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Conceptual Physics

Fundamentals

Chapter 3:

EQUILIBRIUM AND LINEAR

MOTION

This lecture will help you

understand:

• Aristotle on Motion

• Galileo’s Concept of Inertia

• Mass—A Measure of Inertia

• Net Force

• The Equilibrium Rule

• Equilibrium of Moving Things

• The Force of Friction

• Speed and Velocity

• Acceleration

Equilibrium and Linear Motion

“When you’re over the hill, that’s when you

pick up speed.”

—Quincy

Jones

The force due to gravity on a body is the body’s

A. mass.

B. weight.

C. density.

D. all of the above.

Conceptual Physics Fundamentals—Chapter 3

A kilogram is a measure of an object’s

A. weight.

B. force.

C. mass.

D. gravity.


Compared with a 1-kg block of solid iron, a 2-kg block of solid

iron has twice as much

A. inertia.

B. mass.

C. volume.

D. all of the above.


One object has twice as much mass as another object, and also

has twice as much

A. inertia.

B. velocity.

C. gravitational acceleration.

D. volume.


When we say that 1 kilogram weighs 9.8 N, we mean that

A. 1 kilogram is 9.8 N.

B. it’s true at Earth’s surface.

C. it’s true everywhere.

D. mass and weight are one and the same.


The mass of 1 kilogram of iron

A. is less on the Moon.

B. is the same on the Moon.

C. is greater on the Moon.

D. weighs the same everywhere.


Natural Motion

•Objects have a proper place

•Objects seek their natural place

•The heavier the object,

the faster it falls.

Violent Motion

•Imposed motion

•A Moving object must have a

force acting on it.

The natural motion of

a body is to remain in

whatever state of

motion it is in unless

acted upon by net

external forces.

Galileo Challenged The Dogma

Of Natural Motion

Galileo Challenged The Dogma

Of Natural Motion with

Experiments

Galileo’s Motion Studies

What causes a rolling ball to stop?

FRICTION

Galileo’s Inclined Planes

If I have a long horizontal plane without friction,

how far will the ball go to reach the same height?

Once the ball rolls down the

incline, what keeps it moving?

Inertia

The tendency of an object to resist a change in motion.

Inertia

When the string is pulled down slowly, the top string breaks,

which best illustrates the:

A. weight of the ball.

B. mass of the ball.

C. volume of the ball.

D. density of the ball.

Mass—A Measure of Inertia

CHECK YOUR NEIGHBOR

When the string is pulled down slowly, the top string breaks,






Explanation:

Tension in the top string is the pulling tension plus the weight of the ball, both of which

break the top string.


CHECK YOUR ANSWER

When the string is pulled down quickly, the bottom string breaks,







CHECK YOUR NEIGHBOR

When the string is pulled down quickly, the bottom string breaks,






Explanation:

It is the “laziness” of the ball that keeps it at rest, resulting in the breaking of the bottom

string.


CHECK YOUR ANSWER

Inertia Question

A quick pull will break which string?

A slow and steady pull will break which string?

The Earth Revolves around the sun at

30,000 m/sec!!! (~67,000 miles/hr)

The Earth Rotates on its axis at

464 m/s (1000 miles/hr)!

The Solar System moves through the Galaxy at

220,000 m/s ( 500,000 miles/hr)

How come we can’t feel these motions?

Cuz we are moving right along with it!

Mass is a Measure of Inertia

Kilogram: KG

Mass & Weight

F ma

W mg

29.8 /g m s

Mass is how much stuff an object has – inertia.

Weight is due to the force of gravity and depends on the mass

and the planet!

Mass & Weight

W mg

29.8 /g m s

Calculate your weight in N.

Calculate your mass in Kg.

1 lb = 4.45 N

Mass on the MoonGravity on the surface of the moon is only 1/6 as strong

as on the Earth. What is the mass of a 10-kg object on

the moon? What is the weight on the moon?

Isaac Newton(1642 -1727)

1687 Published Principia

•Invented Calculus

•3 Laws of Motion

•Universal Law of Gravity

Newton’s First Law(Law of Inertia)

An object will remain at rest or

in a constant state of motion

unless acted upon by external

net forces.

Newton’s First Law(Law of Inertia)

An object will remain at rest or in a

constant state of motion unless acted upon

by net external forces.

0F

Push or a Pull

The unit is a Newton (N)

Net Force• Net force is

the combination of all forces that change an

object’s state of motion.

example: If you pull on a box with 10 N and a friend

pulls oppositely with 5 N, the net force is 5 N

in the direction you are pulling.

A cart is pushed to the right with a force of 15 N while being

pulled to the left with a force of 20 N. The net force on the cart is

A. 5 N to the left.

B. 5 N to the right.

C. 25 N to the left.

D. 25 N to the right.

Net Force

CHECK YOUR NEIGHBOR

A cart is pushed to the right with a force of 15 N while being

pulled to the left with a force of 20 N. The net force on the cart is

A. 5 N to the left.

B. 5 N to the right.

C. 25 N to the left.

D. 25 N to the right.

Net Force

CHECK YOUR ANSWER

Net Force

Vector quantity

• a quantity whose description requires both

magnitude (how much) and direction (which way)

• can be represented by arrows drawn to scale,

called vectors

– length of arrow represents magnitude and arrowhead

shows direction

examples: force, velocity, acceleration

The Equilibrium Rule

The equilibrium rule

• the vector sum of forces acting on a non-

accelerating object equals zero

• in equation form: F = 0


example: a string holding up a bag of flour

two forces act on the bag of flour:

–tension force acts upward

–weight acts downward

equal in magnitude and opposite in direction

when added, cancel to zero

bag of flour remains at rest

The equilibrium rule, F = 0, applies to

A. vector quantities.

B. scalar quantities.

C. both of the above.

D. neither of the above.


CHECK YOUR NEIGHBOR

The equilibrium rule, F = 0, applies to

A. vector quantities.

B. scalar quantities.

C. both of the above.

D. neither of the above.

Explanation:

Vector addition takes into account + and - quantities that can cancel to

zero. Two forces (vectors) can add to zero, but there is no way that two

masses (scalars) can add to zero.


CHECK YOUR ANSWER

Support Force

Support force (normal force) is an upward

force on an object that is opposite to the force

of gravity.

example: a book on table a compresses atoms in the

table, and the compressed atoms produce the

support force

When you stand on two bathroom scales with one foot on each

scale and with your weight evenly distributed, each scale will

read

A. your weight.

B. half your weight.

C. zero.

D. more than your weight.

The Support Force

CHECK YOUR NEIGHBOR

When you stand on two bathroom scales, with one foot on each

scale and with your weight evenly distributed, each scale will

read

A. your weight.

B. half your weight.

C. zero.

D. more than your weight.

Explanation:

You are at rest on the scales, so F = 0. The sum of the two upward

support forces is equal to your weight.

The Support Force

CHECK YOUR ANSWER

Contact Forces

Tension Forces

Support Forces

Friction Forces

Net Force

Direction of applied forces matters!!!

Opposite forces cancel!

Net Forces 0F

W

T2T1

Forces up equal the forces down.

Forces sideways cancel too.

Static Equilibrium 0F

W

T2T1

If the Net Force is zero, then the object remains at

rest – in static equilibrium.

W

Dynamic Equilibrium

0F If the Net Force is zero, then the object moves at a

constant speed – in dynamic equilibrium.

Newton’s First Law

0 => No Change in MotionIf F

Dynamic Equilibrium Static Equilibrium

The person weighs 250 N and the tension in each rope is 200N.

What is the weight of the staging?

a) 50 N

b) 100 N

c) 150 N

d) 200 N

Net Force Question

Do Workbook page 5

Equilibrium of Moving Things

Equilibrium

• a state of no change with no net force acting

– static equilibrium

example: hockey puck at rest on slippery ice

– dynamic equilibrium

example: hockey puck sliding at constant speed on

slippery ice


Equilibrium test

• whether something undergoes changes in motion

example: A refrigerator at rest is in static equilibrium. If it

is moved at a steady speed across a floor, it is

in dynamic equilibrium.

A bowling ball is in equilibrium when it

A. is at rest.

B. moves steadily in a straight-line path.

C. both of the above

D. none of the above


CHECK YOUR NEIGHBOR

A bowling ball is in equilibrium when it

A. is at rest.

B. moves steadily in a straight-line path.

C. both of the above

D. none of the above


CHECK YOUR ANSWER

The Force of Friction

Friction

• occurs when objects rub against one another

• applies to solids, liquids, and gases

• acts in a direction to oppose motion

example: When an object falls down through air, the

force of friction (air resistance) acts upward.

The Force of Friction• depends on the kinds of material and how much they are

pressed together

• is due to tiny surface bumps and to “stickiness” of the atoms on a material’s surface

example: friction between a crate on a smooth wooden floor is less than that on a rough floor

The force of friction can occur

A. with sliding objects.

B. in water.

C. in air.

D. all of the above


CHECK YOUR NEIGHBOR

The force of friction can occur

A. with sliding objects.

B. in water.

C. in air.

D. all of the above

Comment:

Friction can also occur for objects at rest. If you push horizontally on

your book and it doesn’t move, then friction between the book and the

table is equal and opposite to your push.


CHECK YOUR ANSWER

When Josh pushes a refrigerator across a kitchen floor at a

constant speed, the force of friction between the refrigerator and

the floor is

A. less than Josh’s push.

B. equal to Josh’s push.

C. equal and opposite to Josh’s push.

D. more than Josh’s push.


CHECK YOUR NEIGHBOR

When Josh pushes a refrigerator across a kitchen floor at a

constant speed, the force of friction between the refrigerator and

the floor is






CHECK YOUR ANSWER

When Josh pushes a refrigerator across a kitchen floor at an

increasing speed, the amount of friction between the refrigerator

and the floor is






CHECK YOUR NEIGHBOR

When Josh pushes a refrigerator across a kitchen floor at an

increasing speed, the amount of friction between the refrigerator

and the floor is





Explanation:

The increasing speed indicates a net force greater than zero. The refrigerator is not in

equilibrium.


CHECK YOUR ANSWER

Do Workbook page 6 #4

Speed & Velocity

How fast How far is changing.

The rate at which an object moves.

distance

Velocity

Velocity is a vector. It has both magnitude (speed) and direction.

Instantaneous velocity is the velocity at any instant.

distance

total distance traveledAverage Speed =

total time

d

t

•Speed: Scalar (magnitude)

•Velocity: Vector (magnitude AND direction)

•Unit is m/s

• s and v often interchanged …..

Speed & Velocity

speed , distancem

ms

Speed Question

A motorcycle travels 1000 m in 2 minutes.

What is its average speed?


total time

Distance

averaged v t


total time

Average Speed x total time= total distance traveled

If you travel an average of 80

km/hr for 15 minutes, how far have

you traveled in that time?

AccelerationHow fast How fast is changing.

The rate at which the speed is changing.

Speeding up

Slowing down

Speeding up or slowing down?

change in velocity

change in time

va

t

Velocity from Acceleration

change in velocity

change in time

va

t

v a t

v at

If you start from rest and accelerate at

a rate of 5m/s every second (5 m/s2)

for 10 seconds, what will be your

final speed?

Acceleration and velocity do not

have to be in the same direction.

Hill Question

On which of these hills does the ball roll down with increasing

speed and decreasing acceleration? a) b) c)

a) b) c)

Tracks Question

Two balls are released simultaneously from rest at the left

end of equal length tracks A and B as shown. Which ball

reaches the end of its track first?

Free Fall

In the absence of air resistance,

all objects fall due to the force of

gravity with an acceleration “g”:

2 29.8 / ~10 /g m s m s

Free FallIn a vacuum, all objects fall with the same

acceleration due to gravity: 10 m/s2.

Free Fall Speed

25d t

210 /a g m s

10v t

Do Work Book page10

v at

Free Fall: Throwing UPWhat is the speed at the top of the

path?(assume g = 10m/s2 )

ZERO!

What is the acceleration at the top?

g=10m/s2

What is the speed at the same

height on the way down?

-30 m/s

+y

Free Fall Symmetry

SAME!

The gravitational field is symmetric

(in the absence of air resistance.)

Which ball has the greatest speed when it hits the ground?

Free Fall Summary

25d t

For an object without an initial velocity and without air resistance.

210 /a g m s

10v t

If there is an initial velocity, then add it!

( ) 10iv t v t 2( ) 5id t v t t

Do Aunt Minnie problems in the Practice Book.

Do Workbook page 9

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