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 _________________ Ing = 9.8 m/s 2  g = ___________________ ___________________ 3/ British: __________ (don’t need to know) ≈15 kg

II. __________w is the ____________________ (F g ) (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 _____________ : w or F g mass of object more mass  ________________ denser planet mass m w _______ 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, _____________________________________________. F g = 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 the right. 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 below from 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.__________ – (F g ) 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 wire The ___________ is the force exerted by the wire as it _______________on the weight. Ex: ceiling

2. ______________, F f : 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 sliding along floor to the right. block v The surface _______________ to the ________ on the block.

v = 0 Ex: 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, F N : 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 hillside by 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 hanging from a wire: ceiling

Ex 4: block pulled to left on frictionless table by a pull P Ex 6: block on floor being pulled to left by a rope but not moving P Ex 5: block on table sliding to the left, no pull, but with friction v Notice: v is _______________ ! rope

E. Forces can be added like any other vectors: head to tail: parallel- ogram: Add: and: F1F1 F2F2 F1F1 F2F2 F1F1 F2F2 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 ) Resultant Magnitude of resultant F: Biggest possible magnitude  __________ the magnitudes Smallest possible magnitude  __________ the magnitudes As  increases, the magnitude ________________.

F. Forces can be _______________ (broken down into _____________________ )like any other vectors: F F y =  PhysRT: (Mechanics section) F x =

Ex: Find the x and y components of the F below: 120 N   F y = F x =

Newton’s 1st Law of Motion: If the ____________________ force, F net, 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 _________. F net = 0 really means: ________ = 0

Ex: A 20-N box on a table at 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 horizontal frictionless 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 the first 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 ones acting 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 F net = _____ so a must = ____. Add up the forces:

Restatement of 1 st Law: If an object is ____________ or moving with _____________________, it is_________________. Then the net force (F net ) acting on it _________. weight ≈ 1.3 x 10 6 N thrust ≈ 75 x 10 3 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 produce equilibrium? F1F1 First way to solve: Find resultant force F The answer is -F: -F ___________________ the other two forces. F2F2

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 F net =________. It is sometimes called the ________________ because it is what is needed to produce ___________________. F1F1 F2F2 F1F1 F2F2 head to tail:

wire beam building 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 each wire w = 10 N 10 N T = ____ in each wire T = ____ in each wire 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 an object at rest tends to _________________. The _______________________ that “makes” this true is called its ___________. more __________  more___________ inertia mass 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 object needs __________________ to maintain its motion. This is why Newton's _____________ is called the ________________. F net a Law of Inertia

Newton’s _____ Law: If a net force F net acts on an object of mass m, the object’s acceleration a will be: a = Net forces ___________________ mass ________________________ F net a m a Compare: a = Δv/t is a _________________ of a a = F net /m tells the _____________ of a

1/ Units: a = units: = = 1 N = the _____________ that produces an acceleration of __________ when applied to a mass of _________ 1 kg 1 N frictionless surface F net m =

2/ a is a vector: a = 5.0 m/s 2, east a/ The magnitude of a is also called the________________________. vectormagnitude displacement velocity acceleration Ex. Names of vectors and their magnitudes.

b/ The direction of a is ________________ the direction of F net. 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 F net ____ 0 there (and everywhere else).

3/ Compare: a = __________ F's are _______________  ____________________ Newton’s 1 st Law: Newton’s 2 nd Law: F N = 20N w = 20 N pull = 10N F f = 10 N a = ___  ___________ v or v = ______ F's are _____________  __________________ F N = 20N w = 20 N pull = 10N F f = 2 N F net = __________ 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 F net and a. 2.0 kg F net = ______________ or ___________ = = = F net m a =

Ex: Add a friction force of 4.0 N to the previous example. Again, draw all forces acting on the mass, find F net and find a. 2.0 kg Now, F net = ____________ F net m a is _________ now b/c F net is___________. a =

Which way is the mass in the previous problem moving? ___________. Why? Because F net is to the right, a is _____ _______. But a only tells the direction of _______, not ____. 2.0 kg Case 1: positive v vivi 2.0 kg F net v f ___ v i so  v = v f - v i ___ 0 and so a =  v/t __ kg vivi 2.0 kg F net Case 2: negative v In both cases, F net is ________, so  v and a are ________ but, in Case 2, v is ________________. v f ___ v i so  v = v f - v i ___ 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 F net and a. 2.0 kg F net = __________ = ________ The box is _________________, because F net and v are in ______________________________. v F net m a =

Ex: Why do all objects fall with same acceleration in free fall (no air resistance)? small mass big mass: a = Newton's 2 nd Law : Which object gets pulled down with a greater force? Which object resists more? Which accelerates most? a = = = = =

Ex. A block is pulled along a frictionless table by a force that makes an angle  to the horizontal. 2.0 kg  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 accelerating up or down, the y-forces are ________________. equilibrium: w = x-direction: Only 1 force  _________________ a x = F  F x ___creases, so a ________ _____________. F  Notice: w _____ F N

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? force of fist on paper: force of paper on fist: force of fist on block: force of block on 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 greater magnitude?

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 a cat'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 of Earth 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 down the incline, you need to choose new axes that are ______________ ( ) and __________________ ( ) to the plane’s surface.  w FNFN Notice: The incline angle ____ is _________ as this one. New Axes:

w ┴ = ________ w || = _________ w ||  The__________________ and _________________ components of ____ are the sides of a ___________ triangle: adj hyp = = ______  opp hyp = = ______  side

w ||  w ┴ = _______ w || = ________ Now return to the full free body diagram and replace ____ by its ________________. ___ is unbalanced and equals F net = ______________ FNFN ____ is balanced by _____:  ___ = _________

So what is the acceleration a ? a = F net m  m = = = Ex: Find the acceleration of a 0.4-N block down a frictionless incline if the angle is Notice that the result is independent of ________. a = Test: release from rest: d = v i t + (1/2) a t 2 d = a =  m

Case 1: What is a if  = 90 0 ? a = = Case 2: What is a if  = 0 0 ? 90 0 == _____ To see if the equation a = _________ makes sense 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, F net = ___, which means all forces must ____________________. F f = ____ = _________ (now in __________________). F N = ____ = _________ (equilibrium as before). w 

Ex. A 3.0-kg block rests on an incline that makes an angle 30 0 to the horizontal. Determine the magnitude of the normal force and the friction force acting on the block w = F f = ____ = _________ = _____________ = __________ F N = ____ = _________ = _____________ = __________ ____ = __________ __________

FNFN w  FNFN w  FfFf ___ = _________ F net = __ F N = ____ = _________ F f = ____ = _________ F net = ____ = _________ C. Summary of inclined plane basics Without friction: With friction and at rest or constant v:

Ex: If there is friction, but the block is ____________________, it must be that _____ > _____. In that case, the net force F net = ________ 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. FNFN w 

Final notes: 1/ On a horizontal surface: F N = ____ w BUT, On an incline (either with or w/o friction): F N = w ┴ = ______ and NOT: F N = ____ w 

2/ What happens to F f and F N if  is increased and the block remains the same and at rest?  w FNFN  w┴w┴ w || FfFf inc.  w F N __________ F f ___________ w ____________ original incline: As _____ increases:

The force of_________________, F f : 1. F f = 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: car skidding on road ________ energy heats 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 least force  __________  ___________  __________  force

A 10-N object at rest: 10 N Now pull it with a 2 N force but it doesn’t move: 10 N pull F p = 2N F net =____ All About ___________ Friction:

__________ _______ friction = _____ Pull it with a 4 N force and it still doesn’t move: 10 N pull = 4 N F net =____ When you increase the force to 6.0 N, it _______________: 10 N pull = 6 N F net ___ 0

Once it starts moving, you only need a _______ pull to keep it moving at _____________________: 10 N pull = 5 N F net = ____ ___________ static F f,max __________ friction F f, k __________ __________ friction = _____

Note: 1._____________ friction, F f  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, F f,k is the friction that occurs when an object moves at ____________________.  always ___ the__________ static friction: F f,max  As it slides, the surface _________ are constantly ____________ and________________ Ex: Same wooden box __________ F f,k a/ On different sides: b/ At different speeds: F f,k is roughly independent of a/ ________________, and b/ _______________. v v __________ F f,k v v

FfFf Static ___ can be ____ value in here bonds ______ _________ Friction ____________ Friction Static _______ > _______ A graphical view of static vs. kinetic friction: bonds _____________ bonds ____________ and ______________

In either static or kinetic friction, sliding friction depends on two factors: 1. The____________________________ – waxed skis on snow, rubber on dry concrete, etc Usually, smoother surfaces  __________ friction 2. The force that________________________________  This force is the ____________ force: ______ F N = ______ But press down on the block: F N =_________ F Block on a table:

These 2 factors are summed up in the equation: F f =   is called the _________________ of friction, and is the Greek letter “______. ” It: - describes effect of surface ______________ on F f - is usually _____________ for rougher surfaces - has ____ units:  = _______  units _________ - has different values for: 1/ maximum static friction: _____ 2/ kinetic friction :   and with ____ > ____.

For maximum static F f,max, use: F f =  F N For kinetic F f,k, use: F f = ____F N 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, and 2/ keep it moving at constant velocity 1/ max. static: F f =  F N 2/ kinetic: F f =  F N How would you answers change if another 2000 N were added to the sled? = = = = = =