General Physics I

Spring 2011

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Forces and Newton’s Laws of Motion

Forces and Interactions

• The central concept in understanding why things move is

force. If a tractor pushes or pulls a trailer, the tractor exerts a

force on the trailer. Importantly, the trailer also exerts a force

on the tractor at the same time.

• Forces result from interactions between different objects or

parts of a system (e.g., the tractor and the trailer). A

completely isolated object cannot exert a force or have a

force exerted on it because there is nothing for it to interact

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force exerted on it because there is nothing for it to interact

with.

• Contact forces are forces that arise from direct contact

between interacting objects.

Examples: tension, spring force, friction, normal force.

• Long-range forces are exerted across empty space.

Examples: gravitational force, electric force, magnetic force.

Force is a Vector Quantity• Force is a vector quantity. It

has a magnitude and a

direction.

• In addition, numerous

experiments have shown that if

more than one forces act

simultaneously at a single

point, the effect is the same as

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point, the effect is the same as

if a single force, equal to the

vector sum (resultant) of all the

forces, acted at the point. The

resultant force is called the net

force. Its symbol is .

• The SI unit of force is the

newton (N).

netF�

Two forces with magnitudes 3.0 N and 4.0 N act on an

object. Which one of the following could not be the

magnitude of the net (resultant) force?

1. 1.0 N

2. 5.0 N

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2. 5.0 N

3. 6.6 N

4. 7.3 N

Workbook: Chapter 4, Question 1, 2

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Newton’s First Law• It is clear that an object that is

at rest will stay at rest unless it is disturbed. What about when an object is in motion? Will it stay in motion or come to rest on its own?

• To see what happens, we launch a hockey puck in exactly the same way on

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exactly the same way on three different surfaces. The puck goes farther as the surfaces get smoother. It becomes clear that if a surface were perfectly smooth, the puck would not stop! It would travel at constant speed in a straight line until it was disturbed.

Newton’s First Law

• What do we mean by “disturbed”? To change the motion of

the puck, someone could use a hand to deflect or stop it.

The hand applies a force to the puck. (Just as a hand

applied a force to the puck to start its motion.) We see that

an object will maintain its motion unless an unbalanced

force causes the motion to change. This is the essence of

Newton’s First Law.

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• If there is no net force acting on an object, then if it is at rest,

it will remain at rest; if it is moving, it will continue to move in

a straight line with constant speed.

Inertia• Newton’s first law tells us that an object tends to maintain

its current state of motion. In other words, it exhibits a

resistance to changing its motion. This resistance to

changes in motion is called inertia. It is a property of all

objects.

• If you launch two pucks glued together across an air table,

they will move with half the speed of a single puck

launched in the same way. Thus, two pucks undergo half

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launched in the same way. Thus, two pucks undergo half

the change in motion (i.e., change in speed for straight-line

motion) as one puck under the same launch conditions.

Hence, two pucks have twice as much inertia as one puck.

• The mass of an object is a quantitative measure of its

inertia. The SI unit of mass is the kilogram (kg).

Some Common Forces

• Spring force: If a spring is

compressed or stretched, it

will exert a force on the

objects to which it is

attached (at both ends).

This is called the spring

force. The magnitude of the

spring force increases with

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spring force increases with

the extension (or

compression) of the spring.

Some Common Forces

• Tension: If the ends of a rope (or string) are pulled until the rope is taut, the rope will exert a force on the objects to which it is attached (at both ends). This force is called tension.

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Some Common Forces

• Weight: The weight of an object is the gravitational force

that the Earth exerts on it. The gravitational force acts

vertically downward on all objects; therefore, the weight of

every object is always vertically downward.

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Some Common Forces• Normal force: Consider a book lying at

rest on a horizontal table. The book’s weight is one force that acts on it. Can that be the only force? No! Otherwise, the motion of the book would change due to the presence of a net force. The other force acting on the book is in the vertically upward direction and arises because of the contact

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arises because of the contact between the book and the table. This contact force is the normal force.

• More precisely, the normal force is a contact force that acts in a direction perpendicular to the surfaces that are in contact. Here, “normal” means perpendicular.

Ultimately, the normal

force is due to the slight

displacement of atoms

from their usual positions.

Some Common Forces

• Friction: Like the normal force, friction is a contact force.

However, friction acts parallel to the surfaces that are in

contact. Friction also always opposes the motion of one

surface relative to the other.

• If an object is in contact with a surface and moving relative

to it, the friction force is called kinetic friction. If an object is

not moving relative to a surface and friction prevents it from

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not moving relative to a surface and friction prevents it from

moving, the friction force is called static friction.

Workbook: Chapter 4, Questions 4, 5

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Force and Changes in Motion• We will use a spring to apply a

constant force to a block that

moves over a very smooth surface

so that friction can be neglected.

The magnitude of the force can be

varied by changing the extension

of the spring. The motion of the

block will be measured by a

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block will be measured by a

motion detector.

• The velocity-versus-time graph

that is generated when a constant

force acts on a block is shown to

the right. We see that a constant

force results in a constant

acceleration.

Force and Changes in Motion• Next, we investigate how the

acceleration depends on the applied force. To do this, we conduct the experiment with the spring extension at a certain value. Then we repeat the experiment with the spring extension doubled, so the magnitude of the force is

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magnitude of the force is doubled. Repeat the experiment with the magnitude of the force tripled, and so forth.

• The results are shown to the right. We see that the acceleration increases by the same factor as the force, i.e., the acceleration is directly proportional to the force.

Force and Changes in Motion• Next, we investigate how the

acceleration depends on the number of blocks with the force held constant throughout. To do this, we conduct the experiments with the spring extension always at the same value. The first experiment is done with one block. Repeat the

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done with one block. Repeat the experiment with two blocks glued together, and so forth. The results are shown to the right. We see that the acceleration decreases by the same factor as the number of blocks increases, i.e., the acceleration is inversely proportional to the number of blocks.

Force and Changes in Motion

• Recall that two blocks have twice the inertia as one block.

Since mass is a direct measure of inertia, two blocks have

twice the mass as one block. Thus, with the force held

constant, the acceleration is inversely proportional to the

mass.

• For a given force, we see that an object with a greater mass

has a smaller acceleration. Thus, the mass of an object

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has a smaller acceleration. Thus, the mass of an object

determines its acceleration in response to an applied force.

Newton’s Second Law

• From our experiments we see that acceleration is directly

proportional to force and inversely proportional to mass.

Many experiments have shown that the acceleration is

actually proportional to the net force acting on an object.

Thus, we can write

,netF

a m=

�

�

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where is the vector sum of all the forces

acting on the object and m is the mass of the object. The

acceleration is in the same direction as the net force. This

relation is Newton’s Second Law.

• Note that since , the unit of force (newton) is equal

to the unit of mass times the unit of acceleration.

m

1 2...

netF F F= + +

� � �

netF ma=

��

Workbook: Chapter 4

Questions, 9, 14, 15, 16

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Textbook: Chapter 4, Problem 13

(Homework)

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Free-Body Diagrams

• A free-body diagram is a diagram showing all the forces

acting on an object. When solving problems using

Newton’s second law, drawing a free-body diagram is

essential.

• Use the following steps:

(1) Identify all the forces acting on the object.

(2) Draw an x-y coordinate system with the object at the

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(2) Draw an x-y coordinate system with the object at the

origin. (The object is represented by a dot or small circle.)

(3) Draw and label vectors representing the forces. The tails

of the force vectors should be attached to the object. The

lengths of the vectors should be proportional to their

magnitudes.

Free-Body Diagrams

• Consider a book that accelerates to the right as it is pushed

by a hand across a rough horizontal table. The forces

acting the book are its weight, the normal force, kinetic

friction, and the force applied by the hand to the book.

y

n�

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x

w�

n

kf�

pushF�

• Which diagram correctly represents an elevator that

is moving upward and slowing to a stop? The

elevator is suspended by a cable.

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Workbook: Chapter 4, Question 19

Textbook: Chapter 4, Problems 31, 35

(Homework)

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Forces and Interactions• Forces result from an interaction

between two objects. For example, friction and the normal force arise from the interaction between two objects due to contact between the objects. A completely isolated object cannot exert or experience a force. Note that one force acts on

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force.

• Consider two interacting objects A and B. Each object experiences a force due to the interaction. Object A exerts a force on Object B and Object B exerts a force on Object A. The two interaction forces are collectively called an action/reaction pair.

Note that one force acts on

A and the other acts on B.

Thus, the forces act on

different bodies.

Newton’s Third Law• Newton’s third law is concerned with the forces that constitute

an action/reaction pair. Newton’s third law states that

If object A exerts a force on object B, then object B

simultaneously exerts a force that is equal in magnitude but

opposite in direction on object A.

• Newton’s third law holds regardless of the motion of the

objects.

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Newton’s Third Law: Example

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Newton’s Third Law: Example

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• The car accelerates because of the force that the road exerts

on the tires. The ground experiences a force of equal

magnitude, but does not move perceptibly because the mass of

the Earth is very large (so negligible acceleration).

Can you identify other action/reaction pairs?

System and Environment• To study the motion of a group of

objects, it useful to divide the group into two categories: the system and the environment.

• The system comprises the specific objects whose motion we wish to study. All other objects comprise the environment.

• Forces exerted by the

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• Forces exerted by the environment (objects outside the system) on objects within the system are called external forces.Forces of interaction between objects within the system are called internal forces. Internal forces are action/reaction pairs, both within the system (but acting on different parts of the system).

Free-body diagrams only

need to be drawn for the

system.

Workbook: Chapter 4, Question 23

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