Energy

Energy

Physics 11

Page 217

Multilab… Sources of Energy http://www.youtube.com/watch?

v=iLXDirj4JUA&feature=related

Try giving an example of…

As many different types of energy and an example that goes with each

What is energy?

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

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

Types of Energy 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 (potential 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=0ASLLiuejAo

Work and Energy Relationship

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 Ek = KE = ½ mv2

Eg = PE = mgh

Units: Joules (J)

NOTE: h = height of the object measured from the reference level (measured in metres).

What is the effect of doing work on an object?

You can give an object more kinetic energy by doing more work on it.

W = ΔKE

W = KEf – Kei

W = ½ mvf2 - ½ mvi

2

Example 1

A 145g tennis ball is thrown 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

Ex 2: Work on an moving object

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

Answers

JJJW

W

mvmvW if

300100400

)10(22

1)20(2

2

12

1

2

1

22

22

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?

JW

W

dgmW

dFW

176

)5.1)(81.9)(12(

mghE

WE

g

g

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

Assignment on Energy – Kinetic and Potential

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 = PE + KE

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 enter or leave the system.

Isolated - no net external force is exerted on it.

Energy cannot be created or destroyed

E1 = E2

KE1 + PE1 = KE2 + PE2

Examples Book Drop

Collision into a spring

Car coasting up a hill

00 221

fi

ffii

mvmgh

PEEKPEKE

h v

2212

21 00 fi

efKfeiKi

kxmv

EEEE

ffi

GfKfGiKi

mghmvmv

EEEE

2

212

21 0

vx

hvv

Example 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

Example 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 = 10.8m/s

Example 3:

A 4.0 x 104 kg roller coaster starts from rest at point A. Neglecting 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

Page 287 Questions 1, 2, 3, 4, 6, 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!