74 Chapter 2

Newton’s Second Law of Motion

• Newton’s second law of motion relates the acceleration of an object to themass of the object and the net force acting on it. The equation is

a� = �F�

mnet� or F�net = ma�.

• Newton’s second law is applied in many problem-solving situations.

2.5 Newton’s Third Law of MotionWhen astronauts go for a “space walk” outside the International Space Station(the ISS), they travel along with the station at a speed of about 30 000 km/h rel-ative to Earth’s surface. (You should be able to use the first law of motion toexplain why: since the station and the astronaut are both in motion, they remainin motion together.) However, to move around outside the station to makerepairs, the astronaut must be able to manoeuvre in different directions relativeto the station. To do so, the astronaut wears a special backpack called a mobilemanoeuvring unit, or MMU (Figure 1), a device that applies another importantprinciple named after Sir Isaac Newton.

Newton’s first law of motion is descriptive and his second law is mathemat-ical. In both cases, we consider the forces acting on only one object. However,when your hand pushes on the desk in one direction, you feel a force of the deskpushing back on your hand in the opposite direction. This brings us to the thirdlaw, which considers forces acting in pairs on two objects.

SUMMARY

Understanding Concepts

1. When the Crampton coal-fired train engine was built in 1852, itsmass was 48.3 t (1.0 t = 1.0 × 103 kg) and its force capability wasrated at 22.4 kN. Assuming it was pulling train cars whose totalmass doubled its own mass and the total friction on the engineand cars was 10.1 kN, what was the magnitude of the accelera-tion of the train?

2. Determine the net force needed to cause a 1.31 × 103-kg sportscar to accelerate from zero to 28.6 m/s [fwd] in 5.60 s.

3. As you have learned from Chapter 1, the minimum safe distancebetween vehicles on a highway is the distance a vehicle cantravel in 2.0 s at a constant speed. Assume that a 1.2 × 103-kg caris travelling 72 km/h [S] when the truck ahead crashes into anorthbound truck and stops suddenly.(a) If the car is at the required safe distance behind the truck,

what is the separation distance?(b) If the average net braking force exerted by the car is

6.4 × 103 N [N], how long would it take the car to stop?(c) Determine whether a collision would occur. Assume that the

driver’s reaction time is an excellent 0.09 s.

Section 2.4 Questions

Figure 1

The astronaut is wearing a manoeuvring unit(the backpack) that illustrates an applicationof the third law of motion. Expanding gasesexpelled from the unit propel the astronaut ina direction opposite to the direction of theexpelled gases.

Forces and Newton’s Laws of Motion 75

Newton’s third law of motion, often called the action-reaction law, states:

To illustrate the third law, imagine a ball shot horizontally out of the tube ofa toy cart on wheels, as shown in Figure 2. When the ball is pushed into the cart,a spring becomes compressed. Then, when the spring is released, the spring (andthus the cart) pushes forward on the ball. We call this force the action force. At thesame instant, the ball pushes backward on the spring (and thus the cart). We callthis the reaction force of the ball on the cart. The action and reaction forces areequal in size but opposite in direction, and act on different objects. (Do notworry if you have difficulty deciding which of an action-reaction force pair is theaction force and which is the reaction force. Both forces occur at the same time,so either way works.)

Sample Problem

Draw an FBD of the ball shown in Figure 2 while it is still pushed by the spring.

Solution

The FBD is shown in Figure 3. The force of thespring on the ball is to the right. While the ballis still in the tube, the normal force exerted bythe tube is equal in magnitude to the force ofgravity on the ball. Notice that there are noaction-reaction pairs of forces in the diagrambecause an FBD is a drawing of a single object,not two objects, and an FBD shows only theforces exerted on the object, not any forcesthat the object might exert on something else.

Do action-reaction forces exist on stationary objects? Yes, they do, but theymight not seem as obvious as the example of the ball being shot out of the toycart. Consider, for instance, an apple hanging in a tree, as in Figure 4. The forceof gravity on the apple pulling downward is balanced by the upward force of the stem holding the apple. However, these two forces act on the same object (the apple), so they are not an action-reaction pair. In fact, there are two action-

2.5

third law of motion: for every actionforce, there is a reaction force equal in magnitude, but opposite in directionThird Law of Motion

For every action force, there is a reaction force equal in magnitude, butopposite in direction.

Figure 2

When the spring is released, it exerts a for-ward force on the ball, and simultaneouslythe ball exerts a force on the spring (and cart)in the opposite direction. The ball moves for-ward and the cart moves backward.

Fg

FN

FA

+y

+x

Figure 3

Figure 4

(a) The downward force of gravity on theapple is balanced by the upward forceexerted by the stem. (This is not anaction-reaction pair of forces.)

(b) One action-reaction pair of forces existswhere the stem and apple are attached.

(c) A second action-reaction pair existsbetween Earth and the apple.

force of stem on apple

force of apple on stem

force of stem on apple

Fg (force of Earth on apple)

Fg (force of Earth on apple)

force of appleon Earth

(a)

(c)

(b)

Your teacher will set up demonstrations of the third law of motion. In eachcase, predict what you think will occur, then observe what happens, andfinally summarize your observations in tabular form using these headings:

Object Predicted Observed Description Description Diagram ofobserved result result of the action of the reaction the action-

force(s) force(s) reaction pair(s)

Try ThisActivity

Demonstrating Newton’s Third Law

76 Chapter 2

reaction pairs in this example. One is the downward force of the apple on thestem, equal in size but opposite in direction to the force of the stem on the apple.The other is the downward force of Earth’s gravity, equal in size but opposite indirection to the upward force of the apple on Earth. Of course, if the stem breaks,the apple accelerates toward Earth, and Earth also accelerates toward the apple.However, because Earth has such a large mass, and acceleration is inversely pro-portional to mass, Earth’s acceleration is extremely small.

Practice

Understanding Concepts

1. Draw an FBD of the cart in Figure 2 when the spring is released.

2. Draw an FBD of the apple hanging from the stem in Figure 4. Arethere any action-reaction pairs of forces in your diagram?

Applying the Third Law of Motion

The third law of motion has many interesting applications. As you read the fol-lowing descriptions of some of them, remember there are always two objects toconsider. One object exerts the action force while simultaneously the other exertsthe reaction force. In certain cases, one of the “objects” may be a gas such as air.

(a) When someone is swimming, the person’s arms and legs exert an actionforce backward against the water. The water exerts a reaction force forwardagainst the person’s arms and legs, pushing his or her body forward.

(b) A jet engine on an aircraft allows air to enter a large opening at the front ofthe engine. The engine compresses the air, heats it, then expels it rapidlyout the rear (Figure 5). The action force is exerted by the engine backwardon the expelled air. The reaction force is exerted by the expelled air forwardon the engine, pushing the engine and, thus, the entire airplane in theopposite direction.

(c) A squid is a marine animal with a body size ranging from about 3 cm to 6 m.It propels itself by taking in water and expelling it in sudden spurts.Theaction force is applied by the squid backward on the discharged water.The reaction force of the expelled water pushes the squid in the oppositedirection.

Observing Newton’s Third Law

Electronically

You can observe verification of Newton’sthird law of motion by using simulation soft-ware or by accessing the Nelson scienceWeb site. Follow the links for Nelson Physics11, 2.5. Alternatively, if the interfacing tech-nology is available, your teacher can demon-strate the third law using force sensorsmounted on two dynamics carts. When thecarts collide, the magnitude of the force eachcart exerts on the other can be measured.The law for various mass combinations andinitial velocities can be observed.

DID YOU KNOW ?

airintake

fuel intake

nozzleCompression fans draw air in and compress it.

Combustion chamber: Fuel burns continuously in the air and the resulting hot gases expand rapidly.

Spinning turbines are used to drive the compressor fans.

Expanded gases leave the nozzle and exert a reaction force on the engine, pushing the airplane forward.

Figure 5

The design of a turbo jet engine

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Forces and Newton’s Laws of Motion 77

Practice

Understanding Concepts

3. Explain each event described below in terms of Newton’s third law ofmotion.(a) A space shuttle vehicle, like the one shown in the photograph in

Figure 1 of section 2.3, is launched.(b) When a toy balloon is blown up and released, it flies erratically

around the room.

4. You are a passenger on a small rowboat. You are about to step fromthe boat onto a nearby dock. Explain why you may end up in thewater instead.

5. According to Newton’s third law, when a horse pulls on a cart, thecart pulls back with an equal force on the horse. If, in fact, the cartpulls back on the horse as hard as the horse pulls forward on thecart, how is it possible for the horse to move the cart?

Newton’s Third Law of Motion

• Newton’s third law of motion, which always involves two objects, statesthat for every action force, there is a reaction force equal in magnitude, butopposite in direction.

• Action-reaction pairs of forces are applied in many situations, such as aperson walking, a car accelerating, and a rocket blasting off into space.

SUMMARY

2.5

Figure 6

The space probe, Deep Space 1, was launchedin 1998 to observe the asteroid Braille. Theprobe used ions ejected from the exhaust grid (the grey disk) to propel itself forward.This successful mission will help scientistsdevelop ion propulsion systems for the future.

Understanding Concepts

1. Use the third law of motion together with a diagram of theaction-reaction pair(s) to explain each situation.(a) A person with ordinary shoes is able to walk on a sidewalk.(b) A rocket accelerates in the vacuum of outer space.

2. (a) A certain string breaks when a force of 225 N is exerted on it.If two people pull on opposite ends of the string, each with aforce of 175 N, will the string break? Explain.

(b) Draw a diagram of the situation in (a) showing all the action-reaction pairs of forces.

Making Connections

3. What is meant by the term “whiplash” in an automobile colli-sion? Explain how and why whiplash occurs by applyingNewton’s laws of motion.

4. An “ion propulsion system” is a proposed method of space travelusing ejected charged particles (Figure 6). Locate information onthis system and analyze how it relates to the third law of motion.Follow the links for Nelson Physics 11, 2.5.

Reflecting

5. How important are diagrams in helping you solve problemsinvolving forces and motion?

Section 2.5 Questions

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There are many different types of careers that involve the study of forces andmotion in one form or another. Have a look at the careers described on this page and find out more about one of them or another career in forces andmotion that interests you.

Careers in Forces and Motion

78 Chapter 2

Civil Engineer

It takes about four years at university to com-plete a civil engineering degree. Qualified civilengineers help to plan and design buildings,foundations, roads, sewage systems, andbridges. These engineers work with architectsand use computer programs to design structures.Some work for private construction companiesand government agencies, while others work asprivate consultants to businesses or the govern-ment. All civil engineers must be members of theAssociation of Professional Engineers.

Mechanical Engineer

Mechanical engineering is a four-year universitydegree course. Upon completion of their studies,many mechanical engineers obtain work in the manu-facturing sector, in the areas of safety and qualitycontrol. The work done by mechanical engineers canvary from designing heating and cooling systems tooverseeing assembly line work in car manufacturing.This line of work often requires extensive use ofcomputers. A mechanical engineer must be amember of the Association of Professional Engineers.

Kinesiologist

Kinesiologists must study for about four years to obtain a bachelor’s degree inscience, majoring in kinesiology. To obtain entry into this course, good marks inhigh school mathematics, physics, and biology are essential. Most of the time,kinesiologists work with their hands and with computers. They also use elec-tromyography instruments that measure the electrical activity in muscles totreat and diagnose physical problems. These professionals often work inclinics and hospitals. Increasingly, kinesiologists may be found working asergonomic consultants, in offices and factories, and teaching people how towork safely with various forms of technology.

Practice

Making Connections

1. Identify several careers that require knowledge about forces andmotion. Select a career you are interested in from the list you madeor from the careers described above. Imagine that you have beenemployed in your chosen career for five years and that you areapplying to work on a new project of interest.(a) Describe the project. It should be related to some of the new

things you learned in this unit. Explain how the concepts fromthis unit are applied in the project.

(b) Create a résumé listing your credentials and explaining why youare qualified to work on the project. Include in your résumé• your educational background — what university degree or

diploma program you graduated with, which educational insti-tute you attended, post-graduate training (if any);

• your duties and skills in previous jobs; and• your salary expectations.

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