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### Physics TAKS Review

The stuff your government wants you to know as a matter of national security

Speed

- The rate at which an object moves from one point to another.
- Speed = Distance/time
- s=d/t

Questions

- 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

- 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

- 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

- 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

- 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 GravityReality Check

- 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’)

- 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)

- 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’)
- 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

- Smaller masses will change velocity easily because they have less inertia.
- Larger masses do not change their velocity easily because they have more inertia

Newton’s Laws of Motion1st Law

- 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

- 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

- 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)

- 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.

- 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

- 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)

- 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 GravityQuestions

- 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 & Energyan alternative way of viewing motion

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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.

Question 1

- 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

- 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.

- 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

Simple Machines(making work easier, not less)

- 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

- 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 Machines

- 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

- 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

- 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.

- If you put another solid object with slower atoms next to it,

- 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.

Convection

- 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

- 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

- 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.

When Waves Collide…er… I Mean Interfere.

- 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.

More Interfering Waves

- 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

- 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/Twave01Applet.html

Longitudinal Wave

- 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/Lwave01/Lwave01Applet.html

Transverse Waves Can Be Polarized

- 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

- 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.

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