Chapter 6: Forces

Layout of Chapter 6 6.1 Force

s and

Motion • Contact v.

Long Range • Force

Diagrams• F = ma (2nd

Law)• Combining

Forces• Measurement• 1st Law—

Inertia 6.2 Using Newt

on’s

Laws • Mass and

Weight• Friction Force• Periodic

Motion

6.3 Interaction Force

s

• Identifying them

• Newton’s 3rd Law

• Fundamental Forces

• Ropes and Strings

FORCE AND MOTION6.1

4.1 The Concepts of Force and Mass

A force is a push or a pull.

Contact forces arise from physicalcontact .

Action-at-a-distance or long-range forces do notrequire contact and include gravity and electrical forces.

An Introduction

Describing Motion video clip

F

Mathematically, the net force is written as

where the Greek letter sigma denotes the vector sum.

Newton’s Second LawWhen a net external force acts on an objectof mass m, the acceleration that results is directly proportional to the net force and hasa magnitude that is inversely proportional tothe mass. The direction of the acceleration isthe same as the direction of the net force.

m

Fa

aF

m

MEASURE FORCE? IN A NEWTON, OF COURSE

How do we

SI Unit for Force

22 smkg

smkg

This combination of units is called a newton (N).

DIAGRAM FORCE ON AN OBJECT

How do we

Arrows are used to represent forces. The length of the arrowis proportional to the magnitude of the force.

15 N

5 N

The net force on an object is the vector sum of all forces acting on that object.

The SI unit of force is the Newton (N).

Individual Forces Net Force

10 N4 N 6 N

Individual Forces Net Force

3 N

4 N

5 N64

Free Body Diagrams

Vector arrows represent all the forces acting in a situation.

What does unbalanced really mean?

• In pursuit of an answer, consider a physics book at rest on a table top. There are two forces acting upon the book. One force – the Earth's gravitational pull – exerts a downward force. The second force – the push of the table on the book (sometimes referred to as a normal force) – pushes upward on the book.

Balancing Act• Since these two forces are of equal

magnitude and in opposite directions, they balance each other. The book is said to be at equilibrium. There is no unbalanced force acting upon the book and thus the book maintains its state of motion. When all the forces acting upon an object balance each other, the object will be at equilibrium; it will not accelerate. (Note: diagrams such as the one above are known as free-body diagrams and will be discussed in detail in Lesson 2.)

Another Pictorial Example

Object in motion

Balanced or Not? • To determine if the forces acting upon an

object are balanced or unbalanced, an analysis must first be conducted to determine which forces are acting upon the object and in what direction. If two individual forces acting on an object are of equal magnitude and opposite direction, then these forces are said to be balanced. An object is said to be "acted upon by an unbalanced force" only when there is an individual force acting on the object which is not balanced by another force of equal magnitude and in the opposite direction . Such analyses are discussed in Lesson 2 of this unit and applied in Lesson 3.

Check your Understanding• Copy this down for information used

in further examples. • Luke Autbeloe drops a 5.0 kg box of

shingles (weight approximately 50.0 N) off the barn house roof into a haystack below. Upon hitting the haystack, the box of shingles encounters an upward restraining force of 50.0 N . Use this description to answer the following questions.

Example 1 • 1. Which one of the following

velocity-time graphs best describes the motion of the shingles? Support your answer with sound reasoning.

Answer 1• Graph B• The shingles experience negative

acceleration until they hit the haystack. At that point the forces are balanced, so velocity becomes constant

Example 2 • 2. Which one of the following ticker

tapes best describes the motion of the falling shingles from the time they are dropped to the time they hit the ground? The arrows on the diagram represent the point at which the shingles hit the haystack. Support your answer with sound reasoning.

Answer to #2• Tape A is correct.• It shows the negative

acceleration and constant velocity.

Example 3 (has many parts)• 3. Several of Luke's friends were

watching the motion of the falling shingles. Being "physics types", they began discussing the motion and made the following comments. Indicate whether each of the comments is correct or incorrect. Support your answers.

• A) A. Once the shingles hit the haystack, the forces are balanced and the shingles will stop.

Correct or Incorrect? • Incorrect. • They stop accelerating but do not

stop moving.

Part B• B. Upon hitting the haystack, the

shingles will accelerate upwards because the haystack applies an upward force.

Answer to B• Incorrect• The balanced forces on the shingles

will keep velocity constant.

Example C• C. Upon hitting the haystack, the

shingles will bounce upwards due to the upward force.

Answer to C• Incorrect• Forces are balanced

Example 4 • 4. If the forces acting upon an

object are balanced, then the object

• A. must not be moving. • B. must be moving with a

constant velocity. • C. must not be accelerating. • D. none of the above.

Answer to #4• A is possible but is not

necessarily true at all times• B an object with balanced forces

cannot be accelerating• C It could be at rest and staying

at rest or could be in motion with constant velocity but not accelerating making C the correct answer

A free-body-diagram is a diagram that represents the object and the forces that act on it.

The net force in this case is:

275 N + 395 N – 560 N = +110 N

and is directed along the + x axis of the coordinate system.

If the mass of the car is 1850 kg then, by Newton’s second law, the acceleration is

2sm059.0kg 1850N110

m

Fa

4.4 The Vector Nature of Newton’s Second Law

4.4 The Vector Nature of Newton’s Second Law

Force x component y component

+17 N

+(15 N) cos67

0 N

+(15 N) sin67

+23 N +14 N

The net force on the raft can be calculatedin the following way:

P

A

2sm 018.0

kg 1300N 23

m

Fa x

x

2sm 011.0kg 1300N 14

m

Fa y

y

An object continues in a state of restor in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force.

The net force is the vector sum of allof the forces acting on an object.

Newton’s First Law

Ladder of Inertia

Inertia In Motion

NEWTON’S 1ST LAW, OTHER FORCES, AND MISCONCEPTIONS OF FORCE

Looking into

Force Sub Definition Direction

Friction Fric or f

The contact force that acts to oppose sliding motion between two surfaces

Parallel to the surface and opposite the direction of sliding

Normal N The contact force exerted by a surface on an object.

Perpendicular to and away from the surface

Spring Sp A restoring force, that is, the push or pull a spring exerts on an object

Opposite the displacement of the object at the end of the spring

Tension T The pull exerted by a string, rope, or cable when attached to a body and pulled taut

Away from the object and parallel to the string, rope, or cable at the point of attachment

Thrust thrust A general term for the forces that move objects such as rockets, planes, cars, and people

In the same direction as the acceleration of the object barring any resistive forces

Weight grav or g

A long range force due to gravitational attraction between two objects, generally Earth and an object

Straight down toward the center of the earth

Misconceptions about Forces

WRONG1. When a ball has been

thrown, the force of the hand that threw it remains on it.

2. A force is needed to keep an object moving.

3. Inertia is a force. 4. Air does not exert a

force5. The quantity ma is a

force.

Right 1. No, it is a contact

force; therefore, once the contact is broken, the force is no longer exerted.

2. It will continue moving with no change in velocity or direction.

3. Inertia is a property of matter.

4. Air exerts a huge, usually balanced force.

5. F = ma

6.2

Using Newton’s Forces

An Review of Newton’s Laws

Video Clip

4.1 The Concepts of Force and Mass

Mass is a measure of the amount of “stuff” contained in an object.

Weight is actually a force and can be found by using Newton’s 2nd Law W = mg

Weightless and Apparent Weight

Apparent Weight• The force exerted on the scale

measuring your weight at any point

• If there is additional force pushing down (i.e. you are in an elevator accelerating upward), your apparent weight is greater than your mass.

• If there is less force pushing down on the scale (i.e. the elevator is now accelerating downward) then you have a weight less than your mass.

Weightless• Specific

circumstance of acceleration = g

• Condition of free fall

• Your weight is zero but you are not without mass

FRICTIONLooking into

In nature there are two general types of forces, fundamental and non-fundamental.

Fundamental Forces

1. Gravitational force

2. Strong Nuclear force

3. Electroweak force

Examples of non-fundamental forces:

friction

tension in a rope

normal or support forces

FRICTIONA force that opposes motion between two surfaces

Friction

Eliminating Friction

Static Friction

The force that resists the initiation of sliding motion between two surfaces

that are in contact and at rest

Kinetic Friction

The force that opposes the movement of two

surfaces that are in contact and are sliding

over each other

Ways to reduce harmful friction

• Lubricants (grease, oil, water)• Replace sliding friction with rolling

friction• Make the surface smoother (sanding)

Ways to increase helpful friction

• Make surfaces rougher• Increase the force pushing the

surfaces together

How cars move• Car’s wheels push against the road • Road pushes back • Without friction between the tires

and roadway, there would be no net force and no movement

Air Drag and Terminal Velocity

• Air or fluids cause friction that is dependent on speed

• As speed increases, so does the friction

• An object’s shape and density also affect the friction as well as the nature of the fluid itself.

• Terminal velocity is reached when the drag force equals the force of gravity

Don’t try this at home! • A common physics demonstration

relies on this principle that the more massive the object, the more it tends to resist changes in its state of motion. The demonstration goes as follows: several massive books are placed upon the physics teacher's head. A wooden board is placed on top of the books and a hammer is used to drive a nail into the board. Due to the large mass of the books, the force of the hammer is sufficiently resisted (inertia). This is demonstrated by the fact that the blow of the hammer is not felt by the teacher. A common variation of this demonstration involves smashing a brick over the teacher's hand using a swift blow of the hammer. The massive brick resists the force and the hand is not hurt at all. (CAUTION: Do not try these demonstrations at home!)

For you to try• 1. Imagine a place in the cosmos

far from all gravitational and frictional influences. Suppose an astronaut in that place throws a rock. The rock will:

• a) gradually stop.• b) continue in motion in the

same direction at constant speed.

Try this one: • 2. An 2-kg object is moving

horizontally with a speed of 4 m/s. How much net force is required to keep the object moving with the same speed and in the same direction?

And this one: • 3. Mac and Tosh are arguing in

the cafeteria. Mac says that if he throws his jello with a greater speed it will have a greater inertia. Tosh argues that inertia does not depend upon speed, but rather upon mass. With whom do you agree? Why?

Example 4 • 4. If you were in a weightless

environment in space, would it require a force to set an object in motion?

Example 5 • 5. Mr. Wegley spends most

Sunday afternoons at rest on the sofa, watching pro football games and consuming large quantities of food. What effect (if any) does this practice have upon his inertia? Explain.

Example 6• 6. Ben Tooclose is being chased

through the woods by a bull moose which he was attempting to photograph. The enormous mass of the bull moose is extremely intimidating. Yet, if Ben makes a zigzag pattern through the woods, he will be able to use the large mass of the moose to his own advantage. Explain this in terms of inertia and Newton's first law of motion.

Example 7 • 7. Two bricks are resting on the edge

of a lab table. Shirley Sheshort stands on her toes and spots the two bricks. She acquires an intense desire to know which of the two bricks is more massive. Since Shirley is vertically challenged, she is unable to reach high enough and lift the bricks; she can, however, reach high enough to give each brick a push. Discuss how the process of pushing the bricks will allow Shirley to determine which of the two bricks is more massive. What difference will Shirley observe and how can this observation lead to the necessary conclusion?

Another Look at Inertia• As you learned in the

previous unit, an object which is not changing its velocity is said to have an acceleration of 0 m/s2. Thus, an alternate definition of inertia would be:

• Inertia is the tendency of an object to resist accelerations.

Example

• 1. Several physics teachers are taking some time off to play a little putt-putt golf. The 15th hole at the Hole-In-One Putt-Putt Golf Course has a large metal rim which putters must use to guide their ball towards the hole. Mr. Schmidgall guides his golf ball around the metal rim. When the ball leaves the rim, which path (1, 2, or 3) will the golf ball follow?

Answer• 2 because it will go in an inertial

direction which is a straight path

Pictorial Review

Pictorial Representation

Example 1 • An applied force of 50 N is used to accelerate an

object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance.)

Answer 1 • Since there is no VERTICAL acceleration, there is

no net vertical force so • Fnorm = F grav = 80 N• The mass can be calculated using F = mg or 80

N = m (10 m/s2) = 8 kg• Fnet is the sum of all forces• Fnorm – Fgrav = 0 N• 50 N right – 10 N Left = 40 N right• Fnet = m a • 40 N = (8 kg) a • a = 5 m/s2

Example 2 • An applied force of 20 N is used to accelerate an

object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the coefficient of friction (µ) between the object and the surface, the mass, and the acceleration of the object. (Neglect air resistance.)

Answer 2 • Again, no vertical acceleration so Fgrav = Fnorm =

100 N• Mass can be found by W = mg or F = mg • 100 N = m (10 m/s2) = 10 kg• m = Ffric/ Fnorm = 10 N /100 N = 0. 1 • Fnet is the sum of all forces • 100 N up – 100 N down = 0 N• 20 N right – 10 N left = 10 N right• Fnet = m x a (10 N) = 10 kg x a • a = 1 m/s2

Example 3 • A 5-kg object is sliding to the right and

encountering a friction force which slows it down. The coefficient of friction (µ) between the object and the surface is 0.1. Determine the force of gravity, the normal force, the force of friction, the net force, and the acceleration. (Neglect air resistance.)

Answer 3 • Since there is no vertical

acceleration, there is no vertical force, so Fgrav = Fnorm = 50 N

• Ffric = m Fnorm Ffric = 0.1 (50 N) = 5 N• Fnet is the sum of all unbalanced

forces. • 50 N up – 50 N down = 0 N• 5 N left is unbalanced = 5 N left• Fnet = m x a 5N = 5 kg x a • A = 1 m/s2

Word of Caution • Avoid forcing a problem into the form of a

previously solved problem. Problems in physics will seldom look the same. Instead of solving problems by rote or by mimicry, utilize your conceptual understanding of Newton's laws to work towards the solution. Use your understanding of weight and mass to find the m or the Fgrav in a problem. Use your conceptual understanding of net force (vector sum of all the forces) to find the value of Fnet or the value of an individual force. Do not divorce the solving of physics problems from your understanding of physics concepts. If you are unable to solve physics problems like the ones above, it is unlikely that you are having a math difficulty; rather it is more likely that you are having a physics difficulty.

PERIODIC MOTIONLooking at

Simple Harmonic Motion• If the force that restores the

object to its equilibrium position is directly proportional to the displacement of the object, the motion is called simple harmonic motion

• Period = time needed to repeat one complete cycle of motion (T)

• Amplitude = maximum distance the object moves from equilibrium

The pendulum• A pendulum is an example of

simple harmonic motion• T = 2 x x (1/g)

Resonance• Small forces applied at regular

intervals to a vibrating or oscillating object resulting in a greater amplitude

• The time interval between applications of force is equal to the period of the oscillation.

• Examples: rocking a car to get out of snow bank or rhythmically jumping on a trampoline or pushing a swing to get higher

Newton’s Third Law

Action-Reaction Law

Recap• A force is a push or a pull upon an

object which results from its interaction with another object. Forces result from interactions! As discussed in the last lesson, some forces result from contact interactions (normal, frictional, tensional, and applied forces are examples of contact forces) and other forces result from action-at-a-distance interactions (gravitational, electrical, and magnetic forces are examples of action-at-a-distance forces).

Moving on…• According to Newton, whenever objects A

and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body. There are two forces resulting from this interaction — a force on the chair and a force on your body. These two forces are called action and reaction forces and are the subject of Newton's third law of motion. Formally stated, Newton's third law is:

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

But what does it mean?

• The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the force on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. Forces always come in pairs – equal and opposite action-reaction force pairs.

Implications

• A variety of action-reaction force pairs are evident in nature. Consider the propulsion of a fish through the water. A fish uses its fins to push water backwards. But a push on the water will only serve to accelerate the water. In turn, the water reacts by pushing the fish forwards, propelling the fish through the water. The size of the force on the water equals the size of the force on the fish; the direction of the force on the water (backwards) is opposite to the direction of the force on the fish (forwards). For every action, there is an equal (in size) and opposite (in direction) reaction force. Action-reaction force pairs make it possible for fishes to swim.

What makes birds fly?

• Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air downwards. In turn, the air reacts by pushing the bird upwards. The size of the force on the air equals the size of the force on the bird; the direction of the force on the air (downwards) is opposite to the direction of the force on the bird (upwards). For every action, there is an equal (in size) and opposite (in direction) reaction. Action-reaction force pairs make it possible for birds to fly.

Motion in everyday • Consider the motion of your automobile on your

way to school. An automobile is equipped with wheels that spin backwards. As the wheels spin backwards, they push the road backwards. In turn, the road reacts by pushing the wheels forward. The size of the force on the road equals the size of the force on the wheels (or automobile); the direction of the force on the road (backwards) is opposite to the direction of the force on the wheels (forwards). For every action, there is an equal (in size) and opposite (in direction) reaction. Action-reaction force pairs make it possible for automobiles to move.

Example 1 • 1. While driving, Anna Litical

observed a bug striking the windshield of her car. Obviously, a case of Newton's third law of motion. The bug hit the windshield and the windshield hit the bug. Which of the two forces is greater: the force on the bug or the force on the windshield?

Answer 1 • For every action there is an EQUAL

reaction. The fact that the bug splatters only means that with its smaller mass, it is less able to withstand the larger acceleration resulting from the interaction.

• The forces are EQUAL in size.

Example 2 • 2. Rockets are unable to accelerate

in space because ...A) there is no air in space for the

rockets to push off of. B) there is no gravity is in space. C) there is no air resistance in space. D)... nonsense! Rockets do accelerate

in space.

Answer 2 • It is a common misconception that

rockets do not accelerate in space. Rockets do accelerate in space. Rockets are able to accelerate due to the fact that they burn fuel and push the exhaust in a direction opposite to the direction they wish to accelerate

• Answer is D

Example 3• 3. A gun recoils when it is fired. The

recoil is the result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet pushes the gun backwards. The acceleration of the recoiling gun is ...

a) greater than the acceleration of the bullet.

b) smaller than the acceleration of the bullet.

c) the same size as the acceleration of the bullet

Answer 3 • The force on the gun equals the force

on the bullet. However, acceleration depends on both force and mass. The bullet has a great acceleration due to the fact that it has a smaller mass. Remember acceleration and mass are inversely proportional.

• The correct answer is B

Example 4 • 4. In the top picture, a physics student is pulling

upon a rope which is attached to a wall. In the bottom picture, the physics student is pulling upon a rope which is held by the Strongman. In each case, the force scale reads 500 Newtons. The physics student is pulling

a) with more force when the rope is attached to the wall.

b) with more force when the rope is attached to the Strongman.

c) the same force in each case.

Answer 4 • The rope transmits the force from the

physics student to the wall (or Strongman) and vice versa. Since the force of the student pulling on the wall and the wall pulling on the student are action-reaction force pairs, they must have equal magnitudes. Inanimate objects such as walls can have push and pull.

• The correct answer is C. The student is pulling with 500 N in both cases.

Identification of action-reaction pairs

Force Pairs

• According to Newton's third law, for every action force there is an equal (in size) and opposite (in direction) reaction force. Forces always come in pairs — known as "action-reaction force pairs." Identifying and describing action-reaction force pairs is a simple matter of identifying the two interacting objects and making two statements describing who is pushing on whom and in which direction. For example, consider the interaction between a baseball bat and a baseball.

Label the diagram Which is action and

reaction pairs?

• The baseball forces the bat to the right (an action); the bat forces the ball to the left (the reaction). Note that the nouns in the sentence describing the action force switch places when describing the reaction force.

Examples for you to try

Consider the following three examples. The action force is

stated; determine the reaction force.

Athlete pushes bar upward

• Bar pushes athlete downward.

Bowling ball pushes pin rightwards.

• Pin pushes bowling ball leftward.

Compressed air pushes balloon wall outwards.

• Balloon wall pushes compressed air inward.