Energy

Physics 11

Think about… 5 min

1) Why is energy important?2) Where does energy come from? Where

does it go?3) How do we capture energy?4) How does energy impact kinematics

(motion) and dynamics (forces)?5) Name as many different types of energy

as you can. Think of an example to go with each.

Quick “Lab” – 10 min Go around the room to inspect the

different toys. Decide what type(s) of energy makes

them work (move, make noise, etc) and write ALL the energy types down on the sheet provided by each toy.

Think about… 5 min

1) Why is energy important?2) Where does energy come from? Where

does it go?3) How do we capture energy?4) How does energy impact kinematics

(motion) and dynamics (forces)?5) Name as many different types of energy

as you can. Think of an example to go with each.

What is energy? (copy definition)

Energy: The measure of a system’s ability to do work.

http://www.youtube.com/watch?v=yUpiV2I_IRI

Minutes 13 onward 19:30 onward

Types of Energy (Summary) There are 2 main classifications of energy: 1) Potential Energy – The energy stored

in a body or system as a consequence of its position, shape or form. Example: An object being held up has potential

energy because of its position (gravitational potential energy).

Example: A compressed spring has potential energy (elastic potential energy to spring open).

2) Kinetic Energy – The energy of motion Example: When you walk across the classroom

you have kinetic energy.

http://www.youtube.com/watch?v=iLXDirj4JUA&feature=related

Start at 1min

Work and Energy Relationship (Copy)

There is not much difference between work and energy.

In order to do work, an object must have energy.

In order to have energy, an object must have work done on it.

Energy Formulae Kinetic Energy = Ek = KE = ½ mv2

Gravitational Potential Energy= Eg= PE= mgh

Units: Joules (J) – same as work!

NOTE: h = height of the object measured from the reference level (measured in metres). It can be d from our kinematics equations as well as long as it is vertical distance.

What is the effect of doing work on an object? (Copy)

You can give an object more energy (any type of energy) by doing more work on it.

W = ΔE = change in energy (kinetic, gravitational, elastic)

W = Ef – Ei

Work- Energy Theorem

W = ΔE

The work done is equal to the change in total energy of an object.

Example 1

A 145g tennis ball is thrown horizontally at a speed of 25m/s.

A) What is the ball’s kinetic energy? B) How much work was done to reach

this speed assuming the ball started from rest.

Answers

A) 45 J B) W = ΔKE = 45 J – 0J

** It was thrown from rest so kinetic energy initial is zero!!!

Ex 2: Work on a moving object

A 2kg object is moving at 10 m/s when a force is applied to it accelerating it to 20 m/s over a distance of 5m horizontally. What is the work done on the object?

Answer

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Worksheet – Kinetic Energy

Check your understanding A 1500. kg car is travelling at a speed of

50.0km/h when the driver applies the brakes. The car comes to a stop after travelling 15 m.

a) How much work was done by friction in stopping the car?

b) What was the magnitude of the average frictional force applied to the car?

c) If the same car were travelling at 100. km/h when the driver applied the brakes and the car experienced the same frictional force, how far would the car travel before coming to a stop?

For your own viewing

http://www.youtube.com/results?search_query=potential+and+kinetic+energy&oq=potential+and+kinetic+energy&aq=f&aqi=g4&aql=&gs_sm=e&gs_upl=50335l56318l0l56512l40l36l4l20l21l4l307l2755l1.1.8.2l12l0

Ex 3: Potential Energy and Work

What is the work done on a 12kg object to raise it from the ground to a height of 1.5m?

Potential Energy and Work

What is the work done on a 12kg object to raise it from the ground to a height of 1.5m?

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Ex 4:

A 1000kg car moves from point A to point B and then point C. The vertical distance between A and B is 10.m and between A and C is 15 m.

A) What is the PE at B and C relative to A? B) What is the ΔPE (ΔPE = PEf – PEi) when it

goes from B to C? C) Repeat a) and b) but take the reference

level at C (switch all letters).

Answers

A) B: 98100 J 98000J, C: -147150J -150 000J

B) a decrease of 245250 J 250000J C) A: 150 000J

B: 245250 J 250 000J

Difference from A to B: increase of 100000J

Worksheet – potential energy

Comprehension Check A truck pushes a car by exerting a

horizontal force of 500. N on it. A frictional force of 300. N opposes the car’s motion as it moves 4.0m.

A) Calculate the work done on the car by the truck.

B) Calculate the work done on the car by friction.

C) Calculate the work done on the car overall (net work).

Answers

A) W = Fd = 500 x 4 = 2000 N = 2.00 x 103 J

B) W = Fd = -300 x 4 = -1200. J C) Wnet = 2000 – 1200 = 800J

Comprehension Check

Calculate the work done by a horse that exerts an applied force of 100. N on a sleigh, if the harness makes an angle of 30’ with the ground and the sleigh moves 30.m across a flat, level ice surface (ie, no friction).

Answer

W = Fd cosΘ = (100)(30)cos(30)= 2.6 x 103 J

Comprehension Check A 50. kg crate is pulled 40. m along a

horizontal floor by a constant force exerted by a person (100. N) which acts at an angle of 37’. The floor is rough and exerts a force of friction of 50.N. Determine the work done by EACH FORCE acting on the crate, and the net work done on the crate.

DRAW A DIAGRAM!!!

WFg = FdcosΘ Work is 0J as the force is perpendicular to gravitational force.

WFN = 0J (same reason as above) WFapp = Fdcos Θ =(100)(40)cos37’ =

3195J S.F. 3200 J WFf = Fd = -50(40) = -2000 J -2.0 x 103J Wnet = 3200 – 2000 = 1200 J

Comprehension Check Mrs. Evans is holding a 2.4kg textbook at a height of

3.4m above the floor. a) What is the type of energy (potential or kinetic)?

How do you know? b) How much energy is there (use your equation)? c) What is the velocity of the book at this point (ie,

velocity initial)? d) If Mrs. Evans drops the book, what is the final

velocity assuming she doesn’t throw it (use your kinematics equations!)?

e) If Mrs. Evans drops the book as in d), what is the type of energy when the book hits the floor?

f) How much of this energy is there when it touches the floor?

g) Is there any time when there are both kinds of energy? If so, when? Explain.

Answers A) Potential: It is not moving, it has the potential to

move (fall). B) PE = mgh = 2.4x9.81x3.4 = 80.J C) v = 0 (at rest, not thrown) D) vf2 = vi2 + 2ad = 2(9.81)(3.4) = 66.708Vf = 8.2m/s [down]E) KE = ½ mv2 = ½ (2.4)(8.2)2 = 80.JF) 80.JG) When the object is falling, there is both PE and KE.

When it falls 1.7m, there is equal PE and KE. Before this point (higher than 1.7m) there is more PE. After this (lower than 1.7m) there is more KE.

advv if 222

Work-Energy Theorem

“The net work done on an object is equal to its change in energy"

If the object is experiencing KE: if Wnet is +ve, KE increases (moves in direction of

force or speeds up) if Wnet is -ve, KE decreases (moves in direction of

friction or slows down)

If the object is experiencing PE: if Wnet is +ve, PE increases (is lifted) if Wnet is -ve, PE decreases (is lowered)

Total Energy and Work-Energy Theorem

The total energy of an object is the kinetic energy added to the potential energy.

As an object is dropped, the kinetic energy changes to potential energy until there is 0 PE and only KE.

ET = Ee + Ek + Eg

Law of Conservation of Energy Within a closed, isolated system, energy can change form, but

the total amount of energy is constant

Closed - no objects (mass) enter or leave the system.

Isolated – a system that does not exchange either matter or energy with its surroundings. We consider in physics 11 the Earth to be a closed and isolated system.

Energy cannot be created or destroyed

Ei = Ef

So Far…

Eki + Egi = Ekf + Egf

Conservation of Mechanical Energy

Conservation of Mechanical Energy

Example 1

Solution This is an example of a situation that is much easier to

analyze using conservation of energy, since a kinematics analysis would involve calculating the accelerations using vectors and using the distances to calculate final velocities.

So what do we know? Since both balls are released from rest, they have no

initial kinetic energy. Their initial potential energy is the same, since they are

released from the same height. When they reach the bottom, neither ball has any

potential energy. Same initial energy means same final energy (due to

conservation of energy). Since all of the energy is kinetic, having the same

kinetic energy (and same mass) means that they are going the same speed.

Example 2

Solution

Example 3

http://video.mit.edu/watch/work-potential-energy-demo-lecture-11-2854/

Solution

SkatePark Assignment

The skatepark assignment shows how this works!

Check Your Understanding

2. If the car has a speed of 12.0 m/s at point A,a) What will its speed be at point C?b) What is the highest hill (above the ground) that the car couldreach on this roller coaster?

Worksheet

Check Your Understanding

1) A heavy object is dropped. If this object reaches the floor at a speed of 3.2 m/s from what height was it dropped?

Answer Etop = Ebottom KE + PE = KE + PE 0 + PE = KE + 0 mgh = ½ mv2

NOTE: The masses will cancel! gh = ½ v2

9.81h = ½ (3.2)2

h = 0.52 m

Question 2:

A heavy box slides down a frictionless incline. The incline has a slope of 30° and the length of the incline is 12m. If the box starts from rest at the top of the incline what is the speed at the bottom?

Answer

V = 11 m/s

Question 3:

A 4.0 x 104 kg roller coaster starts from rest at point A. Assuming no friction, calculate its potential energy relative to the ground, its kinetic energy and its speed at points B,C and D in the illustration above.

Answer

Conservation of Total Energy

What is Q?

Heat energy!

Example 1

A 250 g car rolls down a ramp. The car starts from a height of 32 cm, and reaches a speed of 1.7 m/s at the bottom of the ramp. Was mechanical energy conserved?

Solution

To determine if mechanical energy was conserved, we must calculate the total initial energy and the total final energy. We will use the bottom of the ramp as the reference level.

Example 2

Solution

Problem Solving Hints

Conservation of Energy Hints

Check Your Learning

Solution

Worksheet

Page 287 Questions 1, 2, 3, 4, 6, 7, 8

A 15.0 kg box slides down an incline. If the box starts from rest at the top of the incline and has a speed of 6.0m/s at the bottom, how much work was done to overcome friction?

NOTE: The incline is 5.0m high (vertically) and the incline that the box goes down is 8.0m long (hypotenuse).

Remember: W = ΔE

Try This … A skier is gliding along with a speed of

2.00m/s at the top of a ski hill. The hill is 40.0m high. The skier slides down the icy (frictionless) hill.

A) What will the skier’s speed be at a height of 25.0m?B) At what height will the skier have a speed of 10.0m/s?

HINT: Use similar triangles!

Known: vi = 2.00m/s h1 = 40.0m h2 = 25.0m

REMEMBER…

W = ΔE

That E can be potential or kinetic energy!

http://www.youtube.com/watch?v=0ASLLiuejAo

Examples Book Drop

Collision into a spring

Car coasting up a hill

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