___________________ p is a vector.Its magnitude: p = _____Its direction: same as the direction of ____The plural of momentum is _________________.

units of p = [ ] [ ] = NOT a newton:

(1 N = )

pp

m v

Ex: Find the momentum of a 7.0-kg bowling ballthat is rolling east at 3.0 m/s.

p =

=

=

7.0kg

v = 3.0 m/s

=

Ex: Give the direction of p in each case below.

1/ ball moving up during free fall

2/ ball falling down during free fall

3/ ball fired up at an angle at the four points

shown below:

a

b

c

d

At which of the four points shown is the

magnitude of the momentum the greatest?

All p's are___________to the ___________because the______ are.

1st idea: p = mv is similar to____________

more mass more difficult to _____________

4.0 kg

a/ If v = ___ : p = mv = m( ) =____, but it ____________________ .

1.0 kg

How is p different from inertia?

v =

v =

b/ Two objects with _____________ inertias can have ____________momentum. How?

3 Big ideas in momentum:

Important:

Each term will be:

positive if the object is moving _________________

negative if the object is moving ________________

2nd idea:

The total momentum pT for a __________

(group) of objects is found by ____________

the p's for each object as vectors (showing

____________):

pT = + + + …

= + + +

Ex: Find the total momentum for the systemof two objects shown below:

5.0 kg

8.0 kg

v = 4.0 m/s v = 2.0 m/s

Adding as vectorspT = p1 + p2:

pT =

= =

=

=

3rd idea: Collisions and ___________ in p: ____

A. ____________ (“hit and stick”) Collisions

vi = 4.0 m/s

wall

vf =__

p = pf - pi

= -

= -

= -

=

m = 0.5 kg

p = pf – pi

= =

=

=

=

OR

Ex: _____________ Inelastic Collision:

B. _______________ (“hit and bounce”) Collisions

vi = 4.0 m/s

wall

m = 0.5 kg

Ex: ______________ Elastic Collision:

p = pf - pi

= -

= -

= -

=

p = pf - pi

= =

=

=

=

OR

vf =

Momentum changes more during ________collisions because the object must first be___________ (one change), and then it must be _________________ (an additional change).

1. The magnitude of p is _______________ when an object bounces . Why?

Inelastic:Stopped only

Elastic:Stopped and _____________

The momentum

goes from:

to this:

So p =

The momentum

goes from:

to this:

Sop =

2. Why is p is ______________ in the above two examples?

wall

Inelastic:

Elastic:

vi

vf = 0

vi

vf ≠ 0

In both cases, p is _________ by the _________ of the ________ acting on the _____. This force is ______________ , and this makes p ____________ .

C. Most collisions are ___________ “perfectly”

inelastic or elastic. The object bounces

back, but with ________________ than it had

initially:vi = 4.0 m/s

wallvf = -2 m/s

These are called ________________ elastic

collisions. In these, the ______________ of p

will be somewhere ______________ the values

for inelastic and elastic collisions.

ARealisticImpact:

A_________Impact:

Fnet

Think of how a baseball bat _________ (comes intocontact with) a ball as a function of _________.

bat first_________ ball

ball _________the bat

t

___________force of bat on ball

Area =

_______

Fnet

t

The ________ of and ____________ (time) of impact

determine the future __________ of the ball.

The quantity _______ is called the _____________

It is a ______________ quantity.

magnitude: J = _______

direction: same as the dir. of ______

units of J: [ ] [ ] = _______ (derived)

J J

tFnet

Ex 1: A net force of 25 N to the right acts on a 40-kg snowman for 3.0 s. Calculate the impulse exerted on Frosty.

J =

=

=

40kg

Fnet = 25 N

Ex 2: Give the direction of the impulse for a:

A/ ball moving up during free fall

B/ ball falling down during free fall

C/ ball fired up at an angle at the four

points shown below:

All J's are___________because thatis the directionof ___________

_____________ changes ________________

Newton's Second Law: Fnet =

Rewrite a as v/t: Fnet =

Multiply both sides by t: Fnet =

But mv = p, so write: Fnet =

Since Fnet t = ____, the last line can be written:= =

(Historical note: Newton actually first wrote hissecond law using _____ , and not ____ .)

[J] = [ ][ ] = [ ] [ ]

J = Fnett =

From this last equation, the _______ of impulseJ can be written two ways:

This is true because: 1 N·s = 1 ( ) s

= 1

If you re-write p = pf - pi and substitute in,

you get:

J = Fnett =or:

[J] = ( ) ( ) = ( ) ( )

=__________ ____________

Ex: An impulse of 24 N·s north is applied to a 0.15-kg baseball initially moving at an initial speed of 40 m/s south. What is the change inmomentum of the baseball?

Equation:

Given: J = m = v =

Unknown:

Answer: p =

=

Ex: A 0.5-kg ball is moving at 4.0 m/s to the right when it hits a wall. Afterwards, it moves 2.0 m/s to the left. Determine the impulse exerted on the ball by the wall.

vi = 4.0 m/s

wall

vf = -2 m/s

m = 0.5 kg

This can be written: J =

And can be rearranged to: pf =

This says, "J is what you add to ___ to get ___."

pi = mvi

= (0.5)(4) = 2 kgm/s

Before theimpulse:

Ex. The last example found p = J = -3 Ns = ___ kgm/s

p= =Fnet tJ

pi = 2

Adding the impulse of -3 Ns Ns from the wall to pi:

The impulse J is ______________ (to the left) in theprevious example because _____ from the wall is.

The wall in the previous example exerts its force for a time of 0.12 seconds. Calculate the net force that acts on the ball during that time.

The equation: Ft = p has many applicationsin sports and collisions….

1. To ______________ (make the most of) p, you can:

apply a ____________ F ___t (hit harder)

____________ the impact time: F___ (follow through)

Both of these help you to take a ball moving in one direction and allow you to send it in another direction with a _____________________ velocity.

2. Suppose 2 identical cars (m=1000 kg), traveling at the same initial vi (30 m/s) both come to rest: a/ Car A hits a _________ wall and stops in 1 s.b/ Car B hits _________ barrels and stops in 4 s.

For both cars:p = mfvf – mivi

= =

A: F t = p

F ____ = -30,000

F = ________

•__________ time to stop•_________ force of impact

Apply Ft = p to each car to find force on car:

B: F t = p

F ____ = -30,000

F = ________

•__________ time to stop•_________ force of impact

_________________ are a fact of life:1. In _________: Hands, feet, heads, bats, rackets, clubs, collide with balls, nets, goals, posts, people, diving boards, etc. _________collide with each other.2. __________ collide with other cars, buildings, people, bicycles, etc.3. __________ or parts of atoms collide with other atoms. Light collides with ____________.4. Planets, stars, and galaxies collide with __________________.

Physics uses _____________________ to study collisions because it allows us to ignore the ____________ between the objects, which can be very __________________ during a collision.

The total ______________ of a system of objects will change if a net ____________ is applied to it:

impulse = change in momentum

=

=

A collection of objects that _____________ with each other is called a ____________ of objects:

12

3

_________forces:

SYSTEM

12

3

Any ___________ (outside) force exerts _________ force on the system

The “system” exerts no force, such as__________ on the “outside”

No Fnet no ____ no _____

ptotal _____________________

But what if there is ________ impulse acting on the system? This can only happen if the system is ________________, which means there is no net ____________ acting on it.

SYSTEM

= (In ___________)

If the “system” consists of 2 objects, this is written:

=

=

The Law of Conservation of Linear Momentum: The __________ momentum of an isolated system of objects ____________________ . This means that the total p _________ a collision (or anexplosion) equals the total p ________ the collision:

the prime symbol: ' represents “_______”

Ex 1: ___________ Collision. A 1.0-kg block and a 2.0-kg block slide on a horizontal frictionless table as shown.

1.0kg

2.0kg

The "system" consists of _____ blocks.

The system is "isolated," b/c there is no ___________.

The two blocks collide and ____________ (exert forces on each other). After the collision, they move apart with the velocities shown below:

1.0kg

2.0kg

Conservation of momentum says:

(Velocities have direction: left is_____________ )

=

=

=

=

=

=

=

=

=w/units:

Ex 2: ______________ Collision. A 4.0-kg block and a 2.0-kg block slide on a horizontal frictionless table as shown below.

2.0kg

4.0kg

After they collide, they ________________ and move ________.

What is the velocity of the "stuck together" mass?

2.0kg

4.0kg

Notice that the final v does not have _______________1 or 2, because both masses ____________________________________________ .

Conservation of momentum says:

(The ______________ on _____ are dropped.)

The combined mass moves to the ________ .

=

=

=

=

=

=

=

=

w/units:

Ex 3: ___________ /Spring Release. A 3.6-kg mass and a 1.2-kg mass are connected by a spring and __________ on a horizontal frictionless table:

When the spring _______________ , the 3.6-kg mass moves off to the left at the speed given. Determine the speed of the 1.2-kg mass.

1.2kg

3.6kg

1.2kg

3.6kg

Conservation of momentum says:

Both masses begin at rest ________ for both.

=

=

=

=

=

=

=

=

=

w/units:

In this example:1. The total momentum of the system _________the spring is released equals ______ because both masses begin _____________ .2. The total momentum of the system ________ the spring is released equals ______ because of the Law of ___________________ of Linear Momentum.3. __________ mass receives a greater force b/c ofNewton's 3rd Law: ________ but ____________ forces.4. The smaller mass moves ___________ because acceleration a = F/m is _____________ proportional to mass, and its mass is _____________ . It has ____ less mass, so it gains ____ more speed.

In sum: ________________ , is used in 3 cases:

1. _____________ (bouncing):

2. _______________ (sticking):

3. ____________ /__________ release:

total p = ____ total p = ___________

v ____________

_______________ mass

Newton’s Law of Universal Gravitation:

Two objects of mass m1 and m2 separated by

a center-to-center distance r ___________ each other with a gravitational force:

…where G = ____________________________is called the _______________ gravitational constant.

Fg =

Notes:1. Fg is an _________ range, _______________ force.

2. Fg is stronger when the objects are__________ .

3. The constant G is very __________ Fg is the

________________ of the fundamental forces.

4. Fg is always ___________________.

5. Both masses pull each other with ____________magnitude forces, but in _____________ directions.6. Equation is only true for ____________ masses.

for spheres, you must assume mass is concentrated at __________________

for complicated shapes, _____________ is needed, but equation works ________________ anyway.

Ex. A mass of 1.8 x 103 kg (F-150) is 0.50 meter from a mass of 6.0 x 101 kg (student). Find the magnitude of the force of gravitational attraction between the two masses. Show all work.

Fg =

Which mass pulls with a greater force?

Fg =

Fg =

Fg =

Fg =

Fg

m1

Fg

m2

Fg

r

Double m1 Fg ________________

Triple m2 Fg ________________

Double both m1 and m2 Fg ________________

Triple m1 and double m2 Fg ________________

Double r Fg ________________

Halve r Fg ________________

Triple r Fg ________________

Double m1 and r Fg ________________

Double m1, m2 and r Fg ________________

Ex: If the Fg is between an object of mass m and a planet, then Fg is called the _________: Fg = ___

Fg =

Gm1m2

r2r =

Re = ________________Me = ________________

Fg =

mEx: Earth

Fg =

w =

g = =

Me

The space shuttle orbits at ≈ _______ = __________ above Earth's surface. Its __________ distance from Earth's center isr = _____ + _____ Mm = _______ Mm. = ________ ReSo the ___________ (Fg) of the shuttle and all its contents in orbit, compared to its weighton land, is:

Ex: Are you weightless in the space shuttle (mass = ms)?

Re = ___________

≈ ___________

Earth

Fg =GMems = =

GMems

ms

Ex: r is the ____________________ distance

Earth

r = 1 Re

r = __ Re

r = __ Re

__ Re above surface

__ Re above surface

A

B

C

If Fg at surface = 200 N,what is the weight (Fg) at A?

At B? At C?

__ Re above surface

r = __ Re

Ex: A 20-N box on a table is lifted from 1 m to 2 mabove the floor. Since the height was doubled,the new weight should be w = 20/22 = 5 N ??????

20 N

table

1 m

5 N ?

2 m

This _______________________because theseheights are ______________from _____________________ .

Ex: A 600-N volleyball player jumps in the air. What is the force of gravity acting on her…

1/ …while in the air?

2/ …as she is landing?

3/ …when she is again at rest on the ground?

4/ What is her weight inall three cases above?

Ex:

d/ What is the reaction force to the weight of the rock in each case?

A rock in freefall:

Same rock at rest on a table:

b/ What is the net force acting on the rock in each case?

Fg = 1.33 N

free fall: Fnet = ______

on table: Fnet = ______c/ What is the acceleration of the rock in each case?

free fall: a = ______on table: a = ______

a/ What is the weight of the rock in each case?

Fg = 1.33 N

Ex: Cavendish "Weighing the Earth" Experiment:

m1

thin wire

Pb barbells

When a ____ sphere (m2) was broughtclose to the barbells, the _______________attraction caused the thin wire to _________ .

Then Fg, r, m2 and m1 were substituted into:

Fg = and this was solved to find ______ .

Once _____ was known, an object of known mass m and weight w were used to find ___________ unknown mass Me using

r

From the wire'sproperties, the______________needed to makethe wire twist that much could be _____________

G m

Re2

w =

One last note:

g =

Fg =

Even though g appears in the equation for w,an object does NOT have to be ________________ to use this equation. Think of g as simply a ________________________ between ____ and ____ . In fact, g can have ___________________ in differentlocations, which is why ____________ may changeeven though _________ remains the same.

________equation

acceleration____________

=

In PhysRT:

Not in PhysRT:

Solve this for:

A __________ is an idea used to explain howobjects can ________________ on each anotherwithout touching ("at a _____________" forces)even if separated by a ____________:

Examples of fields:1.__________________2. _________________3. _________________

object 1 object 2

All fields are _________because they represent____________ .

field of 1

field of 2

the 2 fields ____________with each other

The force of ______________ is explained by sayingthat a gravitational ___________ exists around every______________ . Here is how it works:

2. To study that field, put a ______ mass m in it, and measure the gravitational ________ Fg pulling on it:

1. Suppose there is a _______ somewhere near here (not shown). Because of that mass, there must be a _________________ field all around it.

Then the ____________ (magnitude) of the field g is given by the force _______ mass:

units of g: [g] = [ ] / [ ]

[g] =

[g] =

And since 1 N = __________ , these units can bewritten:

=

derived _________ = __________ fundamental

direction of g: ____________________

Ex: A 5.0 kg mass experiences a gravitationalforce of 30.0 N when placed at the position shown here.

Determine the strength (magnitude) and direction of the gravitational field at the point shown.

strength: g =

= =

=

30 N5.0 kg

direction: Same direction as_____

Ex: What will a 0.10 kg stick of butter weigh when placed in the gravitational field shown?

g =

=

=

g = 8.2 N/kg

g = same as g =

When Fg is due to a planet, we call it _________.So you can write:

planet Butterway

What is the force of gravity acting on the butter?

>

>

>

>

>

>> >

Ex: To find the shape of the g field around a "point" mass m, use a “test” mass mt.

_____ fieldline in thecircle out here

_____ field lines in thecircle in here

m

The force arrows are connected into ____________ .

Notes:• The lines are __________ to the forces. They are

“__________________ " that act on a test mass m.

2. Closer lines _____________ field ________

the mass. Also, the lines ________________

because then one point

would have _______________

3. The arrows show______________ by pointing

in towards the mass. We say g is directed

_______________________ .

As seen from far away, Earth's fieldis very similar to a __________ mass. The g field lines are ______________to the surface.

____________ to Earth, the lines don’t spread out as much:

surface

>

>

> >

>>> >

E

Coming even closer,________ spreading

surface

g at Earth's surface is ___________ because on the surface you remain the same ___________ from Earth's center (one Earth _____________ ).

In fact, g is simply the _________________ due to gravity. Its value is ____________ near Earth'ssurface. This means that an easy way to find g would be to __________ an object and measureits ____________________ in free fall.

Close to the surface, the lines appear __________spaced and ___________ .

> > >

surface

>

>

> >

>

>

> >E

The field g around Earth (or a point mass) isproportional to ________ because _______ is .

g = ( )/m

g =

g = ~

At the surface, r = ___ , so g = =

But at greater r's, g will be _________ .

(Note: For any planet, use: gp = )

/m

>

>

>

>

>

>

> >

E

Ex. g as a function of distance from Earth's center:

g = ____

g = ____ /22 = _____

g = ____ /32 = _____

g = ____ /42 = _____

Compare:

Big G = ________________________ never

changes!

g

r1Re 2Re 3Re 4Re

9.81

1Re

2Re

3Re

4Re

In sum: g = the gravitational ____________

= the ________________ due to gravity

direction: _____________________________

units of g: derived: ______________

fundamental: ______________

How to find g:

1. Take a mass and weigh it (find Fg):

Calculate: g = =

2. Drop an object and find its _________________ .

3. For a planet of mass Mp and radius Rp:

Calculate: g =

___________ Circular Motion (UCM) occurs when an object moves in a circle at __________________

____________: circular motion around an axis that is ______________________

____________axis

_____________axis

____________: circular motion around an axis that is ______________________

A. The 2 types of "Turning Around:"

B. Two types of Rotational/Revolutionary Speeds:

1. ____________ speed ("omega")

_________ for all points on a solid object

units: _____________ , rpm’s, etc

2.___________ speed v

depends on ______________________ of

rotation or revolution

units: _______, mph, etc

v = ______ =_________

In Regents physics, ______________ is the

only type of speed we deal with

Ex: Earth

rotation axis

equator

= _____________

= _____________

Everywhere on Earth, the __________speed is the same:

But _________ speedv = __________ isgreatest at the ______________ and zero at the _________ .

r

r

NYS latitude

Rockets are launched from ____________ because its _________________________________

C. Linear velocity is always ___________ to the circle in the _____________ of motion.

Ex: _____________ (CW) uniform circular motion:

12

3

45

6

7

8

12

3

45

6

7

8

Ex: __________________ (CCW) uniform circular motion: In _________ CW

and CCW motion:1. The __________ (_____________ of v) remains constant.

2. The ___________ of v is changing. Because of this, the object must be __________________

NOTICE:

D. The direction of _________________ during UCM

From a = _______a has the same direction as ____ .

where Δv =

=

• a is directed towards the circle’s _____________.

• It is called ___________________ acceleration: ac.

• It occurs b/c the velocity _______________________.

Ex: Direction of ____ for ____ and ______motion

1

3

5

v

v

v

7

v

Notice: • Even though a is always ____________________,it is always _____________________ in both cases.

• The angle between v and ac is always _______ .

1

3

5

v

v

v

7

v

E. The _______________ of ac is given by:

ac =

units of ac = [ ]2 / [ ]

=

=

=

acac

v r

ac

m

F. What causes a? What causes ac?

The magnitude of Fc is given by: Fc =

=units of Fc =

=

=

=

Fc Fc

v r

Fc

m

[ ] [ ]2 / [ ]

1. Although Fc is always ___________________ , it is

always towards the __________. This was also true

for ac, because force F and the a that it __________

are always ____________________________ .

G. Direction of ____ for ____ and ______ motion

3

5

v

v

v

7

v

3

5

v

v

v

7

v1 1

2. During UCM, the Fc is an _____________ force and Fnet ___ 0. Remember: _____________ is changing direction (even though __________ is constant), and this is an __________________ .

3. Without Fc, the object would move off on a

____________ (in the direction of its ___.)

4. Fc can be provided by many different forces:

• ____________ holds planets in elliptical orbits.• ____________ keeps cars on road during turns• __________________ allows birds to turn in air• _________ keeps rock turning in a circle• ________________ keeps rider on loop-d-loop ride

Ex: A 1500-kg car moves clockwise in a circle of radius 25 m at a speed of 12 m/s. Calculate a/ the centripetal acceleration of the car;b/ the centripetal force acting on the car.

c/ What direction are v, ac and Fc when the car is at

the point shown?

d/ What provides the Fc that allows the car to turn?

e/ In which direction would the car move if Fc became 0?

ac =

= =

Fc =

= =