I. _________ m is the ______________________ that

an object contains. It is a ______________ .

A. units of mass: SI: _________________

are _____________________ units

have the ____________________________

Other mass units:

1/ _____________This is the approximate mass of a small

_________________ or of a ___________________

Conversions: 1 kg = ________ g = _________ g

1 g = _________ kg

2/ The _______________ mass unit u is defined as: (1/12) the mass of a ____________________

Conversion: 1 u = _______________ (see

PhysRT)

1 proton or neutron mass = __________

Note:

In: m = 10 g g stands for _________________

In g = 9.8 m/s2 g = ___________________

___________________

3/ British: __________ (don’t need to know) ≈15 kg

II. __________w is the ____________________ (Fg)

(usually due to a planet) acting on an object.

It is a _____________ b/c is has _____________

____________________________________________

A. Units of weight are the same as for

__________:

SI: _________________ derived

British: _________________B. The weight of an object depends on:

1/ the ____________ of the object itself;

2/ the ___________ from the center of the planet;

3/ the ___________ of the planet.

Mass m is___________________________.

It is a ____________________ of an object.

planet

For the same object at 3 different _____________ :

wor Fg

mass of object

more mass ________________

denserplanet

mass m w

_______ m

_______ m

w is different in different locations because_________________________________________

Remember: _____________ = __________________

C. Its magnitude can be found from:

where m is the mass of the object _________and g is the _____________________________ .On Earth’s surface, g = _________________Farther from the surface or on other planets,_____________________________________________ .

Fg = PhysRT:

or:

Ex: Find the weight of a 45-kg goblin.

Ex: The weight of a stick of butter is about 1.0 N. What is its mass?

Ex: What is the weight of a 600-N student?

What is the force of gravity acting on the goblin?

I. A force, F, is a ____________________________ .

A. Forces are ______________ .•magnitude – how ___________________•direction –_________ shows dir. of push/pull

Ex 1: F =

SI force units__________________ (derived)

1 N =

1 N ≈ weight of 1______________________

Ex 2: w =

Sketch:

Ex. John pushes Jane with a 25 N force to theright. Joan pulls Jane with a 25 N force to the right. Draw and label both forces using a scale of 1 cm = 5 N.

These two forces are drawn ____________________b/c they have the same __________ & ___________ .

John and Joan are said to __________ a force on or ____________ a force to Jane. We say the forces____________ Jane. Sometimes, forces are called____________ .

Jane

John Joan

B. ____________________________ forces:• most _____________ forces known• can push or pull ______________physical contact.• aka “___________________” or “ __________ ” forces

Ex. Even though ___________ is separated from

__________________ by a ____________ (nothing),

both objects are able to _____________________

on each other.

E m

The 4 __________________ forces are listed belowfrom strongest to weakest:1._________ (nuclear) –force that binds __________ and ____________ within the ______________2._____________________ (e&m)- the force that acts between _____________ charges; the source of ______________ ; responsible for chemical ________between _________ or between __________________3. _________ (nuclear)– causes nuclear __________4.__________ – (Fg) a force between ____________

holds planets, solar systems, and galaxies together, but is the __________________________aka the _____________ (w)

of an object when it is on or near a_____________ .

C. ________________ forces between 2 objects:•result from___________________________•occur when there is _________________

1.___________________, T:

• the _______ of wires, ropes, strings, cables, etc• _____________ is the direction of the wire, etc • ______________ of wire, rope, etc, not important• results from ________________________ between atoms and molecules __________ the wire itself.

weight

wireThe ___________ is the forceexerted by the wire as it_______________on the weight.

Ex: ceiling

2. ______________, Ff :

• usually ____________ motion (or ____________ motion)• direction - usually _____________ of velocity • acts _____________________ between 2 objects• sliding friction: results as electron ________

between the molecules along the surface

__________________________ .

Ex: block slidingalong floor to theright.

block

v

The surface _______________to the ________ on the block.

v = 0Ex: block at rest on an incline

Ex: block being pulled up an incline (ramp)

____________ friction, the block would slide down. This would be its "_______________ " motion. Friction ____________ that motion from happening, so friction must be directed ____________________ .

v

3. The ________________ force, FN :

• occurs when 2 ________________ are in contact• direction is _________________ ( ) to both surfaces • results when electron bonds _____________ as surfaces _______________________ each other

Ex: standing on floor

Ex: block at rest on an incline

The floor _________on _______________.

The incline _________on _______________.

D. Usually __________________ force acts on an

object at a time. ________________ diagrams make

it easier to solve these problems.

Rules for drawing free-body diagrams:

1. Imagine a _____________ surrounding the object.

2. List all:

a/ "______________" forces that cut through it

b/ "_________________" forces that cut through it

3. Draw a _______________ to represent the object.

4. Draw each force in step 2 as an ___________

whose tail begins at that _____________ .

5. Only draw _____ . Do NOT draw _____________ !

Drawing or sketch of object with many forces acting on it:

Free body diagram (FBD) of same object:

hill

rope

Ex: A student holds herself on a hillsideby pulling on a rope.

Draw a FBD of the forces acting on the blocks in each case below.

Ex 1: block in free fall (no air resistance)

Ex 2: block on table at rest

Ex 3: block hangingfrom a wire:

ceiling

Ex 4: block pulled to left on frictionlesstable by a pull P

Ex 6: block on floor being pulled to left bya rope but not moving

P

Ex 5: block on table sliding to the left, nopull, but with friction

v

Notice: v is _______________ !

rope

E. Forces can be added like any other vectors:

head to tail:

parallel-ogram:

Add: and: F1 F2

F1

F2

F1

F2

Magnitude of resultant force: F =

Direction of resultant force: =

Ex: The resultant of two forces, 3 N and 4 N as a function of between them:

(0) ResultantMagnitude of resultant F:

Biggest possible magnitude __________ the magnitudes

Smallest possible magnitude __________ the magnitudes

As increases, the magnitude ________________ .

F. Forces can be _______________ (broken downinto _____________________ )like any other vectors:

F

Fy =

PhysRT:(Mechanics

section) Fx =

Ex: Find the x and y components of the F below:

120 N

Fy = Fx =

Newton’s 1st Law of Motion:

If the ____________________ force, Fnet, acting

on an object equals ________, then that object has____________________ . Its acceleration a = _____ .It is said to be in __________________ .

Because forces are ______________ and have____________ , the x and y _______________ of the forces often must be added up _______________when there are forces along different _________.

Fnet = 0 really means:________ = 0

________ = 0

Ex: A 20-N box on a tableat rest

20-N

Ex: A 20-N box at rest on a table being pushed down with a 5 N force.

"At rest" __________

20-N

Free body diagrams:

5-N

"At rest" _______________

Both of these boxes are in ___________________ .

Ex: Same box sliding to the right on a horizontalfrictionless table at a constant velocity 2.0 m/s

20-N

Draw only the __________ , not the ____________

Notice:1/ The free body diagram is the _________ as thefirst example. Both are in ___________________ .2/ No force is ___________ to keep box moving.The box will continue its motion ________________.

v = 2.0 m/s

"constant velocity" __________

Ex: The forces acting on a 20-N box are shown at right:

This box is in ___________________. It is either:

1/ _____________ (constant velocity = _____);

2/ or _____________ at a constant velocity.

Unless other information is given, it is _______________ to tell if it is at rest or moving.

3.0 N

4.0 N

Ex. The three forces below are the only onesacting on an 2.0-kg object. What is the acceleration of the object?

5.0 N

This object could be _______________ or moving with ____________________________ .

The net force Fnet = _____ so a must = ____ .

Add up the forces:

Restatement of 1st Law: If an object is ____________ or moving with _____________________, it is_________________.

Then the net force (Fnet ) acting on it _________ .

weight ≈ 1.3 x 106 Nthrust ≈ 75 x 103 N/engine x 4 engines

Ex: A B-2 bomber flying at constant velocity:

Ex. The two forces shown below act on an object. What third force is needed to produceequilibrium?

F1

First way to solve:• Find resultant force F• The answer is -F:

-F ___________________ the other two forces.

F2

Second way to solve:1. Add the two forces using head to tail method.2. Add a force to "bring the total force to zero."

original

Notice:• Both ways give ________________________• -F is NOT the ________________ of the other vectors. It is the force that ________________

the other vectors, making Fnet =________. It is

sometimes called the ________________ because it is what is needed to produce ___________________ .

F1

F2

F1F2

head to tail:

wire

beam

build

ing

weight

Ex. Draw the vector that represents the force that the beam exerts on point A.

A A

T

w

The beam force is the ________________ . It must be added to the other forces so that ___________

Ex. Increasing angle between 2 wires supporting a picture:

Case 1: vertical wires

Case 2: greater angle

Case 3: even greater angle

10 N

w = 10 N

T = ____in eachwire

w = 10 N

w = 10 N

10 N

10 N

1 2

1 12 2

12

1 2

T = ____in eachwire

T = ____in eachwire

As increases, the tension _______________ .

1 2

A net force is ________________ to maintain motion. An object will maintain its motion in the ________________ of a net force. This idea was discovered by _____________. An object in motion tends to ____________________ , and anobject at rest tends to _________________ . The _______________________ that “makes” this true is called its ___________ .

more __________ more___________in

ert

iamass

Ex. What has more inertia, a truck or a baseball?

Inertia is the tendency of an object to _________________________ . More inertia (mass) means it is __________________ for an object to…1/ …_____________________ when it is at rest;2/ … __________ when it is already moving; and,3/ … ____________________ from a straight path.In other words, ______________ is why an objectneeds __________________ to maintain its motion.This is why Newton's _____________ is calledthe ________________ . Fnet a

Lawof

Inertia

Newton’s _____ Law:

If a net force Fnet acts on an object of mass m,the object’s acceleration a will be:

a = Net forces ___________________

mass ________________________

Fnet

a

m

a

Compare: a = Δv/t is a _________________ of a

a = Fnet/m tells the _____________ of a

1/ Units: a =

units: =

=

1 N = the _____________ that produces an acceleration

of __________ when applied to a mass of _________

1 kg1 N

frictionless surface

Fnet

m =

2/ a is a vector: a = 5.0 m/s2, east

a/ The magnitude of a is also called the________________________.

vector magnitude

displacement

velocity

acceleration

Ex. Names of vectors and their magnitudes.

b/ The direction of a is ________________ the direction of Fnet.

Ex: In free fall, the weight w equals ________

What is the acceleration at

all five points shown?

magn.: a = __ = ___________

dir.: __________ because it is

the same direction as ______.The acceleration is ____ 0

at the top because Fnet ____ 0

there (and everywhere else).

3/ Compare:

a = __________

F's are ___________________________________

Newton’s 1st Law: Newton’s 2nd Law:

FN = 20N

w = 20 N

pull= 10N

Ff = 10 N

a = ___ ___________ v or v = ______

F's are _______________________________

FN = 20N

w = 20 N

pull= 10NFf = 2 N

Fnet = __________ Fnet = __________

The First Law is really just a _____________________ of

the Second Law that is true when ____________________ .

w = mg = _________________

≈ _____________ = _____

Ex: A force of 16 N pushes horizontally on a 2.0 kg mass on a frictionless surface. Draw all the forces acting on the mass. Then find Fnet and a.

2.0kg

Fnet =

______________

or ___________

= = = Fnet

ma =

Ex: Add a friction force of 4.0 N to the previousexample. Again, draw all forces acting on the mass, find Fnet and find a.

2.0kg

Now, Fnet = ____________

Fnet

m

a is _________ now b/c Fnet is___________ .

a =

Which way is the mass in the previous problem moving?

___________. Why? Because Fnet is to the right, a is _____

_______. But a only tells the direction of _______, not ____ .

2.0kg

Case 1: positive v

vi

2.0kg

Fnet

vf ___ vi so v = vf - vi ___ 0 and so a = v/t __ 0

2.0kg

vi

2.0kg

Fnet

Case 2: negative v

In both cases, Fnet is ________, so v and a are ________

but, in Case 2, v is ________________ .

vf ___ vi so v = vf - vi ___ 0 and so a = v/t __ 0

Ex: A 2.0 kg box slides to the right over a surface with a constant frictional force of 2 N. Draw all forces acting on the mass, find Fnet and a.

2.0kg

Fnet = __________

= ________

The box is _________________ , because Fnet and v are in ______________________________ .

v

Fnet

ma =

Ex: Why do all objects fall with same acceleration in free fall (no air resistance)?

small mass

big mass:

a =

Newton's2nd Law :

Which object gets pulled down with a greater force?

Which object resists more?

Which accelerates most?

a = a == =

= =

Ex. A block is pulled along a frictionless table by a force that makes an angle to the horizontal.

2.0kg

F

a/ Find the x- and y-________________ of F.b/ Replace F in the free body diagram with them:

F

What will happen to a if is increased?

y-direction: Because the block is not acceleratingup or down, the y-forces are ________________.

equilibrium: w =

x-direction: Only 1 force _________________

ax =

F

Fx ___creases, so a _____________________.

F

Notice: w _____ FN

Newton’s ______ Law:

In plain words:

For every_____________ ,

there is an equal and opposite____________.

In physics speak:

If object A exerts a __________ (the action) on

object B, then object B exerts a ___________ (the

reaction) that is ________________________ but

__________________________ on object A.”

A B

Ex. Punching things:

Which object exerts a greater force?

Which object exerts a greater force?

force of fiston paper:

force of paperon fist:

force of fiston block:

force of blockon fist:

Action-reaction forces are ______________ in case 2, but both cases are opposite and _________ .

Case 1: punching paper

Case 2: punching a cement block

Forces ALWAYS occur in __________ .

Either force could be called the ___________.

One force does not happen _____________

Both forces occur at the ___________________.

Ex 1: F: Earth ________ you down with _________.

-F: You _______ Earth up with _________.

Both forces are ____________ .

Both forces are ____________

Notice the "same types:"

A/ Both forces are the exact same ___________ .

Ex 2: F: You ________ right on wall with a __________________. -F: Wall __________ left on you with a __________________.

Ex 3: F: Wire ________ up on picture with a _______________. -F: Picture _________ down on wire with a________________.

wall

hand

B/ Action:reaction pairs act on ______________ objects in _____________ directions.

Action: A exerts a F on B.

Reaction: ___ exerts a -F on ____.

Ex 1: F: Earth pulls you down with gravity.

-F: ______ pull _______ ____ with gravity.

subject object direction

____________direction

Notice how subject and object are _____________ ,

and the directions are ________________ .

Ex 2:

F: You push right on wall with a normal force.

-F: ______ pushes ______ on ______ with a

normal force.Ex 3:

F: Wire pulls up on picture with a tension.

-F: __________ pulls _________ on ________with

a tension.

In Sum: To find a reaction force, re-write with:1. the same _________ of force (push/pull

and gravity/normal/tension, friction, etc); but,2. reverse _____________ and _____________ and the _______________ of the force.

"A (subject)

pulls/pushes

in a certain direction

on

B (object)

with a certain force."

Action: Reaction:

" ____ (subject)

_________________

in ___________ direction

on

___ (object)

with _____________force."

Which force, action or reaction, has a greatermagnitude?

Ex: Write the action (A) and reaction (R) pairs.

block

table

Case 1/ Between block and table:

A:

R:

Case 2/ Between block and Earth:

A:

R:

Which of these are contact forces?Which are "at a distance" forces?

Ex: Weight is the force of Earth’s ___________ pulling ______________on an object:

w = ____ = Earth pulls__________ on cat with a ________________ force.

What is the reaction force to acat's weight, w?

The _______ _______ _______on ________ with a__________________ force.”

Ex. Don’t confuse ___________ (which are always equal and opposite) with ___________________ (which depend on _________ and usually are NOT equal and opposite).

Ex: An apple and the Earth (not to scale)

gravitational F ofEarth on ________

gravitational F of apple on _________

apple: a =

≈

=

Earth: a =

Same _____ but different _____ b/c different _____ !

________________: A. Find the acceleration of a block of mass m on a ______________ ramp that makes an angle with the horizontal.

a =

To determine a, you need ______, which means you need the ___________ that act on the block.

To find the force that accelerates the block downthe incline, you need to choose new axes that are______________ ( ) and __________________ ( ) to the plane’s surface.

w

FN

Notice:

The incline

angle ____

is _________

as this one.

NewAxes:

w┴ = ________

w|| = _________

w

||

The__________________ and _________________components of ____ are the sides of a ___________triangle:

adj hyp

= = ______

opp hyp

= = ______

side

side

w

|| w┴ =

_______

w|| =

________

Now return to the full free body diagramand replace ____ byits ________________.

___ is unbalanced and equals Fnet = ______________

FN

____ is balanced by _____: ___ = _________

So what is the acceleration a?

a = Fnet

m m

= = =

Ex: Find the acceleration of a 0.4-N block down a frictionless incline if the angle is 100.

Notice that the result is independent of ________ .

a =

a =

a =

Test: release from rest:

d = vit + (1/2)at2

d = a = a = a =

m

Case 1: What is a if = 900?

a =

a =

=

Case 2: What is a if = 00?

900

= =

_____ _____

To see if the equation a = _________ makessense for the incline, see what happens when has the "_______________ " values:

=

B. Now solve the problem, but with the block _________ or moving with __________________due to _____________.

If the block is not moving, Fnet = ___ , whichmeans all forces must ____________________ .

Ff = ____ = _________ (now in __________________).

FN = ____ = _________ (equilibrium as before).

w

Ex. A 3.0-kg block rests on an incline that makesan angle 300 to the horizontal. Determine the magnitude of the normal force and the friction force acting on the block.

300

w =

Ff = ____ = _________ = _____________ = __________

FN = ____ = _________ = _____________ = __________

____ = __________ __________

FN

w

FN

w

Ff

___ = _________ Fnet = __

FN = ____ = _________ FN = ____ = _________

Ff = ____ = _________Fnet = ____ = _________

C. Summary of inclined plane basics

Without friction: With friction and at restor constant v:

Ex: If there is friction, but the block is ____________________ ,it must be that _____ > _____ .In that case, the net force

Fnet = ________

Ex: Notice that the incline __________ or weakens gravity because it is not _______________ , but only the ________________________ that is pulling the block along the __________of the incline.

FN

w

Final notes:

1/ On a horizontalsurface: FN = ____

w

BUT,On an incline (either with or w/o friction):

FN = w┴ = ______

and NOT:

FN = ____w

2/ What happens to Ff and FN if is increased and the block remains the same and at rest?

w

FN

w┴

w||

Ff

inc.

w

FN __________

Ff ___________

w ____________

original incline:

As _____increases:

The force of_________________, Ff:

1. Ff = A ____________ force that ____________

motion. It is caused by the ________________________________________________________ between an object and _________________________. 2. Friction usually results in __________ when motion energy is transferred to ______________ in the object and its environment. This results in a temperature _____________ or a _________________, such as _____________.Ex: carskiddingon road

________ energyheats up ______and _________molecules

Three basic types of friction:A._____________ friction– due to collisions with fluid molecules; increases with speed Ex: _________________________________B._____________ friction –reduces amount of friction because there is less __________________Ex: ___________________C. ______________ friction – when two _______ _____________ slide past each other; what we are going to learn most about.

most leastforce __________ ___________ __________ force

A 10-N object at rest:

10 N

Now pull it with a 2 N force but it doesn’t move:

10 Npull Fp = 2N

Fnet =____

Fnet =____

All About ___________ Friction:

_________________ friction = _____

Pull it with a 4 N forceand it still doesn’t move:

10 Npull = 4 N

Fnet =____

When you increase the forceto 6.0 N, it _______________:

10 Npull = 6 N

Fnet ___ 0

Once it starts moving, you only need a _______ pull to keep it moving at _____________________:

10 Npull = 5 N

Fnet = ____

___________

static Ff,max

__________

friction Ff,k

____________________ friction = _____

Note:

1._____________ friction, Ff

friction when body is_______________can be _____ amount up to _______________ static friction

2. Maximum static friction, __________ friction just before the object ________________

During static friction, the _________________ molecular _________ between the object and the surface are ________________ microscopically, at first a little, then __________________. As the bonds reach the ________________ point, _______________________ friction occurs.

3. _________ friction, Ff,k is the friction that occurs when an object moves at ____________________ .

always ___ the__________ static friction: Ff,max

As it slides, the surface _________ are constantly ____________ and________________ Ex: Same wooden box

__________ Ff,k

a/ On different sides: b/ At different speeds:

Ff,k is roughly independent of

a/ ________________ , and b/ _______________ .

v v

__________ Ff,k

v v

Ff

Static___ canbe ____valuein here

bonds______

_________ Friction ____________ Friction

Static _______ > _______

A graphical view of static vs. kinetic friction:

bond

s __

____

____

___

bonds ____________and ______________

In either static or kinetic friction, sliding frictiondepends on two factors:

1. The____________________________ – waxed skis on snow, rubber on dry concrete, etcUsually, smoother surfaces __________ friction

2. The force that________________________________ This force is the ____________ force: ______

FN = ______

But press down on the block:

FN =_________

F

Block on a table:

These 2 factors are summed up in the equation:

Ff =

is called the _________________ of friction,

and is the Greek letter “______. ” It:

- describes effect of surface ______________ on Ff

- is usually _____________ for rougher surfaces - has ____ units: = _______ units _________ - has different values for: 1/ maximum static friction: _____ 2/ kinetic friction : and with ____ > ____ .

For maximum static Ff,max, use: Ff = FN

For kinetic Ff,k, use: Ff = ____FN

Notice:

1.This should say

___________ Static

2. k ___ s

From the PhysRT, page ___ :

Ex: A 12,000-N crate is on waxed skis on snow. Find the force needed to…1/ start it moving, and2/ keep it moving at constant velocity

1/ max. static: Ff = FN

2/ kinetic: Ff = FN

How would you answers change if another 2000 N were added to the sled?

=

=

=

=

=

=