# Kinetic energy of an object is the energy that it possesses due to its motion

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## Full text

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### energy

Power is measured in Watts (w)

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### Comparison

● Work is the amount of energy transformed by a force

● Energy is work stored

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### But first, some terms….

Potential energy (also referred as PE)

Potential energy is the energy that is made from stress on the object. In other words, energy from gravity.

EX: If you were to press a spring, it would have all that stress build up, and want to go back to its original form. This object would then have great potential energy

Equation used for PE: M x G x H M - mass (in kilograms) G - gravity H - height (in meters)

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### More terms...

Kinetic Energy (also referred as KE)

Kinetic energy is the energy an object has because of its motion.

EX: If you were to drop a ball off the top of the Stratosphere, it would first start with lots of potential energy. Once you drop it, that potential energy turn into Kinetic energy, because of its motion.

Equation for KE: 1/2MV^2

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### Even more terms….

Mass

Mass is an important factor for conservation of energy.

It helps find both Kinetic Energy and Potential Energy.

Without it, you can not find Kinetic or Potential energy values

It is found in both equations

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### Sam’s practice problems

A ball with a mass of 10.0kg is lifted to a height of 2.00m above the ground. The ball is then allowed to fall to the ground. Disregard any friction force while answering these questions.

A) Calculate the potential energy of the ball when raised to 2.00m above the ground. PE = mgh = 10.0kg * 9.8m/s2 * 2.00m = 196J

B) How much kinetic energy does the ball have when held 2.00m above the ground? 0J (it’s not moving)

C) How much kinetic energy does the ball have just when it reaches the ground? How do you know? 196J – Law of Conservation of Energy (since it has no PE, all energy must be KE)

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### Sam’s practice problems

A ball with a mass of 5.00kg is put at the top of a ramp shown below, which is 3.00m high. Again, disregard any frictional force. A) Calculate the potential energy the ball has at the top of the ramp.

PE = mgh = 5.00kg * 9.8m/s2 * 3.00m = 147J

B) If the ball fell from the top, straight down the right side, what would its kinetic energy be the instant it reaches the ground? How do you know?

147J – Law of Conservation of Energy (since it would have no PE)

C) How much potential energy would the ball have at the ground after falling in Ques. 3B? How do you know? 0J – no height

D) If the ball rolled down the ramp on the left above, how much potential energy would it have at the bottom of the ramp? How do you know?

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### Sam’s practice problems

A ball is raised to a height of 30.0m above the ground. What would its velocity be when it has fallen to a height of 15.0m above the ground? You must solve this as a conservation of energy problem, and can do it in one step!

KE + PE = KE’ + PE’ KE before = 0J so therefore PE = KE’ + PE’ mgh = mv2 /2 + mgh’ simplify: gh = mv2 /2 + gh’ rearrange

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### Sam’s practice problems

When is the sum potential and kinetic energy equal to zero?

Total energy is sum of kinetic energy and potential energy. T.E. = K.E. +P.E.

So it can be zero if

m=0 Or

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### Sam’s practice problems

A pendulum with a mass of 405kg reaches a maximum height of 2.4m. What is its velocity at the bottommost point in its path?

First solve for the potential energy of the pendulum at the height of 2.4m. PE = mgh

PE = (405kg)(10m/s2)(2.4m) = 9720J

This must be equal to the maximum kinetic energy of the object. KE = ½mv2

9720J = ½mv2

Plug in the mass of the object (405 kg) and solve for v. 9720J = ½(405kg)v2

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### Andrew’s practice problems

Q:A 3,000,000 kg train is zooming down a train track at 27 m/s. Suddenly, the train

conductor saw a family of cats crossing the track, so he pulled on the brakes to stop the train as fast as he could. How much heat would be generated by the brakes?

A: First, this question is about an object that was moving, so we will be using the kinetic energy formula, which is KE = ½(m)(v^2). Now knowing what formula to use, we can now plug in the numbers. The mass would be 3,000,000 kg and the velocity would be 27 m/s. Replace the m for 3,000,000 and the v for 27. Our equation is now ½

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### Andrew’s practice problems

Q: Find the kinetic energy of a 625 kg roller coaster car that is moving with a speed of 18 m/s.

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### Andrew’s practice problems

Q: A 3 kg cart is being pulled to the top of a hill that is 5 m tall, what is the potential energy of the cart at the top of the hill?

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### Andrew’s practice problems

Q: Let’s take the same scenario as the problem as before, but instead we double the mass of the cart. Will the potential energy be more or less?

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### Andrew’s practice problems

Q: A ball has a value of 5000J right before hitting a pool of water. If the ball has a mass of 100 kg, what is the speed of the ball.

A: This is a kinetic energy question, so the equation that will be used is KE = ½(m)(v^2). The solution would be set up as 5000 = ½(100)(v^2). 10,000 =

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If the potential energy starts at 50 from point A, will the potential energy be 50 at point E?

NO!! It will be different because the height changes.

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### Javier’s practice problems

If the potential energy starts at 50 from point A, and it has 25 PE at point

C,how much kinetic energy will it have at point C?

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### The Relationship Between Momentum and Impulse

The impulse-momentum theorem states that the change in momentum of an object equals the impulse applied to it.

J = Δp

If mass is constant, then…

F̅Δt = mΔv

If mass is changing, then…

F dt = m dv + v dm

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### Basic Calculation of Momentum

A 1000 kg car moving at 15 m/s. Calculate the momentum of the car?

Momentum = Mass x Velocity

P= 1000 x 15

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### Example of Momentum

A car travel down the road is slow down slightly when the break are gently tapped. Would the momentum change?

Yes, because the force of the break exert over a small amount of time, that's the resulting in small impulse and a small change in momentum.

Two football players of equal mass are traveling toward each other, one moving at 5m/s and the other moving at 8m/s. Who would move the other backwards?

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### Units

Impulse (J): Newton Second (N•sec)

Momentum (p): Kilogram meter per second

Mass (m): kilograms

Velocity (v) : meters per second

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### Collisions

Inelastic vs Elastic

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### Going Back to the Basics

Momentum= mass x velocity P = m * v

Momentum is the measurement of inertia in motion.

With units: (Kg * m)/ s = kg * m/s

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### Going Back to the Basics

Calculating kinetic energy is crucial to elastic collision problems.

Kinetic energy= ½ mass x ^(velocity)^2 KE= ½ mv^2

With units: J = ½ kg * (m/s)2

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### What is Inelastic?

Inelastic collision is when two objects collide they don't bounce back.

1. Draw a picture + choose direction

2. MVP Chart

3. Solve p = m * v

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### General Collision Example Problem

Finding the Velocity after an Inelastic Collision - One Object Initially At Rest

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### Inelastic Collision Example Problem

Finding the Velocity After an Inelastic Collision - Both Objects Initially Moving

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### Inelastic Collision Example Problem

1. Draw a picture + choose direction

2. MVP Chart

3. Solve p = m * v

4. Set pinitial = pﬁnal

M 4 kg 2 kg 6 kg

V 6 m/s -4 m/s ?

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### What is Elastic?

Elastic Collision is when two objects collide and then bounces off.

-Bounces off

mA is the mass of the object A

VAi is the initial velocity of the object A

VAf is the final velocity of the object A

mB is the mass of the object B

VBi is the initial velocity of the object B and

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### Elastic Calculations

2kg 4kg

10m/s -2m/s

2kg 4kg

v=?? v=???

M 2 4 2 4

V 10 -2 va vb

P 20 -8 2va 4vb

12 = 2va+4vb KE=(½)*2*102 (½)*4*22

100 8

108= Va2 + V

b

2

(½)*2*Va2 (½)*4*Vb2 Va2 2Vb2

Va = b-2vb 108 = (b-2vb)2+2v

b 2

0 = 4vb2-24v

b+30+2vb 2-108

0 = 6vb2-24v b-72

-12 2 -4 -6 0=6(vb2-4vb-12)

0=6(vb-6)(vb+2) vb=6m/s va2-6m/s

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### Review Questions

1. Two meatballs are speeding directly toward each other. One is a 4 kg meatball moving with a speed of 6 m/s, and the other has a mass of 2 kg and a speed of 4 m/s. If they collide inelastically, what will be the speed of the resulting 6 kg meatball immediately after the collision? Find the equations.

2. A 10 kg mass boy named Sam traveling 2 m/s meets and collides elastically with a 2 kg mass Amanda traveling 4 m/s in the opposite direction. If they collide inelastically, Find the ﬁnal velocities of both objects.

3. What is the momentum of a 5 kg cow rolling at a speed of 3 m/s?

4. A green ball having a mass of 2kg is at rest. A red ball weighing 1 kg traveling 4m/s crashed into it. The collision causes the red ball to come at rest and the green ball to go forward. What is the velocity of the green ball?

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### Coulomb’s Law

F=force(newtons) N

Q1=charge(coulombs)C

Q2=charge(coulombs)C

r=distance(meters) m

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### Coulomb’s Law

● Coulomb’s Law describes the force or magnitude of a charge or charges ● Force is negative when forces are ATTRACTING

What would the force be on an object if there is an attracting force of -25 C charge on the first pool ball and the second pool ball is feeling a force of 5 C? The

distance between them is 20 meters.

F=k*Q1*Q2/r2

-F=(9*109)(-25)(5)/202

-F=-2812500000

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### Types of Charging

● Charging by Friction: objects rub against each other resulting in a transfer of electrons.Ex: rubbing balloons on hair will transfer the electrons to the balloon making it negatively charged and the hair positively charged.

● Charging by Contact: When a charged object touches a neutral object and electrons are transferred to the neutral object. Ex: A negatively charged rod touches a neutral sphere and electrons are transferred to the sphere.

● Charging by Induction: When a charged object moves towards a neutral

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### Types of Charging

Charging by Contact: Charging by Friction:

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### Types of Charges

● Proton: positive charge (+)

● Neutron: no charge or neutral charge ● Electron: negative charge (-)

● Like charges REPEL (-) <-- --> (-)

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### How to solve electric potential energy

● Q=charge of the particle in an electric field ● V=voltage at the charge’s location

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### Question 4

Top: 1000000 Ohms Top: 0.01 Ohms Bottom: 1000 Volts Bottom: 10 Volts

Which circuit, if you had to choose one to stick a fork into, will not kill you?

High voltage does not necessarily kill you unless it is accompanied by a low

resistance. If the resistance is high enough, the current will not be high enough to kill you. The human lethal threshold is 0.3 amps. The circuit on the left is

1000V/1000000 Ohms which equates to 0.01 amps. The one on the right is

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### What is circuits?

★ Any complete path along which charge can ﬂow.

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### Parallel vs. Series Circuits

● Objects in series circuits are placed in a row, attached end to end.

● Objects in parallel circuits are placed side by side, each object connected to the same point in circuit.

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### Compare and Contrast Parallel & Series

Series Circuits Parallel Circuits What happens if one

resistor is

disconnected?

No current would be flowing in circuit. However, if one or more of resistors is removed but circuit is reconnected, then there would be current.

There would be current that still flows through them.

Current

1

2

3

total

R1

R2

R3

Voltage

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### More Compare and Contrast Parallel & Series

Series Circuits Parallel Circuits Equivalent

Resistance

series

1

2

parallel

1

2

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Voltage?

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### Find the current and voltage for each resistor.

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First ﬁnd simplify to only resistors in parallel. From there use ohm’s law and trace values back to ﬁnd the missing values.

Series

Current

6 V 3 A

Parallel

Voltage

10 V 2 A

10 V 3 A

4 V 2 A

10 V 2 A

6 V 2 A

4 V 1 A

6 V 1 A

10 V 2 A

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### Find the ﬁnal current for the diagram below.

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Simplify resistors in series Simplify r esistors in par allel Simplify resistors in series

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### Induction and Lenz’s Law

● Induction is when voltage is “created” by changing the strength of a magnetic ﬁeld around a conductor

● Lenz’s Law: the idea that the direction of the induced current made by an external change will create a magnetic ﬁeld that will try to cancel out the change between the new and old magnetic ﬁeld

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## THE END

### OR IS IT???

Because, you know, magnetic fields are loops and

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-9 -2 0 5 10

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### Temperature

Which graph contains the coolest star in this diagram?

Larger wavelength means cooler objects. This means the red

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ertzsprung

ussell

### Diagrams

What does the HR Diagram graph?

Temperature (x) and Magnitude (y)

What types of stars are on the HR Diagram?

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### Brightness

Which part of the main sequence is the brightest?

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### Mass

Which part of the main sequence has the most mass?

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Which stars have the shortest lifetime?

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uman

esources

### Diagrams

Where are the main sequence stars?

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Where do stars go to die?

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Which stars have the longest lifetime?

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Where do stars burn higher elements than hydrogen?

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Which stars burn hydrogen as fuel?

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### Lorallax I speak for the trees (Space Facts)

But the trees are speaking in vietnamese

Cut me down i break your knees

Sooo why is it so hard for us to travel the vast universe?

SPACE is made mostly of NOTHING.. Just empty space like my empty heart. Traveling from our Sun to Sirius A take

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### Redshift and Blueshift

Because of the doppler effect we can tell that stars are either moving towards or away from us. Stars moving away from us have their wavelength increased and therefore are redshifted, and stars moving toward us have their wavelength

decreased and are therefore blueshifted

1

2

Which is redshift?

Which is blueshift?Unshifted

Redshifted

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### Parallax

Parallax is the apparent displacement of an object because of a change in the observer's point of view.

We use the equation d=1/p

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## FIN

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### The Size and Scale of the Universe

Planet - orbits a star, is roughly spherical, and has no debris in its orbit

Example: Earth, Mars, Jupiter, etc.

Star - luminous spheres of plasma

Example: Sun, Betelgeuse, Sirius, etc.

Galaxy - collection of stars, planets, dust, and gas in one area due to gravity

Example: Milky Way, Andromeda, Cigar Galaxy, etc

Galaxy Group - groups of galaxies in a relative area

Example: Local Group, M81 Group, Bullet Group, etc

Supercluster - collection of galaxies, the largest things in the universe

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### Black Holes

-Black holes are formed when a star with a mass greater than our sun by ﬁfteen times burns up the rest of its fuel.

-The equation to ﬁnd the radius of a black hole is, 2(G⋅m)/c2

G: Gravitational Constant (G=6.67⋅1011) M: Mass of the object

C: Speed of light (C=3⋅108).

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### Nuclear Fusion

Fusion is the process that powers the sun and the stars. It is the reaction in which two atoms of

hydrogen combine together, or fuse, to form an atom of helium. In the process some of the mass of the hydrogen is converted into energy.The easiest

fusion reaction to make happen is combining deuterium (or “heavy hydrogen) with tritium (or “heavy-heavy hydrogen”) to make helium and a neutron.

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### There is a lot of Hydrogen

In the aftermath of a nuclear explosion of enormous magnitude, it resulted in 75% of the atoms in the universe were those of hydrogen, while 24% of the atoms in the universe were helium. The rest of the atoms were all other

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### Cosmic Microwave Background (CMB)

The Cosmic Microwave Background or CMB is the result of the beginning of the universe when it was entirely amassed of volatile plasma. The plasma has long since gone, however they did leave behind the Cosmic

Microwave Background

which is invisible light that is in uniform strength

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