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___________________ 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 =
= =