Download Physics TAKS Review

Physics TAKS Review
The stuff your government wants
you to know as a matter of
national security
Speed
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The rate at which an
object moves from one
point to another.
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Speed = Distance/time
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s=d/t
Questions
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If it takes you three hours to reach Houston
which is 250 mile away, are you breaking the
speed limit? (speed limit=70mi/h)
Yep, your speed is 83 mi/h.
If you travel to Houston at a speed of 70 mi/h
how long will it take?
3.6 hours (roughly 3 hours 36 min)
Can you handle the extra 36 min?
Acceleration
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The rate at which an object changes its speed.
Speeding up or slowing down
Acceleration = change in speed / time
a=(sf-si)/t or ∆s/t
Questions
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If a Ferrari can go from 10 m/s to 40 m/s in
2.0 s what is it’s rate of acceleration.
Δs = 40m/s – 10 m/s = 30 m/s
t = 2.0 s
a = Δs/t = (30 m/s)/2.0 s = 15 m/s2
Sounds fun, yea?
Until it breaks down of course.
Questions
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If you punch the gas on a Toyota Corolla it
will accelerate at a lazy 2.5 m/s2. How many
seconds does it take to reach a speed of 20
m/s if it starts from rest.
Δs = 20m/s – 0.0 m/s = 20 m/s
a = 2.5 m/s2
a = Δs/t → t = Δs/a = (20 m/s)/(2.5 m/s2) = ?
t = 8.0 s
Acceleration of Gravity
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When you drop something it accelerates as it falls.
And it doesn’t matter what you drop (a marble, a
Toyota, some bloke named Galileo) they all
accelerate at the same rate.
This is the acceleration of gravity and it’s equal to
9.8 m/s2.
That means every second something falls it
increases its speed by 9.8 m/s.
After falling for two seconds an object would have a
speed of about 20m/s (9.8m/s2 x 2.0s)
Acceleration of Gravity
Reality Check
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However, if you drop a feather and a bowling ball off
the leaning tower of Pisa at the same time, they will
not accelerate at the same rate.
This is because the feather is significantly affected
by air resistance. It doesn’t have as much ‘oomph’
to push its way through all those air molecules on
the way down.
But if you remove the air from the city of Pisa and
drop the feather and the bowling ball. They will both
accelerate at the same rate, 9.8 m/s2.
This is not a science project I would recommend.
Mass
(‘stuff’)
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In Chemistry it’s convenient to think of mass
as the amount of ‘stuff’ there is, because
chemistry is interested in how much ‘stuff’
you get when you combine this ‘stuff’ and that
‘stuff’.
2 moles H2 + 1 mole O2 = 2 moles H20
Or
4 g H2
+ 32 g O2 = 36 g H2O
Mass
(‘inert’ia)
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In Physics it is better to think of mass in the
way that it influences motion so we
sometimes call it inertia. (key word ‘inert’)
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Inertia is how much an object does not want
to change how it is moving. Inertia is how
much it wants to be inert.
Mass
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Smaller masses will
change velocity easily
because they have less
inertia.
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Larger masses do not
change their velocity
easily because they
have more inertia
Newton’s Laws of Motion
1st Law
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All this talk of mass or inertia naturally leads us to Newton’s
three laws of motion.
1st Law – Objects in motion tend to stay in motion and objects
at rest tend to stay at rest, unless acted upon by an outside
force.
Pretty simple yea?
2nd law of motion
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The second law relates how much force is
required to change the motion of a certain
mass.
More force is required to accelerate a given
mass a lot.
And more force is required to give large
masses a certain acceleration.
The second law is an equation: F=ma
2nd Law Questions
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How much force is required to accelerate a
10 kg mass by 2.5 m/s2?
F=ma=(10kg)(2.5m/s2) = 25 N
Force is measured in Newton’s
How much would a 5 kg object accelerate
under the same force?
a=F/m=(25N)/(5kg)=5.0m/s2
Twice as much acceleration because ½ as
much inertia
3rd Law
(proof of karma)
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Every force has an equal and opposite force.
If you push on an object.
it pushes back on you.
They are called the action and the reaction.
F(A→B) = -F(A←B)
3rd Law cont.
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In the previous picture both skaters had the same mass so
they accelerated by the same amount and had the same
velocity in the end.
If the masses are different they still put the same force on
each other, but the larger mass will accelerate the least
because of Newton’s 2nd Law. It’s a heavier mass, so it
accelerates less.
3rd Law question
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A person jumps off a diving board and the
Earth puts a force of gravity downward on
them of about 750 N. Does this mean that
they also pull upward on the Earth with 750 N
as they fall?
Yep. This force causes the person to
accelerate at 9.8 m/s2 downward but the
same force on the Earth gives it negligible
acceleration upward. The Earth has a lot of
inertia!
Force of Gravity
(AKA Weight)
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A force you probably experience more than
any other force is the force of gravity.
The force of gravity is also called ‘weight’.
Weight is the amount that an object is pulled
down by gravity and it only depends on the
mass of the object and the acceleration of
gravity.
Fg=mg (g=9.8m/s2, on the surface of the
Earth)
Force of Gravity
Questions
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If your mass is 70 kg, what is your weight on
the planet Earth?
(70kg)(9.8m/s2)=690N
What is your weight on the Moon, where the
acceleration of gravity is 1.7m/s2?
(70kg)(1.7m/s2)=120N
How massive would you be on Earth if you
had a weight of 120N?
(120N)/(9.8m/s2)=12kg
Work & Energy
an alternative way of viewing motion
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One of the simplest forms of energy is kinetic energy
or energy of motion.
When an object is moving it is said to posses a
certain amount of kinetic energy that depends on
how fast it is moving.
The faster an object moves the more kinetic energy
it has.
Kinetic energy = K = ½ ms2
Kinetic Energy is generally measured in Joules.
Work
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Work is a transfer of energy into or out of an
object.
Think about when you do work. It causes
you to lose energy because the energy you
had has gone elsewhere.
In order for work to be done, a force has to
be applied to an object and the object has to
move a distance.
W=Fd (work equals force times distance)
Work and Kinetic Energy
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Work is measured in joules, just like kinetic energy
is measured in joules.
When work is done to an object it either gains or
looses its K. (speeds up or slows down)
W=ΔK
Questions
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If you push on a wall are you doing work?
Not unless the wall moves somewhere or changes
its kinetic energy (speeds up or slows down).
If you put a 40 N force on a cart to push it 3.0 m.
How much work did you do?
W = Fd = (40 N)(3.0 m) = 120 J
How much kinetic energy did you give the cart?
120 J
About those 120 j in the last
slide
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Sometimes an object isn’t moving (therefore no K) and
you push on it and move it a distance (therefore you
did work) but afterward it’s still not moving (still no K).
You might think, “I did work! I transferred energy!
Shouldn’t it’s K increase? Shouldn’t it be moving
afterward?”
Well, friction also did work, but in the opposite way.
So all of the energy you gave the object was taken
away by friction. Friction transferred that energy back
out of the object.
Friction always does work to take energy out of things.
Darn that friction!
Power
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Power is the rate at which work is done.
If you do a certain amount of work fast, you have a
lot of power.
If you do it slow you have little power.
P=W/t (power is measured in Watts)
Questions
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How much work does a 100 W lightbulb do in
1.0 min
P=100 W, t = 60 s
P = W/t → W = Pt = (100 W)(60 s) = 6.0E3 j
If you use a different light bulb that puts out
the same amount of light but only has a
power of 25 W, how much energy do you
save in that minute?
4.5E3 J because you only use 1.5E3 J.
Gravitational Potential Energy
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Sometimes an object can have energy in it but it
isn’t moving. For example: a book high up on a
shelf.
If the book falls it gets faster and faster on the way
to the ground. It’s kinetic energy increases, but
where did that energy come from?
Work was done on the book by the force of gravity.
Gravity transferred energy from a stored form called
gravitational potential energy and turned it into
kinetic energy.
Gravitational Potential Energy
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Gravitational potential
energy is written with the
variable U.
The more height (h) an
object has the more U it
has.
Larger masses can hold
more potential energy.
U=mgh (g = 9.8m/s2)
Potential energy is
measured in Joules like any
type of energy
Questions
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What has more potential energy, A 20.0 kg object
10.0 m from the ground or a 5.00 kg object 20.0 m
from the ground?
U20=mgh=(20.0kg)(9.80m/s2)(10.0m)=1960J
U5=(5.00kg)(9.80m/s2)(20.0m)=980J
20kg wins!!
How high would the 5.00kg mass need to be to have
as much potential energy as the 20.0kg mass?
U=mgh→h=U/(mg)
1960j/(5.00kg x 9.80m/s2)=40.0m
2 Useful Energies and One Not
So Useful Energy
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So far we have talked about two types of energy.
Do you remember what they are?
Gravitational Potential Energy and Kinetic Energy
There are actually several other forms of potential
energy like the energy you can store in a spring or a
battery or the energy stored in the food you eat. But
at this point you only need to know gravity’s
potential energy.
Kinetic energy only comes in one form.
There is one other form of energy. Do you know
what it is?
Thermal Energy
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At it’s heart thermal energy is just a bunch of kinetic and potential
energies at the level of molecules and atoms.
However, those molecules and atoms move around with this
energy in very random and un-useful ways.
Well, not completely un-usefull. You can use it to keep you warm
and to drive chemical reactions. So I guess it’s useful in those
ways.
It can also be turned into potential or kinetic energy by using a
heat engine like the one in your car.
But it’s tricky, and you can never get at all of it. Once energy
becomes thermal energy, it’s pretty much ‘lost’.
More on thermal energy later.
Energy is Conserved
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As an object falls it gets faster or gains kinetic
energy.
It gets that kinetic energy from the potential energy it
had.
This happens the other way to.
If a ball is moving upward into the air it slows down.
It’s potential energy is increasing because it’s kinetic
energy is decreasing.
Simply put, energy never just disappears. If you
loose it as one form you will gain it as another form.
Energy is Conserved
Question 1
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A ball has 20 j of potential energy while sitting
still (K=0 j) at the top of a hill. It starts rolling
down the hill and soon has only 5 j of
potential energy because of its change in
height. How much kinetic energy does it
have?
15 j
It lost 15 j of potential energy and gained 15 j
of kinetic energy.
Question 2
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Imagine a book sliding down an
incline with 20 j of K and 15 j of
U at point A. (K+U=35j)
Because of friction the book
slows to a stop at a lower point
(B) where there is only 5 j of
potential energy.
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How much kinetic and potential energy does it have now?
K=0j U=5j K+U=5j
Where’d the other 30j go? Energy is conserved right?
How much thermal energy was created by friction?
30 j
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Simple Machines
(making work easier, not less)
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If you have to lift a 50 kg object
upward 2.00m you will have to
do 980 j of work.
You’re lifting against the force
of gravity (AKA weight, Fg=mg)
so you have to supply as much
force as the force of gravity to
lift it. (mg=490 N)
You’re lifting it 2.0 m so work is
being done
(W=Fd=(490N)(2.0m)=980j)
490N is not small potatoes.
That’s a lot of force to have to
apply.
Especially if you haven’t been
working out.
Simple Machines
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This is where a simple machine like a lever or a
system of pulleys would be useful.
A simple machine allows you to use less force to do
a certain amount of work (W=Fd).
The trade off is that you put the smaller amount of
force over a longer distance.
So basically, you input a small force over a long
distance and the simple machine outputs a large
force over a short distance. See the next slide for
some examples.
Simple Machine Examples
Simple Machines
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Although you don’t have to exert as much force you will end up
having to do more work. It will take more of your energy to
complete the task with a simple machine.
This is because no machine can perfectly transfer your input
work to the output side of the machine. There is always some
loss of energy as thermal energy.
If you think about it, it kind of makes sense. When have you ever
gotten as much out of something as you put into it.
However, The extra energy needed isn’t that bad because the
input force is less, which makes the job easier.
Lets Talk a Little More About
Thermal Energy Because It’s Cozy
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Thermal energy has some peculiar ways of
getting around from one place to another.
It can conduct,
It can convect (←I’m not sure that’s a word),
and it can radiate.
Conduction, convection, and radiation require
different things and generally happen with
different substances.
Conduction
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Consider an object with a
bunch of atoms closely
bound together into a solid
state. Those atoms are
always moving around with
their thermal energies.
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The atoms will collide and eventually both objects will have
the same speeds for their atoms and also the same
temperature (temperature relates to the atoms’ speeds).
That’s conduction. It requires contact between the two
substances so the collisions can happen (thermal contact)
and it generally happens with solids.
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If you put another solid object
with slower atoms next to it,
Convection
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When stuff in the gas or liquid state gets warmer the
atoms move faster, spread out and the gas or liquid
becomes less dense.
If there is cooler more dense stuff around it, that
stuff will slide underneath and push the warmer
more dense stuff upward.
The warmer more dense stuff carries it’s thermal
energy with it.
This is yet another way that thermal energy can get
around. It’s what drives most weather patterns, and
it mostly happens with liquids and gasses.
Radiation
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This one’s a little weirder er… more weird.
When atoms jostle around with their thermal energy
as they do, they create an electromagnetic
disturbance in the space around them.
This disturbance is a lot like light. It can move at the
speed of light and can move through empty space.
Eventually the disturbance will reach other atoms
and cause them to jostle around too.
Therefore, the thermal energy has traveled through
empty space from one spot to another.
This is how the warmth gets to us from the Sun.
Waves
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An oscillation is any motion that repeats itself.
Essentially any object that moves back and
forth is in oscillation
If that object is attached to other objects
around it then the oscillation will travel
through the objects.
This is called a wave.
Basic Parts of a Wave
When Waves Collide…
er… I Mean Interfere.
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When two waves head toward each other
and they are both peaked or both troughed
they make one big wave.
This is called constructive intereference.
When two waves head toward each other
and one is peaked and the other is troughed.
they can cancel completely
This is called destructive interference.
Have a look at the next slide.
Interfering Waves
More Interfering Waves
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Here’s another representation
as waves spread out from two
sources
The sources could be two
stereo speakers or two kids
splashing in a swimming pool,
anything that makes waves.
The dark regions are where
peaks and troughs are coming
together, so destructive
interference.
I bet you can guess what’s
happening in the lighter
regions.
Transverse Wave
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In this wave, the medium (the letters) move
transverse (perpendicular) to the way the wave
moves.
The wave is moving this way ggggg
The letters move this way hihihihihi
An example of a transverse wave is light
If your computer supports Java (and I don’t mean
coffee) look at this:
www.surendranath.org/Applets/Waves/Twave01/Tw
ave01Applet.html
Longitudinal Wave
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In this wave, the medium (the letters) move
longitudinal (parallel) to the way the wave
moves.
The wave is moving this way ggggg
The letters move this way gfgfgfgfg
Sound is a longitudinal wave.
Look at this:
www.surendranath.org/Applets/Waves/Lwave
01/Lwave01Applet.html
Transverse Waves Can Be
Polarized
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Transverse waves can oscillate in many different
ways.
Imagine that instead of moving to the right on the
screen the wave is coming out at you.
There are many ways to be perpendicular to that.
Up and down.
Right and left.
Diagonal.
And everything in between.
Polarization
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If you can restrict all the different ways that a
transverse wave can oscillate
to just one way
that’s called polarization.
Polarizing filters can do this, like the ones on
some sunglasses. Some gems can do this
too.
Look at the next slide for some visualizations.
Polarization
OK! Now You’re Ready To Do
Some TAKS Physics.