Chapter 4: Forces and the Laws of Motion

A Review…. Force

push or pull exerted on some object - Unit of Force is a NEWTON (N)

1 kg x m/s2

- Force is a VECTOR Has a magnitude and direction

Review

Acceleration is a change in velocity per unit of time interval. It has both

magnitude and direction.

Vectors have both magnitude and direction.

What causes motion?

Why do some objects accelerate at higher rates than others do?

4.1 Changes in Motion

How does force affect the motion of an object? Forces can cause

Changes in velocity (fig 4-1) Stationary objects to move (throwing a

ball) Moving objects to stop (catching a ball) A change of direction (hitting a ball)

These all involve a change in velocity an acceleration

Force the cause of acceleration, or the change in an object’s velocity

4.1 Weight vs. Mass The weight of an object is a measure

of the magnitude of the gravitational force exerted on an object. (mass is a measure of an object’s inertia) It’s the result of the objects mass

interacting with Earth’s gravitational field.

Terms we often use to describe weight are really units of force

Ex. A ¼ lb. stick of butter has a weight equivalent to a force of 1N.

1 lb. =4.448N 1N=0.225 lb

Contact and Field Forces

Forces can act through contact or at a distance Contact force is a force that arises from

the physical contact of two objects (like a push or a pull) Usually easy to identify

Ex: frictional force Tension force air resistance Applied force

Field Forces

Forces that do not involve physical contact are called field forces The presence of an object affects the space

around it so that a force is exerted on any other object placed within that space. The region of influence is called a field

Ex: Gravity – earth exerts a force on an object even when it’s not in immediate contact with the object (also electrical and magnetic)

Ex: the attraction or repulsion between electrical charges

Forces Applied Force Fapp a force that is applied to an

object by a person or another object. (a person pushing a desk across the room)

Gravity Force F grav (also known as weight) the force with which the earth or other large objects attract another object towards itself (not the same as mass)

Normal Force Fnorm the support force exerted upon an object that is in contact with another stable object. (like a book resting upon a surface, the surface is exerting an upward force on the book in order to support the weight of the book)

Forces Friction Force Ffrict the force exerted by a

surface as an object moves across it or makes an effort to move across it. (Both sliding and static friction) Friction results from the two surfaces being

pressed together closely, causing intermolecular attractive forces between molecules

Air Resistance Force Fair frictional force that acts upon objects as they travel through the air (usually negligible except for objects traveling at high speeds or having high surface area)

Forces

Tension Force Ftens Force transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends.

Spring Force Fspring the force exerted by a compressed or stretched spring upon any object that is attached to it.

Mass the amount of matter that is contained by the object. (how much stuff is there)

Weight the force of gravity acting upon an object (the pull of the earth on that stuff)

Force Diagrams If you push a toy car, it does not move

as fast as it does when you give a harder push. The effect of force depends on its

magnitude The effect of force on an object’s motion

also depends on the direction of the force A force diagram is a diagram of the

objects involved in a situation and the forces exerted on the objects

(a) force diagramshows all the forces

acting in a situation(b) free-body diagram shows only the forces acting on a particular object

Force Diagrams

Show force vectors as arrows Tail of the arrow is attached to the

object on which the force is acting Used as tools to analyze collisions For now, disregard the size and

shape of the object and assume that all forces act on a point at the center of an object

FREE BODY DIAGRAMS

A free-body diagram helps analyze a situation Used to analyze only the forces affecting the

motion of a single object Work just like vector diagrams – find component

and resultant forces Ex. Engineers use to analyze test-car crashes to

determine which forces affect the car and passengers

Tow truck example

There are many forces acting on this car The tow truck exerts a force on the car in

the direction of the cable The road exerts forces on the car The car is acted on by gravitational force To draw a free-body diagram, you must first

isolate and identify all the forces acting on the car

Figure 4-4

Free Body Diagrams isolate an object

and the forces acting on itSteps to draw free body diagrams:1.Draw a diagram to represent the

isolate object (b). Draw in same position as the actual object.

2. Draw and label vector arrows of all external forces acting on the object (c). All forces are assumed to act on a single point at the center of an object.

a) Label the arrow with the size of the force

b) The force of the tow truck exerts 5800 N on the car. The arrow is pointing in the same direction as the force of the cable on the car.

Drawing Free Body Diagrams

3. The gravitational force acting on the car is 14700 N directed toward the center of the earth (d).

4. The road exerts an upward force of 13690 N (e).

5. Because of the interaction between the road and the car’s tires, the road also exerts a backward force of friction equal to 775 N (f).

Drawing Free Body Diagrams6. Make sure that only the

forces acting on the car are included in the free body diagram. (leave off the forces the car is exerting on other objects)

7. F is the completed free-body diagram.

A free-body diagram can be used to find the net external force acting on an object, using the rules for vector analysis.

Section Review 1-6

NEWTON’S LAWS OF MOTION

3 Laws of Motion

Newton’s 1st Law Predicts the behavior of stationary

objects and moving objects. (Insert chart from physicsclassroom.com) An object at rest remains at rest and an

object in motion continues in motion with a constant velocity unless acted on by an outside force

Law of Inertia

Also known as the LAW OF INERTIA Inertia the tendency of an object not to

accelerate When the net external force on an object is

zero, its acceleration (or change in velocity) is zero

If the forces acting upon an object are balanced, then the acceleration of that object will be 0 m/s2

Objects tend to “keep on doing what they’re doing”.

Newton’s First Law

Acceleration is determined by net force Net external force is the total force

resulting from a combination of external forces on an object; sometimes called the resultant force It’s the vector sum of all the forces acting on an

object When all external forces are known, the net

external force can be found by finding the resultant vector

An objects acceleration is determined by all the forces acting on it.

Newton’s first law concepts Mass is a measurement of inertia

A basketball and a golf ball that are side by side on the ground remain at rest as long as no net external force acts on them.

If you strike each ball with a golf club, which one will accelerate more?

The basketball experiences a smaller acceleration because it has more inertia than the golf ball.

The inertia of an object is proportional to its mass. The greater the mass of the body, the less

the body accelerates under an applied force.

Newton’s First law concepts Objects in motion tend to stay in

motion.

The Zebra’s stripes stay in motion!

Equilibrium

Objects that are either at rest or moving with constant velocity are said to be in equilibrium. All forces are balanced

Newton’s first law describes objects in equilibrium, whether they are at rest or moving with constant velocity.

For equilibrium to occur, the net external force must be zero.

Equilibrium The bob on the fishing line

is at rest. We know Fnet is equal to

zero If a fish bites the bait, the

fish exerts a force on the line, the bob accelerates downward.

To return the bobber to equilibrium , the person must apply force to the fishing line.

Equilibrium The force that brings an accelerating object

into equilibrium, must be equal and opposite to the force causing the object to accelerate.

An object is in equilibrium when the vector sum of the forces acting on it is equal to zero.

The easiest way to do this is to resolve forces into their x and y components.

When the sum of all forces in the x direction is zero (Fy=0). Then the vector sum is equal to zero and the body is in equilibrium.

Newton’s Second Law

Newton’s Second Law Predicts the behavior of objects for

which all existing forces are NOT balanced.

States: The acceleration of an object is dependent on two variables: Fnet and mass.

Newton’s Second Law

Acceleration is directly proportional to the Fnet acting on the object and inversely proportional to the object's mass. As force is increased, acceleration is increased As mass is increased, acceleration is decreased

Acceleration = Net Force divided by mass a= Fnet/m

Net Force = mass * acceleration Fnet=m*a

Newton’s Second Law Remember that

1 Newton (N) = kg * m/s2a= F/m

Example: Roberto and Laura are studying across from each other at a wide table. Laura slides a 2.2 kg book toward Roberto. If the net external force acting on the book is 2.6 N to the right, what is the book’s acceleration?

EXAMPLE 4B

Given: m=2.2 kg Fnet= F=2.6N to the right

a=? Use Newton’s second law and solve for a.

a= F/m

Practice 4B

Misconception Alert

Be aware of the common misconception that sustaining motion requires a constant force.

Read the scenarios and we will discuss the answers!

Newton’s 3rd Law Forces result from an object’s interaction

Such as contact interactions (normal, friction, tensional and applied)

Action-at-a-distance interactions (gravitational, electrical, magnetic)

When you sit in a chair, you exert a downward force on the chair and the chair exerts an upward force on your body

These two forces are called action and reaction pairs “a pair of simultaneous equal but opposite

forces resulting from the interaction of two objects”

Newton’s Third Law

Newton’s Third law deals with action and reaction pairs For every action there is an equal and

opposite reaction. “If 2 objects interact, the magnitude

of the force exerted on object 1 by object 2 is equal in magnitude of the force simultaneously exerted on object 2 by object one, and these forces are opposite in direction.”

A single isolate force cannot exist!

Action-reaction pair

In every interaction, there is a pair of forces acting on the 2 interacting objects The size of the forces on the first object

equal 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.

Action- Reaction Pair

Either force can be called the action or reaction

Misconception alert: don’t confuse ‘reaction’ with the everyday use of the word. Reaction here does not mean something that happens in response to something, but happens at the SAME TIME as the action force!

Most important to remember: each force acts on a different object.

Action-Reaction forces

Misconception alert: equal and opposite forces do not balance each other a inhibit a change in motion.

Consider a hammer striking a nail? Why doesn’t it remain at rest?

Example

Think of the flying motion of birds. The wings of a bird push air downwards. Since forces result from mutual

interactions, the air must also be 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 the direction of the force on the bird (upwards).

A truck driving down the road runs into a bug flying the other way. a) Which object has the greater force exerted on it? b) Which object will change its motion the most?

FTB

FBT

Both objects have the same small force exerted on them during the collision according to Newton’s third law. The bug squishes easily!

The bug obviously changes its motion significantly more than the truck because of its much lower inertia (mass).

Truck: aT = F / M Bug: - aT = - F / M

The moon moves around the earth. a) Which object has the greater force exerted on it? b) Which object will change its motion the most?

Both objects have the same large force exerted on them during the collision according to Newton’s third law.

The Moon obviously changes its motion significantly more than the Earth because of its much lower inertia (mass).

Earth: aE = F / M Moon: - aM = - F / M

FME FEM

Check for Understanding

Read the questions on “Check for Understanding”, answer them and we will discuss.

Do Section Review 1-5 pg 140

Laws of Motion Review

1st Law what happens when there is no net force (inertia) On object at rest stays at rest and an object

in motion stays in motion 2nd law what happens when a net force

does act Acceleration depends on net force and mass

3rd law forces occur in pairs, no isolated forces (action-reaction law) For every action there is an equal and

opposite reaction

4-4 Everyday Forces

Which weighs more, a bowling ball or a tennis ball? How do you know? Imagine one ball in each hand and

imagine the downward forces acting on your hands.

Because the bowling ball has more mass the force of gravity pulls more strongly on the bowling ball and it pushes on your hand with a stronger force.

Weight vs. Mass

Mass is an inherent property of an object. The mass of a bowling ball is the same on earth as it is the moon.

Weight is NOT an inherent property. It is dependent on the force of gravity- which changes with location.

An astronaut weights 800N (180 lb) on Earth, but only 130 N (30lb) on the moon. Because gravity is smaller on the moon

Weight

Is weight constant on earth? Does your weight vary depending on where you are? Actually, YES ! G decreases as distance

from the center of Earth increases, so objects weigh less at higher altitudes than at sea level.

Also, because earth is not symmetrical, g also decreases a little as latitude decreases.

Weight is the magnitude of the force of gravity acting on an object

The Normal Force

Normal force (Fn )a force exerted by one object on another in a direction perpendicular to the surface of contact. One meaning of the word “normal” is

‘perpendicular’. It is a support force exerted upon an object

that is in contact with another stable object

The Fn is ALWAYS perpendicular to the surface but NOT always opposite of Fg

Perpendicular means at a right angle to

Refrigerator on a ramp

This is a fridge on a loading ramp

Notice the Fn is perpendicular to the ramp but NOT Fg

The magnitude of normal force can be calculated with:

Fn = mg(cos )

The force of Friction

Friction is the force exerted by a surface as an object moves or makes an effort to move across the surface

Two types of friction Static friction (Fs) results when the surfaces

of two objects are at REST relative to one another and a force exists on one of the objects to set it into motion

Kinetic Friction (aka Sliding friction) (Fk) results when an object slides across a surface

Friction

(a) Because the jug of is in equilibrium, any horizontal force will cause it to accelerate

(b) when a small force is applied, the jug remains in equilibrium because the force of friction is equal/opposite to the applied force.

(c) When a larger force is applied, the jug begins to move as soon as the applied force exceeds the opposing static friction force

Friction

Friction opposes the applied force Fapplied increases, static friction also increases

Fs = -Fapplied

Fsmax is when the force of static friction reaches its max value – the applied force is as great as it can be without causing the jug to move

Kinetic friction is less than static friction (Fsmax) The net external force (F) is equal to

the difference between Fapp and Fk (F-Fk)

Friction

The force of friction is proportional to the normal force (due to mass of the object)

Friction depends on the surfaces in contact Objects that appear

smooth really aren’t at the microscopic level

The Coefficient of friction The force of friction also depends on

the composition and qualities of the surfaces in contact.

The coefficient of friction (µ) is a ratio of forces acting between two objects Coefficient of kinetic friction is the ratio of

kinetic friction to normal force µk=Fk/Fn

Coefficient of static friction max is the ration of static friction to the normal force µs=Fsmax/Fn

Sample 4C

A 24 kg crate initially at rest on a horizontal floor requires a 75N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor.

Do Practice 4C