    Porsche Carrera 300 $70,000
    Mitsubishi 3000GT bi-turbo 320 $45,000
    Ford Escort 110 $12,000

  • Horsepowers

    (Courtesy: HowStuffWorks)

    • The term horsepower was invented by the engineer James Watt who is famous for his work on improving the performance of steam engines. Another unit of power called Watt was also named in memory of his work.

    • The story goes back to 1783 when Watt wanted to find out how much power is available from a pony to lift coal at a coal mine. He found that, on average, a mine pony could do 22,000 foot-pounds of work in a minute. Therefore Watt judged that one horse could do 33,000 foot-pounds of work every minute. So he defined one horsepower to be 550 pound-feet per second, i.e. 33,000 foot-pounds per minute. The horsepower can be converted into units of Watt where one horsepower is found to be equivalent to 746 Watts.

    • Horsepower is an arbitrary unit of measure of power that has been used for over centuries. Nowadays, it is still widely used and appears on cars, air conditioners and even on some vacuum cleaners!
    • The standard metric unit of power is the Watt (abbreviated "W"). From the formula of power, a unit of power should be equal to a unit of work divided by a unit of time. A Watt is equivalent to the Joule (unit of work) per second (unit of time). Horsepower is another commonly used unit of power where one horsepower is equivalent to about 750 Watts.


Have you ever noticed any car advertisement with specifications like "this engine makes 267 pound-feet of torque at 4,300 rpm"? In fact, you will find that the torque of a car is often mentioned in many car advertisements. What does the term "torque" means? How is it related with the quality of a car?

The torque of a car
  • Torque is the tendency for a force to rotate or turn things. When you apply a force to a wrench to tighten a screw, you generate a torque. You also generate a torque when you open a jar by twisting its top cover.

    Torque is produced when you screw up a bottle's cap. [vii]

  • To produce a torque on the bottle's cap, you must apply a force at a certain distance from the axis of rotation (tangential to the rim of cap). Therefore, the torque can be expressed as:

    Torque = force × perpendicular distance from the rotational axis

  • The formula implies that the larger the distance between the applied force and axis of rotation, the larger would be the torque. That's why a stubborn bolt can be loosened by a wrench with its handle being extended, as shown in the movie below. By doing so, the distance of the applied force from the axis of rotation of the wrench is increased and thus the torque generated would be larger.

    (Courtesy: Physics Video)

  • From the above expression, we know that the unit of torque must contain the unit of distance and the unit of force. English units of torque are pound-inches or pound-feet (lb-ft) while the SI unit is the Newton-meter (Nm).

  • People often mention the torque of the car's engine when they talk about the quality of a car. How is the torque related to the car's engine? In a car engine, torque is created and used to spin the crankshaft that gives the car power to move. This torque is created in the engine by applying a force at a distance. The animation shown below illustrates how the torque is created in the engine of a car.

    Torque is created in a four-stroke car engine. [viii]

  • Thus the torque of a car's engine is a good measure of the engine's ability to do work since it gives the amount of twist or turning power of the engine. In the car's engine, torque varies with the engine's speed. So the torque should be stated with the engine speed, which is usually given in unit of number of rotations per minute (rpm). The table below shows the torques of different types of vehicles.

    Torque for several models of 2002 cars [iii]
    Types of Vehicles Model Torque (lb-ft)
    Family sedans Ford Focus ZTS 135 @ 4500 rpm
    Hyundai XG300 178 @ 4000 rpm
    Honda Accord EX 195 @ 4700 rpm
    Sport sedans Ford Thunderbird 267 @ 4300 rpm
    BMW Z3 214 @ 3500 rpm
    Chevy Corvette Z06 385 @ 4800 rpm
    SUVs Ford Explorer 255 @ 4000 rpm
    Jeep Liberty 235 @ 4000 rpm
    GMC Envoy 275 @ 3500 rpm

Combustion Engine of a Car

2003 Jeep Grand Cherokee Engine [viii]
Engine is one of the most important parts of a car since it provides the power for the motion of the car. The working of the car engine plays a crucial factor in the functioning of the car.

What happens inside a car engine? The car engine is the place in which the fuel gasoline is converted into the power of a car. Therefore, a car engine is an internal combustion engine since combustion takes place internally. Why the external combustion engine is not used as car engine? It is because internal combustion is much more efficient (takes less fuel per mile) than external combustion.

How Things Work
  • Internal combustion

    A good example of internal combustion is the war cannon. A cannon is lighted after the soldiers load it with gunpowder and a cannon ball. And that is internal combustion.
    The "firing" of the potato cannon [viii]

    The internal combustion taking place inside the car engine is very powerful. To let you understand how powerful it is, let us look at a more relevant example --- a device commonly known as potato cannon. It consists of a big piece of plastic sewer pipe, say 3 inches in diameter and 3 feet long, with a cap on one end of it. A tiny drop of gasoline is put into the cannon and a potato is stuffed down the pipe. Then the fuel can be ignited by introducing a spark. After the ignition, you will see that the potato would be launched about 500 feet through the air (just like in the above figure)! There is a huge amount of energy in a tiny drop of gasoline.

    The basic principle behind the potato cannon is the same as that for any internal combustion engine: If you put a tiny amount of high-energy fuel (like gasoline) in a small confined space and ignite it, a huge amount of energy would be released in the form of expanding gas. In the potato cannon, this energy is "translated" into the potato motion and thus the potato can be propelled 500 feet. Besides, if you can create a cycle that allows explosion like this occur hundreds of times per minute and then the energy is harnessed in a useful way, you can get a very huge amount power from this cycle. In fact, this is what happens inside the core of a car engine!

    Today, most of the car engines are the so-called four-stroke compression engines in which the four-stroke combustion cycle is used to convert gasoline into motion. The four-stroke combustion cycle, also named Otto cycle, is invented by the Germans Nikolaus Otto in 1867. The "four-stroke" refers to the four-times movement of the piston over one revolution of the engine in each cycle, namely, intake stroke, compression stroke, combustion stroke and exhaust stroke.

  • What's inside a car engine?

    The internal structure of a four-stroke compression car engine [viii]

    Before studying the details of the four-stroke combustion cycle, let us first take a look on the internal structure of the car engine. The above figure shows a four-stroke compression engine with only one cylinder. In each cylinder, there is a piston (will be discussed in details later) and a confined space called the combustion chamber in which combustion and compression of fuel occurs. At the top of the cylinder, the intake valve allows the air and fuel mixture to enter the combustion chamber while the exhaust valve allows the exhaust gas produced by the combustion to leave the chamber. Note that both valves are closed during compression and combustion of the fuel in order to seal the combustion chamber. To ignite the air and fuel mixture, the spark plug at the top of the cylinder supplies the spark so that the combustion can occur. Of course, the spark must happen at just the right moment for the engine to work properly.

    Just beneath the valves, a cylindrical piece of metal called the piston moves up and down inside the cylinder. Indeed, the piston plays the same role as the potato in the potato cannon, i.e. it will be "fired" by the explosion of the fuel. The connecting rod connects the piston to the crankshaft which converts the piston's up and down motion (linear motion) into rotational motion just like a crank on a jack-in-the-box does. The rotational speed of the crankshaft is indeed the engine speed that people talking about. Since the angle of the connecting rod will be changed as the piston moves and the crankshaft rotates, the connecting rod is made to be capable of rotating at both ends.

    At the bottom of the cylinder, the crankshaft is surrounded by the oil sump containing of some oil being collected in the sump's bottom (the oil pan). The use of the oil is to lubricate the moving parts of the engine like the piston. To prevent the fuel/air mixture and exhaust gas leaking into the sump during compression and combustion, the piston rings are installed between the outer edge of the piston and the inner edge of the cylinder which provides a sliding seal between them. The piston rings can also prevent oil in the sump from leaking into the combustion area, where it would be burnt and lost.

  • The four-stroke combustion cycle

    Let us come back to the discussion about the four-stroke combustion cycle. The animation below illustrates how the four-stroke combustion cycle works in an engine with only one cylinder. When the engine goes through one cycle, the following happens:

    The four-stroke combustion cycle inside a car engine with only one cylinder [iii]

    1. The first stroke is the intake stroke. In this stroke, the intake valve opens as the piston moves down from the top. As a result, a cylinder-full of air and gasoline is taken into the engine. For the combustion to occur properly, the air needs to be mixed with the tiniest drop of gasoline. (Part 1 of the animation)
    2. Then the piston moves back up to compress this fuel/air mixture between the top of the piston and the top of the cylinder. Since the compression raises both the pressure and temperature of the mixture, the explosion becomes more powerful. This stroke is known as the compression stroke. (Part 2 of the animation)
    3. As the piston approaches the top of the cylinder, the spark plug emits a spark to ignite the fuel and air mixture. The resulting explosion produces a lot of exhaust gas leading to a rapid increase in the pressure inside the cylinder. Subsequently, the piston is forced to move back downwards. During this so-called power stroke, power is transmitted from the piston to the crankshaft, which will be in turns transferred to the wheels through the other parts of the car. (Part 3 of the animation)
    4. In the last stroke, the exhaust valve opens and the exhaust gas leaves the cylinder after the piston hitting the bottom of the cylinder. Thus this stroke is also known as the exhaust stroke. (Part 4 of the animation)
    After completing the four strokes, the piston reaches the top of the cylinder again and the condition of the cylinder is restored to be the same as that just before the intake stroke. So now the engine is ready for the next cycle and thus the engine can repeat the cycle again and again.

  • Different types of multi-cylinder engine

    The engine discussed above has only one cylinder. However, most cars engine has more than one cylinder like four, six or eight cylinders. We should aware that the cylinders inside the multi-cylinder engines do not fire at the same moment. For example, if a cylinder is in the stroke one, the other cylinders may be in the stroke two and so on. The exact sequence of the firing of the cylinders is known as the firing order. In a multi-cylinder engine, the cylinders can be arranged in different orders. The typical arrangements of the cylinders are: inline, V or flat (also known as horizontally opposed or boxer). The following animations show how these multi-cylinder engines work.

    A flat four-cylinder car engine [viii] (click the picture for animation)

    An inline four-cylinder car engine [viii] (click the picture for animation)

    A V-6 car engine [viii] (click the picture for animation)

    Different configurations (inline, V or flat) have different pros and cons in smoothness, manufacturing-cost and shape characteristics. They are chosen according to the requirements of different vehicles.

  • Displacement of a car engine

    During the combustion cycle, the piston moves up and down which changes the size of the combustion chamber from its maximum volume to the minimum volume. The difference between the maximum and minimum volume is known as displacement. The displacement is usually measured in liters or CCs (Cubic Centimeters, where 1,000 cubic centimeters equals one liter). For example, a motorcycle might have a 500 cc or a 750 cc engine while a sports car might have a 5,000 cc engine.

    When people mention the displacement of a car engine, they are indeed referring to its total displacement that is given by the sum of the displacements of all the cylinders inside the engine. Thus a 4-cylinder engine in which each cylinder displaces half a liter is called a "2.0 liter engine". On the other hand, if six half-liter displacement cylinders are arranged in a V configuration inside the engine, the engine is called a "3.0 liter V-6 engine".

    In general, the displacement gives you an idea about how much power an engine can produce. A 500 cc cylinder can hold twice the amount of the fuel and air mixture holding by a 250 cc cylinder. Therefore we would expect the 500 cc cylinder produces about twice as much power as the 250 cc cylinder provided that everything else is equal. In other words, the engine with larger displacement is considered to be more powerful. Most modern cars have engine with displacement of ranged from 2000 cc to 5,000 cc while trucks often have displacements much higher than 5000 cc. The following table lists the displacements of the engines of several vehicles.

    Displacement of the engines of several vehicles [iii]
    Model Displacement (cc) Model Displacement (cc)
    Chevy Camaro SS 5665 Ford SVT Mustang Cobra 4601
    Audi A6 4172 BMW S40i 4391
    Lexus GS 430 4293 Dodge Stratus ES 2736
    Honda Accord EX 3000 Chevy 2500 HD 2WD (truck) 8000

    What could be wrong inside the car engine?

    It is not rare that a car suddenly breaks down on a road. Such circumstance is probably due to something wrong inside the car engine. What could be wrong inside the engine?


    The malfunction of the engine are mainly due to the following reasons:

    • Bad fuel mix - If bad fuel mix occurs, the combustion cannot carry out properly and thus the engine cannot run in the proper way. The bad fuel mix may be due to the shortage of fuel in the air and fuel mixture after running out of gasoline. If there is clogging of the air intake, there would be insufficient air in the air and fuel mixture so that it can be burn properly. Besides, the bad fuel mixture might be the product of either inappropriate amount of fuel supplied by the fuel system or existence of impurity (like water in your gas tank) in the fuel.

    • Lack of compression - If the air and fuel mixture is not compressed properly, the combustion process will not work in the right way. The lack of compression might be due to the worn out of piston rings that allows the air and fuel mixture to leak past the piston during compression. If the intake or exhaust valves are not sealed properly, leaking of fuel mixture might also occurs during compression. In addition, the leaking may be due to the presence of a hole in the cylinder. The "hole" is commonly found to be located at the position where the top of the cylinder attaches to the cylinder itself.

    • Lack of spark - If there is only weak spark or even no spark for the ignition of fuel, the combustion process will also work improperly. The lack of spark must be related with spark plug. For instance, if spark plug or the wire leading to it is worn out, the spark will be weak. More severely, there will be no spark if the wire is cut or missing, or if the system sending the spark down the wire is not working properly. On the other hand, problem about the fuel ignition will also arise if the spark occurs either too early or too late during the combustion cycle that makes the fuel does not ignite at the right moment.

    Of course, there are many other causes for the engine to be out of order. For example, it may be resulted from out of power inside the battery so that the engine cannot be started. Another possible cause for the malfunction of the engine may be the running out of oil inside the cylinder and thus the piston cannot move up and down freely.

Braking System of a Car

Suppose you are driving your car on a road. Suddenly, a boy rushes out to the road in front of your car. To avoid hitting the boy, you press the brake petal to stop the car. Whether you can avoid hitting the boy or not depend mainly on the quality of you car's brake system. This story illustrates that a good brake system are vital for avoiding car accidents. In this section, let us take a close look on the brake system, which will cover the basic scientific principle behind the system, the workings of a simple brake system and the antilock braking system (ABS).

A typical brake system [viii]

How Things Work
  • Force of friction

    When the brake is pressed, a huge stopping force would be generated. Obviously, this force would stop the rotation of the wheels in order to stop the motion of the vehicle. How can this be done? In fact, the stopping force slows down the spin of the wheels by generating friction on it. To understand the working mechanism of the braking system, let us begin by taking a quick look on friction.

    When one surface slides over another surface, the so-called frictional force that resists the sliding motion would appears. Friction is a measure of how hard it is to slide one object over another (i.e. for the sliding between the surface of the two objects). It was found that the friction depends on the roughness of the contacting surfaces. Indeed, friction would exists even the surfaces are very smooth.

    Why friction appears?
    The friction is due to the irregularities on a surface. If we look at any surface through the microscope, you will see many small peaks and valleys (the irregularities). If two surfaces rub over each other, the irregularities on the two surfaces would get squished together resulting in a frictional force that opposes the motion. We should note that frictional force exists even the surfaces in contact are not in relative motion. For example, if you push a heavy block slightly, the block might not move. It is because you have not applied a large enough force to overcome the frictional force between the block and the floor under the block.
    Friction at microscopic scale [viii]
    Suppose you want to push two different weight blocks to another location by the bulldozer as shown in the figure below. If the two blocks are made of the same material, which one will be harder to push? In fact, the heavier one will be harder for the bulldozer to push. Why? It is because the weight of the heavier block causes the irregularities on the contacting surfaces to squish together much more and thus gives rise to a larger frictional force for the heavier block. It implies that the amount of force required to move a block is proportional to that block's weight; larger force is need for heavier weight. This principle has been applied for many devices such as brakes and clutches, where a pad is pressed against a spinning disc. More force pressing on the pad would result in greater stopping force.
    Which block has a larger friction? [viii]
    In addition, the friction resisting the slide of a block would also depends on the material made up the block since different materials have different microscopic structures. For example, sliding rubber against rubber is harder than sliding steel against steel.

    The friction force of sliding a block over a surface is measured by the coefficient of friction that is the ratio of the force required to slide the block to the block's weight. The coefficient of friction is a dimensionless unit ranging between 0 to 1 with smaller value meaning a more slippery surface. To be concrete, let us consider an example. Suppose the coefficient of friction for sliding blocks made of certain material over a surface is 1.0, then it would take 100 pounds of force to slide the 100-pound block, or 300 pounds of force to slide the 300-pound block. If the coefficient of friction is 0.1 rather than 1.0, then it will take 10 pounds of force to slide to the 100-pound block or 30 pounds of force to slide the 300-pound block.

    We should be aware that the coefficient of friction would be different if the surfaces of contact are relatively in motion instead of at rest. The coefficient of static friction refers to the case that the two surfaces in contact are not sliding relative to each other. Moreover, the coefficient of dynamic friction corresponds to the case that the two surfaces are sliding relative to each other. The coefficient of dynamic friction is usually less than the coefficient of static friction, which implies more force is required to move a static object than to keep it moving. The following table lists the coefficients of friction for a few instances.

    The coefficients of friction for several cases [iii]
    Coefficient of
    static friction
    Coefficient of
    dynamic friction
    Rubber on concrete 0.90 0.70
    Copper on glass 0.68 0.53
    Oak wood on oak wood 0.54 0.32
    Steel on ice 0.02 0.01

    The table below shows that the coefficient of friction of the tires of a vehicle moving on a concrete road varies a large amount under different circumstances.

    The coefficients of friction of the vehicle's tires under different circumstances [iii]
    Coefficient of
    static friction
    Coefficient of
    dynamic friction
    Dry concrete at low speed 0.9 0.7
    Dry concrete at high speed 0.6 0.4
    Wet concrete at low speed 0.7 0.5

    Besides, the coefficient of friction is also related with the stopping distance that is the shortest distance for a vehicle to stop without skidding. In particular, it was found that the stopping distance is inversely proportional to the coefficient of static friction for the tires to slide over the road. As mentioned before, the coefficient of static friction of the tires changes a lot if the tires becomes worn out or the road condition changes due to the weather (see below table). Therefore, the stopping distance of the vehicle varies a large amount under different circumstances, as shown in the below table. For example, the stopping distance of a vehicle with new tires moving at 60 mph increases eighteen times if the vehicle moves from a dry road to an icy road. In brief, both the road condition and condition of the tires are crucial factors determine whether a vehicle can be easily stopped on a road.

    The coefficients of static friction under various conditions for new and worn tires [iii]
    of tires
    Dry Wet
    (light rain)
    Heavy rain
    At 60 mph
    New 0.9 0.60 0.3 0.050
    Worn 0.9 0.20 0.1 0.005
    At 80 mph
    New 0.8 0.55 0.2 0.005
    Worn 0.8 0.20 0.1 0.001

    The stopping distance of a vehicle moving at 60 mph under different conditions
    Condition Stopping distance (feet)
    Dry (new tires) 134.4
    Light rain (new tires) 201.6
    Light rain (worn tires) 605
    Heavy rain
    (puddles and worn tires)
    Ice (new tires) 2420

  • Basic principle of the brake system

    When the brake pedal is pushed, the car transmits the force from driver's foot to its brakes through some fluid. Obviously, actual brakes require a much greater force than that exerted by driver's leg. Thus the car must magnify the force of driver's foot. In the brake system, the multiplication of force is attained by making use of the two principles:
    1. Leverage
    2. Hydraulic force multiplication
    Let us study these two principles one by one.

    1. Leverage

      Before any force is transmitted to the brake fluid, the pedal multiplies the force from driver's leg several times by using a lever. The force multiplication gained by the use of lever is called the leverage. The lever is based on the principle of lever stating that:

      "The force pushing upward at one end of a lever is equal to the force pushing downward at the other end times the ratio of the distance of the two forces from the pivot point.

      The below figure illustrates the principle of the lever.

      The principle of lever [xii]

      So we can get a bigger force at one end of a lever by applying a force at a suitable position on the other end. Let us consider an example to explain how to do this. In the figure below, suppose a force F is being applied to the left end of the lever which is twice as long (2X) as the right end (X). Then a force of 2F would be available on the right end of the lever. Besides, the force at the right end should act through half of the distance (Y) that the left end moves (2Y). If we change the relative lengths of the left and right ends, the force multiplication by the lever (i.e. the ratio of the two forces) changes.

      Force multiplication by a simple leverage [viii]

    2. Hydraulic force multiplication

      After multiplied by the lever, the force acted on the pedals would be magnified by a hydraulic system consisting of some cylinders with brake fluid inside. In fact, the workings of any hydraulic system is based on the so-called Pascal's principle:

      The pressure exerted on a confined incompressible fluid is transmitted undiminished in all directions and acts with equal force on all equal areas (i.e. pressure is constant).

      where the pressure is the force divided by the area.

      A simple hydraulic system [viii]

      How does a hydraulic system work in practice? Let us consider a simple hydraulic system. In the above figure, two pistons are fit into two oil-filled cylinders which are connected together with an oil-filled pipe. If a downward force is pushed on one piston (the left one, in this drawing), then the force is transmitted to the second piston through the oil in the pipe. Since oil is incompressible, almost all the applied force arrives at the second piston. (Of course, there would be some loss due to friction or other reasons.) The advantage for using the hydraulic systems is that the pipe connecting the two cylinders can be any length and shape. So the connecting pipe can be a fine irregular shape pipe so that it can snake through all sorts of things separating the two pistons. The pipe can also have more than one openings at each end and thus one master cylinder (the cylinder where the force is applied) can drive more than one slave cylinder (the cylinder where the force is transmitted to) just like that in the below figure.

      Master cylinder with two slaves [viii]

      Another advantage for using a hydraulic system is that the force multiplication (or division) can be performed easily. According to the Pascal's principle, the pressure applied at one end of a hydraulic system would be transmitted with constant value throughout the system. Therefore, to change the force on a piston in a hydraulic system, all we have to do is change the size of one piston, as shown below.

      Force multiplication by a hydraulic system [viii]

      We can determine the factor of the force multiplication in the above system by looking at the size of the pistons. Suppose the radius of the piston on the left is 1 inches while the radius of the piston on the right is 3 inches. For a piston (which is in circle shape), the area is equal to Pi*radius*radius. So the right piston must be nine times larger than the left piston as the radius of the right piston is three times larger than that of the left piston. Hence, any force applied to the left-hand piston will increase nine times as it come out on the right-hand piston. That is to say, if a 100-pounds downward force is applied at the left piston, a 900-pound upward force will arise on the right. However, the right piston will only raise 1 inch if the left piston is depressed by 9 inches since the volume of the fluid displaced by the two pistons must be the same.

  • A simple braking system After learning the basic principle of the brake system, let us look at a simple brake system as shown below.

    A simple brake system [viii]

    In this system, the distance from the pedal to the pivot is four times larger than that from the cylinder to the pivot, so the force applied at the pedal will be increased by a factor of four before it is transmitted to the cylinder. Then the hydraulic system magnified the force by nine times since the ratio of the radius of the brake cylinder to that of the pedal cylinder is three. Thus this system all together increases the force of the driver's leg by a factor of 36. For example, if a 10-pound force is pushed on the pedal, a 360-pound force will be generated to squeeze the brake pads at the wheel.

    There are a number of possible problems for this simple system. For instance, what will happens if there is a leak in the system? If there is only a slow leak, eventually the brake cylinder will not have enough fluid for the brakes to work. In contrast, if there is a major leak, then all the fluid will rush out the leak at the first time the brakes is stepped; and the result is a complete brake failure. To avoid accident due to brake failure, the master cylinder in modern cars is designed to handle these potential problems.

  • Antilock braking system (ABS)

    The antilock braking system (ABS) is designed to avoid the car went out of control when the brakes lock up. Thus the system can help the driver to stop his/her car safely even on a very slippery surface. Obviously, a skidding wheel has less traction than a non-skidding wheel. By keeping the wheels from skidding while the driver slow down, anti-lock brakes benefit him in two ways: He'll stop faster, and he'll be able to steer while he stops. The ABS system has been used on cars since the late 1960s. Nowadays, almost all new cars are equipped with this system.

    However, the ABS does not always give rise to a shorter stop for any surfaces. For example, it takes almost the same time for a car to stop on a dry concrete road either by the regular brake system or ABS. However, the ABS would allow the car to stop faster on a wet or icy road. The main function of the ABS is to avoid the driver losing control of the car.

    The components of the antilock brake system (ABS) [viii]

    ABS works by monitoring the speed of all the wheels of the car at all times. Based on the data received from the speed sensors mounted on each wheel, the ABS controller looks for any abnormal decelerations in the wheel. It is because a wheel experiences a rapid deceleration just before it locks up. It might take five seconds for a 60 mph car to stop under ideal conditions; however, a wheel that locks up could stop rotation in less than one second. In other words, if the deceleration were not intervened, the wheel would stop at an abnormally fast rate.

    Knowing that the ABS does not bear such a rapid deceleration, the ABS controller reduces the hydraulic pressure to that brake until the wheel accelerates again. Then it restores the hydraulic pressure until the abnormal deceleration appears again. It can do this so fast that there is no significant change in the speed of the tire. Due to the functioning of the ABS, the tire would slow down at the same rate as the car with the brakes keeping the tires to undergo maximum deceleration for no skidding. It results in maximum braking power for the system.

    Due to the rapid stopping and starting of the hydraulic pressure by the ABS, the person stepping the brakes will feel a pulsing of the brake pedal when the ABS operates. Such pulsing can occur to 15 times per second for some ABS systems.

    The ABS system is a valuable component of modern cars that improves the safety of driving. However, the ABS cannot avoid all skids. For example, the ABS cannot prevent those skids caused by excess speed, sharp turning and slamming on the brakes. In fact, many skidding occurs before the ABS is activated. However, ABS significantly reduces the stopping distance and helps you to keep control of your car.

Driving Safety

In the modern world, road's traffic is busy and traffic accidents happen frequently. In each year, many passengers and drivers are injured or even killed by traffic accidents. In fact, there are many measures that can be taken by drivers or passengers to reduce the chance of getting injured or killed by car accident.

How Things Work
  • Crashworthiness

    A severely crashed car [ix]

    One of the approaches to improve driving safety is reducing the degree of injuries in case of car crash. Crashworthiness is the measure of how well a vehicle protects its occupants during a crash. Therefore, the crashworthiness of a vehicle give us an estimation about how bad the passenger would be hurt if this vehicle crashes with other object like a tree or another vehicle. Since high crashworthiness refers to less expected degree of injuries, it should be more safe for us to ride on a vehicle with higher crashworthiness. In the study of the crashworthiness, researchers investigate the cause and mechanism of the injury of the driver and passenger during a collision. The results of this investigation also allow researchers to develop some means for estimating the severity of a collision. Based on the knowledge gained from the study of the crashworthiness, we can get some clues about whether anything could be done to reduce the chance and severity of human injuries during the car crash.

    We should be aware that crashworthiness is not the same as vehicle safety. When we consider the crashworthiness, we have assumed that the car crash has already happened. Unlike in the study of vehicle safety, we don't care about who is responsible for the accident or whether the accident could be avoided in the study of the crashworthiness. Therefore, it is possible that a relatively safe vehicle has poor crashworthiness. That is to say, even if a car is equipped with many crash avoidance features, it might have features causing severe injuries in case that the car crash really happens.

  • Crash test

    As mentioned above, if we want to know the risk of injury of the occupant of a vehicle during an accident, we can take a look on the crashworthiness of this vehicle. But how do people determine the crashworthiness of a vehicle? It is determined by performing crash test for the vehicle.

    Crash test dummies play an integral part of vehicle crash tests. The use of the dummy is to simulate a human being during a crash and also collect data that cannot be collected from a human occupant. In the United States, all frontal crash tests are conducted using the same family of dummy called the Hybrid III dummy in order to guarantee consistent results.

    The family of the Hybrid III dummy [x]

    A Hybrid III 50th Percentile Male dummy [x]

    During the car crash, the degree of injuries might be different for passengers of different gender and age even they are under the same conditions. So dummies having different dimension and internal structure are used in the crash test of a vehicle. Dummies are classified by the percentile and gender. For example, the 50th percentile male dummy represents the median sized male, i.e. it is bigger than half the male population and smaller than the other half. This dummy weighs 170 lbs and is 5 ft 10 inches tall. It is the dummy most widely used in frontal crash test all over the world.

    Crash test dummies
    To make them human-like, all crash test dummies are built of materials that simulates the physiology of the human body. For example, the upper part of the adult Hybrid III dummy is made of several metal rods with polymer based damping material which simulates the reaction of the chest of an adult during the collision of cars.
    On each dummy, there are three types of instruments:
    Accelerometers - These devices measure the acceleration in a particular direction. The acceleration or deceleration (i.e. the rate of decrease of the speed) of the body during the crash is a crucial factor determining the probability of injury. For example, if you crash your head into a brick wall, the deceleration of your head is very large and so you are probably hurt. In contrast, if you crash your head into a pillow, the deceleration of your head is much smaller and so it doesn't hurt. To measure the acceleration of different parts of the body, accelerometers are installed all over the dummy like dummy's head, chest, pelvis, legs and feet.
    Load sensors - These sensors measure the amount of force acting on different parts of the body during a crash. If we find the maximum load in a bone, we can determine the probability of breaking of this bone.
    Motion sensors - These sensors are installed in the dummy's chest to measure the deflection of the occupant's chest during a crash. If the deflection of the chest is large, it is likely that the occupant is severely injured during the crash.
    Before the crash-test, dummies are placed in the vehicle after researchers has applied paint to them. Different colors of paint are applied to the parts of the dummies' bodies including knees, face and skull which are most likely to be striked during a crash. The paint can help us to locate where the different parts of the body hit the car. For example, in the following photo, the blue paint sticked on the airbag indicates that it was hit by the dummy's face.
    The multicolored paint on the dummy shows the position of the cabin hit by different body parts. [x]
    If the accelerometers in the dummy's head indicate there is a very large acceleration, it means that the risk of injury is very large during the crash. Researchers can look at the paint mark to find out which body part hit what part of the vehicle inside the cabin, helping them to develop improvements to prevent such injury in future crashes.

    The frontal crash tests and the side impact crash tests are the major types of crash test used to determine the crashworthiness of a vehicle. In the frontal crash test, a vehicle moving at a fixed speed strikes straight with a rigid barrier. It is equivalent to the head-on collision between two vehicles having the same weight and same speed as the test vehicle. For frontal crash tests, crash-test dummies are placed in driver and front passenger seats with seat belts fastened. The frontal crash tests can be subdivided into two types --- the full-width frontal crash test and offset frontal crash test. The main difference is that the full width of a vehicle's front is striked in the full-width frontal crash test while only one side of the vehicle's front is striked in the offset frontal crash test. The results from these two tests complement each other and can be used together to assess overall frontal crash safety.

    (Courtesy: NHTSA) (Courtesy: IIHS)
    A full-width frontal crash test demo A offset frontal crash test demo

    In the side impact crash tests, an impactor with a deformable front end representing the front of a car crashes into the side of the test vehicle. It simulates a car that is crossing an intersection being hitted its side by a car running a red light. For side crash tests, dummies are placed in the driver and rear passenger seats at driver's side; and they are both secured with the vehicle's seat belts. We should note that test results of any crash test should be compared only among similar weight vehicles.

    (Courtesy: IIHS)
    A side impact crash test demo

    In the United States, the National Highway Traffic Safety Administration (NHTSA) and the Insurance Institute for Highway Safety (IIHS) conduct crash tests for a large number of different models of vehicles. Based on the results of their crash test, these two organizations set up two systems of safety ratings for the crash of vehicles. NHTSA rates the safety of crash of vehicles by stars with five stars meaning the smallest risk of injury in the crash. On the other hand, vehicles are rated as good, acceptable, marginal and poor by the safety ratings of IIHS. The crash ratings of vehicles can be found on the webpages of NHTSA and IIHS as well as many publications. The table below shows the crash safety ratings for several 2002 vehicles.

    Crash safety ratings for several 2002 vehicles [iii]
    Model NHTSA
    Audi A6 ****/**** Acceptable
    Chevy Impala *****/***** Good
    Infiniti QX4 ****/***** Marginal
    Lincoln LS *****/***** Good
    Ford Taurus *****/***** Good
    Plymouth Neon ****/**** Marginal

    Of course, the best way to reduce the chance of getting injured during a crash is to avoid the crash. The ability of crash avoidance depends on many factors such as the presence of ABS, types of types, how sharp the car can turn and so on. But perhaps the most important factor is whether the driver has good ability and skill or not.

  • Collision protection devices

    The safety system of a car [xi] (Click the picture for full size)

    Most modern cars are equipped with a safety system consisting of many collision protection devices. The seat belt is one of the most important protection devices which have saved thousands of lives in car accidents. By tiding the person with the car, the seat belt makes the person to slow down at the same rate as the car and not be thrown out of the car. To give more protection to the passenger, the air bags are usually used in conjunction with the seat belts. It was found that injuries could be significantly reduced by using air bags with the seat belts. For example, statistics show that air bags reduce the risk of dying in a head-on crash by 30 percent. When car crashes, the air bag is quickly inflated with a large volume of gas and then bursts out to the space just in front of the passenger. Then the passenger would hit on the cushion-like air bag and thus slow down his/her speed over a much longer time. As a result, the amount of force acting on the passenger is reduced. But we should note that it would be dangerous to use the air bags under specific conditions. For example, it was revealed that the air bag could hurt someone who is too close to it. So a passenger might probably injured by the air bag if he/she does not wear a seat belt.

    Another important collision protection device is the crumple zone in the front and rear of the car. A good crumple zone can allow the car to have a longer time of impact and thereby decrease the magnitude of the force acting on it. Other safety features such as collapsible steering wheels, side air bags and headrest are also critical for the protection of passengers during a collision.


Supplementary notes on the laws of motion
(Courtesy: The Physics Classroom)
  • More examples on Newton's first law of motion

    In our daily life, there are many phenomena that could be explained by the Newton's first law of motion. Some of them are listed as follows:

    • Blood rushes from your head to your feet when riding on an elevator that suddenly stops during downward motion.
    • The head of a hammer can be tightened onto the wooden handle by hitting the bottom of the handle against a hard surface (see the picture on right hand side).
    • Headrests are placed in cars to prevent neck injuries due to the rapid back and forth motion of the head during car accident.
    • During a ride on a skateboard, if the motion of the skateboard suddenly halts after hitting an obstacle like a rock, you will fly forward off the board.

  • Some illustrations on movies

    Below are some simple experiments illustrating the first law of motion.
    I. Penny-in-a-glass (Courtesy: Cislunar Aerospace, Inc)
    II. Smash Your Hand (Courtesy: The University of Minnesota)
    III. Car on Cart on Cart (Courtesy: The University of Minnesota)

  • Try to explain the following observation.


    An empty bottle lies on the floor of a train compartment which is at rest. When the train starts moving, the bottle rolls back; while the bottle rolls forward when the train brakes to stop. Why this happens?

    When the train starts, the bottle tends to stay in the state of rest due to its inertia. So it rolls back to the original position as the train starts to move. Similarly, when the train stops, the bottle tends to continue its motion due to its inertia and thus it rolls towards the direction the train was headed. The bottle stays at rest only when the train is moving with constant velocity.

    An empty bottle on the floor of a train while it starts and stops.

  • Mass and weight

    Does mass have the same meaning as weight?
    According to Newton's second law of motion, the behavior of an object depends on its mass. A more massive object has more inertia and is more difficult to be accelerated. So it seems that mass has the same meaning as weight. But this is WRONG!! Indeed, weight and mass are related by:
    Note that weight is a force. The acceleration of gravity is the acceleration of any body undergoing free-fall with the negligence of the air resistance. It is roughly constant at anywhere of the earth's surface with value equal to one "g", i.e. 9.8 m/s2. So we may interpret that weight is the force of gravity acting on a body.
    On the Moon, a person's weight is only 1/6 of his or her weight on the Earth. [vi]
    Obviously, different planets have different force of gravity. If two identical objects (with the same mass) are placed on different planets, their weights will be different; however, their masses will be still the same.

  • More examples on Newton's third law of motion

    Why both two cows fall down from the cliff?

    Two cows are standing on a frictionless cliff as shown in the below comics. In order to push the other down from the cliff, one cow pushes a force on the other. Surprisingly, the result is that they both fall down from the cliff. Why?


    If one cow pushes a force on the other, there will a same magnitude force pushing back the cow who pushes the other, as expected by the Newton's third law. Because the two cows are both standing on a frictionless ground, no frictional force resists their motion and they move in the direction same as the force pushing on them, i.e. towards the edge of the cliff. As a result, both the two cows fall down from the cliff.

    Daily examples in Newton's third law of motion
    We can see many examples of Newton's third law in our daily life. When you hold a water hose with water jet coming out, you would feel a backward force pushing your hand. The third law of motion is also the principle of launching a rocket. The gas coming out from the back of a rocket in a very fast speed pushes the rocket to move forward (i.e. gives the rocket a forward thrust).

    The space shuttle propels into the space by exerting an equal and opposite force with the exhaust gasses. [v]



  1. PhysicsNet
  2. The Physics Classroom
  3. Parker B., The Isaac Newton School of Driving: physics and your car. Baltimore: The Johns Hopkins University Press, 2003.
  5. Physics at BHS
  6. Beyond Books
  7. Southeast Missouri State Univeristy General Chmistry I Laboratory Home Page
  8. HowStuffWorks
  10. National Highway Traffic Safety Administration (NHTSA)
  11. The Science of Gears

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