Transcript Slide 1

___________________ 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 =
)
p
p
m
v
Ex: Find the momentum of a 7.0-kg bowling ball
that is rolling east at 3.0 m/s.
7.0
kg
v = 3.0 m/s
p=
=
=
=
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:
c
b
d
a
All p's are
___________
to the
___________
because the
______ are.
At which of the four points shown is the
magnitude of the momentum the greatest?
3 Big ideas in momentum:
1st idea:
p = mv is similar to____________
more mass  more difficult
to _____________
How is p different from inertia?
a/ If v = ___ : p = mv = m( ) =____,
but it ____________________ .
b/ Two objects with
_____________ inertias
can have ____________
momentum. How?
4.0
kg
1.0
kg
v=
v=
2nd idea:
The total momentum pT for a __________ (group)
of objects is found by ____________ the p's for
each object as vectors (showing ____________):
pT =
=
+
+
+…
+
+
+
Important:
Each term will be:
positive if the object is moving _________________
negative if the object is moving ________________
Ex: Find the total momentum for the system
of two objects shown below:
5.0
kg
pT
v = 4.0 m/s
=
=
=
=
=
Adding as vectors
pT = p1 + p2:
v = 2.0 m/s
8.0
kg
3rd idea: Collisions and ___________ in p: ____
A. ____________ (“hit and stick”) Collisions
Ex: _____________ Inelastic Collision:
vi = 4.0 m/s
vf =__
m = 0.5 kg
Dp =
pf
-
=
-
=
-
=
-
=
wall
Dp =
pi
=
OR
=
=
=
pf
–
pi
=
B. _______________ (“hit and bounce”) Collisions
Ex: ______________ Elastic Collision:
vi = 4.0 m/s
m = 0.5 kg
vf =
wall
Dp =
pf
-
=
-
=
-
=
-
=
Dp =
pi
=
OR
=
=
=
pf
-
pi
=
1. The magnitude of Dp is _______________
when an object bounces . Why?
Inelastic:
Stopped only
Elastic:
Stopped and
_____________
The momentum
The momentum
goes from:
to this:
So Dp =
goes from:
to this:
So Dp =
Momentum changes more during ________
collisions because the object must first be
___________ (one change), and then it must
be _________________ (an additional change).
2. Why is Dp is ______________ in the above two
examples?
vi
Inelastic:
vf = 0
vi
wall
Elastic:
vf ≠ 0
In both cases, Dp is _________ by the _________
of the ________ acting on the _____. This force is
______________ , and this makes Dp ____________ .
C. Most collisions are ___________ “perfectly”
inelastic or elastic. The object bounces back,
but with ________________ than it had initially:
vi = 4.0 m/s
vf = -2 m/s
wall
These are called ________________ elastic
collisions. In these, the ______________ of Dp
will be somewhere ______________ the values
for inelastic and elastic collisions.
Think of how a baseball bat _________ (comes into
contact with) a ball as a function of _________.
A
Realistic
Impact:
___________
force of bat
on ball
Fnet
t
bat first
_________ ball
A
_________
Impact:
ball _________
the bat
Fnet
Area =
_______
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
Fnet
t
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.
40
kg
J=
=
=
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 that
is the direction
of ___________
Newton's Second Law:
Fnet
=
Rewrite a as Dv/t:
Fnet
=
Multiply both sides by t:
Fnet
=
But mDv = Dp, so write:
Fnet
=
Since Fnet t = ____, the last line can be written:
=
=
_____________ changes ________________
(Historical note: Newton actually first wrote his
second law using _____ , and not ____ .)
If you re-write Dp = pf - pi and substitute in,
you get:
J = Fnett =
or:
J = Fnett =
From this last equation, the _______ of impulse
J can be written two ways:
[J] = [
][ ] = [
] [
[J] = (
)( ) = (
)(
__________ 
=
]
)
 ____________
This is true because: 1 N·s = 1 (
= 1
)s
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 in
momentum of the baseball?
Given:
J=
m=
v=
Unknown:
Equation:
Answer:
Dp =
=
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
m = 0.5 kg
vf = -2 m/s
J =
Fnet t
= Dp
This can be written:
J=
And can be rearranged to:
pf =
This says, "J is what you add to ___ to get ___."
Ex.
The last example found Dp = J = -3 Ns
= ___ kgm/s
Before the
impulse:
pi = mvi
= (0.5)(4)
= 2 kgm/s
Adding the impulse of
-3 Ns Ns from the wall to pi:
pi = 2
The impulse J is ______________ (to the left) in the
previous 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 = Dp
has many applications
in sports and collisions….
1. To ______________ (make the most of) Dp, you can:
 apply a ____________ F
(hit harder)
 ____________ the impact time:
(follow through)
___t
F___
 ________
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: Dp = mfvf – mivi
=
=
Apply Ft = Dp to each car to find force on car:
A:
Ft
=
Dp
B:
Ft
=
Dp
F ____ = -30,000
F ____ = -30,000
F = ________
F = ________
•__________ time to stop
•_________ force of impact
•__________ 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.
A collection of objects that _____________ with
each other is called a ____________ of objects:
SYSTEM
_________
forces:
1
2
3
The total ______________ of a system of objects
will change if a net ____________ is applied to it:
impulse = change in momentum
=
=
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.
Any ___________ (outside)
force exerts _________
force on the system
SYSTEM
1
2
3
The “system” exerts no
force, such as__________
on the “outside”
No Fnet  no ____  no _____
 ptotal _____________________
The Law of Conservation of Linear Momentum:
The __________ momentum of an isolated
system of objects ____________________ . This
means that the total p _________ a collision (or an
explosion) equals the total p ________ the collision:
=
(In ___________)
If the “system” consists of 2 objects, this is written:
=
=
 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.
2.0
kg
1.0
kg
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:
1.0
kg
2.0
kg
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.
4.0
kg
2.0
kg
After they collide, they ________________ and move ________.
What is the velocity of the "stuck together" mass?
4.0
kg
2.0
kg
Notice that the final v does not have _______________
1 or 2, because both masses ________________________
____________________ .
Conservation of momentum says:
=
=
=
=
=
(The ______________ on _____ are dropped.)
=
=
w/units:
=
The combined mass moves to the ________ .
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:
3.6
kg
1.2
kg
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.
3.6
kg
1.2
kg
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 of
Newton'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):
v ____________
_______________ mass
3. ____________ /__________ release:
total p = ____
total p = ___________
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:
Fg
=
…where G = ____________________________
is called the _______________ gravitational constant.
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 =
Fg =
Fg =
Fg =
Which mass pulls with a greater force?
Fg =
Fg
Fg
m1
Double m1 
Triple m2 
Double both m1 and m2 
Triple m1 and double m2
Double r 
Halve r 
Triple r 
Double m1 and r 
Double m1, m2 and r 
Fg
m2
Fg
Fg
Fg
Fg
Fg
Fg
Fg
Fg
Fg
r
________________
________________
________________
________________
________________
________________
________________
________________
________________
Ex: If the Fg is between an object of mass m and
a planet, then Fg is called the _________: Fg = ___
Ex: Earth
m
Fg = Gm1m2
r2
r=
Fg =
Me
Fg =
w=
Re = ________________
Me = ________________
g=
=
Ex: Are you weightless in the space shuttle (mass = ms)?
Earth
Re = ___________
≈ ___________
ms
Fg =
GMems
=
GMems
The space shuttle orbits
at ≈ _______ = __________
above Earth's surface.
Its __________ distance
from Earth's center is
r = _____ + _____ Mm
= _______ Mm.
= ________ Re
So the ___________ (Fg)
of the shuttle and all its
contents in orbit,
compared to its weight
on land, is:
=

Ex: r is the ____________________ distance
r = __ Re
C
__ Re above
surface
r = __ Re
B
__ Re above
surface
r = __ Re
A
__ Re above
surface
r = 1 Re
Earth
If Fg at surface = 200 N,
what is the weight (Fg) at A?
At B?
At C?
Ex: A 20-N box on a table is lifted from 1 m to 2 m
above the floor. Since the height was doubled,
the new weight should be w = 20/22 = 5 N ??????
This _________
______________
because these
heights are
______________
from ________
_____________ .
5N?
20 N
2m
table
1m
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 in
all three cases above?
Ex:
A rock in
freefall:
Same rock at rest
on a table:
Fg = 1.33 N
Fg = 1.33 N
a/ What is the weight of the rock in each case?
b/ What is the net force acting on the rock in each case?
free fall: Fnet = ______
on table: Fnet = ______
c/ What is the acceleration of the rock in each case?
free fall: a = ______
on table: a = ______
d/ What is the reaction force to the weight of the rock in
each case?
Ex: Cavendish "Weighing the Earth" Experiment:
When a ____ sphere
(m2) was brought
close to the barbells,
the _______________
attraction
caused the
thin wire
to _________ .
thin wire
r
m1
From the wire's
properties, the
______________
needed to make
the wire twist
that much could
be _____________
Then Fg, r, m2 and m1 were substituted into:
Fg =
and this was solved to find ______ .
Once _____ was known, an object of
w =
known mass m and weight w were used
to find ___________ unknown mass Me using
G
m
Re 2
One last note:
In PhysRT:
g=
Solve this for:
Fg =
Not in PhysRT:
=
________
equation
acceleration
____________
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 different
locations, which is why ____________ may change
even though _________ remains the same.
A __________ is an idea used to explain how
objects can ________________ on each another
without touching ("at a _____________" forces)
even if separated by a ____________:
object 1
the 2 fields
____________
with each other
object 2
field of 1
Examples of fields:
1.__________________
2. _________________
3. _________________
All fields are _________
because they represent
____________ .
The force of ______________ is explained by saying
that 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:
direction of g: ____________________
units of g:
[g] = [
]/[
]
[g] =
And since 1 N = __________ , these units can be
written:
[g] =
=
derived
_________ = __________  fundamental
Ex: A 5.0 kg mass experiences a gravitational
force of 30.0 N when placed at the position shown
here.
5.0 kg
30 N
Determine the strength (magnitude) and direction
of the gravitational field at the point shown.
strength:
g
=
=
=
=
direction:
Same direction as_____
When Fg is due to a planet, we call it _________.
So you can write:
g=
 same as 
g=
Ex: What will a 0.10 kg stick of butter weigh
when placed in the gravitational field shown?
g = 8.2
N/kg
planet Butterway
g=
=
=
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.
>
>
_____ field
line in the
circle out here
m
>
>
_____ field
lines in the
circle in here
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 field
is very similar to
a __________ mass.
The g field lines
are ______________
to the surface.
____________ to Earth,
the lines don’t spread
out as much:
surface
Coming even closer,
________ spreading
E
surface
>
>
>
Close to the surface, the
lines appear __________
spaced and ___________ .
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's
surface. This means that an easy way to find g
would be to __________ an object and measure
its ____________________ in free fall.
The field g around Earth (or a point mass) is
proportional to ________ because _______ is .
>
E
g=(
>
>
>
g=
g=
At the surface, r = ___ , so g =
/m
)/m
~
=
But at greater r's, g will be _________ .
(Note: For any planet, use:
gp =
)
Ex. g as a function of distance from Earth's center:
g = ____ /42 = _____
g = ____ /32 = _____
4Re
3Re
>
2Re
g = ____ /22 = _____
1Re
g = ____
>
E
>
>
9.81
g
r
1Re
2Re
3Re
4Re
Compare:
Big G = ________________________ never changes!
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 __________________
____________
axis
_____________
axis
A. The 2 types of "Turning Around:"
____________: circular motion around an axis
that is ______________________
____________: circular motion around an axis
that is ______________________
B. Two types of Rotational/Revolutionary Speeds:
1. ____________ speed w ("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
Everywhere on Earth, the
__________speed is the
same:
r
w = _____________
NYS latitude
w = _____________
equator
rotation
axis
r
But _________ speed
v = __________ is
greatest at the
______________ and
zero at the _________ .
Rockets are launched from ____________
because its _________________________________
C. Linear velocity is always ___________ to the
circle in the _____________ of motion.
Ex: _____________ (CW)
uniform circular motion:
1
2
8
7
3
6
4
5
Ex: __________________
(CCW) uniform
circular motion:
2
1
8
3
7
6
4
5
NOTICE:
In _________ CW
and CCW motion:
1. The __________
(_____________ of v)
remains constant.
2. The ___________
of v is changing.
Because of this,
the object must be
__________________
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
v
v
1
v
v
3
7
v
v
5
3
7
v
5
v
Notice:
• Even though a is always ____________________,
it is always _____________________ in both cases.
• The angle between v and ac is always _______ .
E. The _______________ of ac is given by:
ac =
units of ac =
[
]2 / [ ]
=
=
=
ac
ac
v
ac
r
m
F. What causes a?
What causes ac?
The magnitude of Fc is given by:
Fc =
=
units of Fc = [
][
]2 / [ ]
=
=
=
Fc
Fc
v
Fc
r
m
G. Direction of ____ for ____ and ______ motion
1
v
v
1
v
v
3
7
v
v
5
3
7
v
5
v
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 ____________________________ .
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.
ac =
=
=
Fc =
=
=
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?