Name______________________



Types of Energy

Energy is the ability to do __work ____.

KINETIC ENERGY – Energy of Motion __________________________________

Units - joules

Examples – boy running, car moving, lady walking

POTENTIAL ENERGY – Stored Energy

____Energy of Location/position___ _____________

Units - joules

Examples – rock on a cliff, stretched rubber band, dog up on a tree

(TME) Total Mechanical Energy- the sum total of the __kinetic____ energy and the

potential___ energy.

Example: KE = 200J KE =1000J KE = _5000_J

PE = 300 J PE = _3000_J PE = 5000 J

TME = ___500___J TME =4000J TME = 10,000J

How do we calculate the amount of Kinetic Energy?

Kinetic Energy(in joules) – energy of motion - KE = 1/2 mv2

Although mass and velocity both have great effects on kinetic energy, it is velocity more significantly determines kinetic energy.

QUESTION: What is the kinetic energy of a 45 kg object moving at 13 m/sec?

1. First we identify the information we are given in the problem:

|[p|mass = ___45 kg_________ |

|ic| |

|] | |

|[p|velocity = ____13 m/s_________ |

|ic| |

|] | |

2. Next, we place this information into the kinetic energy formula:

|[p|KE = 1/2 mv2 |

|ic| |

|] | |

|[p|KE = 1/2 ( 45 kg)( 13 m/sec)2 |

|ic|1/2 (45 )( 169) |

|] | |

| |3802.5_ J |

3. Solving the equation gives a kinetic energy value of _____3802.5_ J

Sample Problem #2 The kinetic energy of a boat is calculated at 52,000 J.  If the boat has a mass of 39,000 kg, with what velocity is it moving?

1. We identify the information given in the problem:

|[p|KE = 52,000 J. |

|ic| |

|] | |

|[p|mass = 39,000 kg |

|ic| |

|] | |

2. We now place the information into the kinetic energy formula:

|[p|KE = 1/2 mv2 |

|ic| |

|] | |

|[p|52,000 = 1/2 (39,000 kg)(v)2 |

|ic| |

|] | |

|[p|1.33 = v2 |

|ic|v = 1.22 m/s |

|] | |

3. Solving the equation gives a velocity value of _____1.22 ___ m/sec

Potential energy, on the other hand, is energy of position, not of motion. It is STORED energy!

Formula #1 – Potential Energy = (mass) (gravity)(height)

Formula #2 – Potential Energy = weight x height

• The amount of potential energy possessed by an object is proportional to how far it was displaced from its original position.

• If the displacement occurs vertically, raising an object off of the ground let's say, we term this Gravitational Potential Energy. 

Sample Problem

A 37 N object is lifted to a height of 3 meters.  What is the potential energy of this object?

1. Identify the information given to you in the problem:

|[p|weight = 37 N |

|ic| |

|] | |

|[p|height = 3 meters |

|ic| |

|] | |

2. Insert the information into the gravitational potential energy formula:

|[p|GPE = weight x height |

|ic| |

|] | |

|[p|GPE = (37 N)(3m)= |

|ic| |

|] | |

3. Solving the problem gives a potential energy value of J.

111 joules

Practice Problems:

Potential Energy = (mass)·(gravity)·(height) PE = mgh

or PE = (weight)(height)

Kinetic Energy = (1/2)(mass)(velocity)2 KE = (.5)(m)(v)2

(joules) (kg) (m/s)

1. A 6 kg rock is thrown with a velocity of 10 m/sec.  What is the kinetic energy of the rock?

KE = (.5)(m)(v)2

KE = (.5)(6)(10)2

KE = (.5)(6)(100) = 300 joules

2. A ball has 475 J of energy while in motion.  If the ball is moving at 30 m/sec, what is the mass of the ball?

KE = (.5)(m)(v)2

475 J = (.5)(m)( 30)2

475 J = (.5)(m)( 900)

475 J = (m)( 450) m = 1.06 kg

3. A 1.8 kg cat climbs upwards 12 meters to sit on the roof of a house.  How much potential energy does it possess while it sits enjoying the sunshine?

PE = mgh

PE = (1.8 kg)(10)(12m) PE = 216 joules

4. A boulder has 5000 J of potential energy while sitting on top of a cliff.  If the cliff is 250 m above the ground, what is the weight of the boulder?

PE = (weight)(height)

5000J = (weight)(250m) weight = 20N

5. The boulder in problem 4 falls off the cliff, but lands on a ledge 50 feet below.  What is potential energy of the boulder now?

PE = (weight)(height)

PE = ( 20 N)(200m) 4000joules

Potential and Kinetic Energy

Potential Energy = (mass)·(gravity)·(height) PE = mgh

(joules) (kg) (m/s2) (m) or PE = (weight)(height)

Kinetic Energy = (1/2)(mass)(velocity)2 KE = (.5)(m)(v)2

(joules) (kg) (m/s)

Problems:

1. A 70 kg rock sits on a hill 20m high. Find its potential energy.

PE = mgh PE = (70 kg)(10)(20m) PE= 14,000 j

2. The potential energy of a brick resting on the edge of a building is 65,000joules. If the brick has a mass of 15 kg, how high is the building.

PE = mgh

65,000j = (15 kg)(10) (h)

65,000j = 150(h)

h = 433.3m

3. Find the kinetic energy of a cat which has a mass of 3kg and runs at a speed of 4m/s.

KE = (.5)(m)(v)2 KE = (.5)(3 kg)(4)2 = 24 joules

(1/2)(m)(v)2

4. The kinetic energy of a roller-coaster car is 23,000 joules. If is is moving at a speed of 25 m/s, find the mass of the roller-coaster.

KE = (.5)(m)(v)2

23,000 = (.5)(m)(25)2

23,000 = (.5)(m)(625)

23,000 = 312.5m

m= 73.6 kg

KE = (.5)(m)(v)2 PE = mgh PE = (weight)(height)

Kinetic Energy and Potential Energy Calculations

Directions: Show all of your work

1. What is the formula used to calculate kinetic energy? What is the formula used to calculate gravitational potential energy?

2. What is the kinetic energy of a car that has a mass of 2,400 kg and is moving at 20 m/s? How does this kinetic energy compare to the kinetic energy of a car with a kinetic energy of 240,000 J?

3. What is the kinetic energy of a 4,000 kg elephant that is running at 2 m/s?

and another elephant with the same mass running at 4 m/s How do the two kinetic energies compare with one another?

4. What is the kinetic energy of a 2,000 kg bus that is moving at 30 m/s?

5. What is the kinetic energy of a 3,000 kg bus that is moving at 20 m/s?

6. What is the gravitational potential energy of a cat that weighs 40 N standing on a table that is 0.8 m above the ground?

7. What is the gravitational potential energy of a diver who weighs 500 N standing on a platform that is 10 m off the ground?

8. What is the gravitational potential energy of a diver who weighs 600 N standing on a platform that is 8 m off the ground?

Energy Conversions

K.E. --> P.E. --> K.E. --> P.E.

Law of Conservation of Energy:

Energy cannot be created or destroyed. It can be converted from one form to another.

_______________________________________________________

A ball is thrown up with a speed of 20 m/s. It reaches the top, stops for a split second (speed is 0 m/s) and continues its parabolic path on the way down. When the ball reaches the bottom, it hits the ground with the same speed that it was thrown up at.

At the bottom

There is no height. Therefore, the potential energy is at a _______________________.

(maximum or minimum)

The ball is moving the fastest, therefore, the kinetic energy is at a _________________.

(maximum or minimum)

At the top

The ball stopped moving; therefore, the kinetic energy is at a ___________________.

(maximum or minimum)

The ball is at maximum height; therefore the potential energy is at a ____________________.

(maximum or minimum)

Energy Conversions in a Roller Coaster

Energy of Motion is __kinetic___ energy.

Energy of Position(location) is __potential____ energy.

Once the object is dropped, the potential energy begins to decrease due to reduced height, but we also now see an increase in kinetic energy because the velocity is also increasing.

1. Energy changes when an object falls: Practice Problems:

TME = 64 J

TME = ___64 __ J

TME = __64 ___ J

TME = ___64 __ J

2. The Law of Conservation of Energy state that energy cannot be ______________________________________________________________________________

But remember, even though the KE and the PE of a falling object changes, the sum of the KE and PE (TME) will always remain ______ __________.

3. Since, KE = (.5)(m)(v)2,

- if the velocity of an object is doubled, its KE will _______________.

- if the velocity of an object is tripled, its KE will _______________.

4. Look at the picture of the pendulum below. The string is pulled to position #1 and let go. It swings back and forth from position #1 to position #2 to position #3 and back to position #2 and back to position #1 and so on and so on.

Remember:

a) Where the height is maximum, the PE is maximum.

b) Where the height is minimum, the PE is minimum.

c) Where the PE is maximum, the KE is __minimum___.

d) Where the PE is minimum, the KE is __maximum____.

• The potential energy is maximum at __1,3__.

• The KE is at its maximum at:_____2____.

• The PE at 1 is equal to the PE at:___3_____.

• The PE at 1 is equal to the KE at:____2_____.

5. Given that KE = (.5)(m)(v)2, An object moving at a speed of

4 m/s possesses 160 J of K.E.. What is the objects mass?

6. As an object falls its KE _________ and its PE ________.

As the object falls the amount of PE that is lost is equal

to the amount of ______________________gained.

7. A ball is sitting on top of a hill. It has 800 joules of potential energy up there.

a. how much kinetic energy does it have at the bottom?

b. how much KE and how much PE does it have half way down?

c. If it has a mass of 5 kg, find the speed at the bottom (the moment it

hits the floor).

Remember: KE = (.5)(m)(v)2

Section II - Work and Power

Work = Force x distance

(joules) = (N) (m)

If you push or pull an object a certain distance and you did work!

Power = Work/Time

(Watts) (J)/(s)

Power – the rate at which _work_ is done.

Write the units for each:

a) Power _watts_ Work _joules_ KE__ joules _ PE __ joules _

b) Work is being done when a force causes an object to

_____move___ in the direction of the force.

c. There are two ways to increase your power: Do more work in

the___less/same_time or do the same work in ___less___time.

d. Power is the amount of work done per unit of __time_.

Power is the time rate of doing _work_

Read the following statements and decide if work was done.

|A teacher applies a force to a wall and becomes exhausted. |No, didn’t move the wall. |

|A mother lifts her baby. |Yes, she exerts a force through a distance |

|A mother pushes her baby in a stroller |Yes, she exerts a force through a distance |

|A rocket accelerates through space. |Yes, it exerts a force through a distance |

|An apple sits on a table. |No |

Work = Force x distance

(joules) = (N) (m)

Power = Work/Time

(Watts) (J)/(s)

1. Amy uses 20N of force to push a lawn mower 10 meters. How much work does she do?

Work = force x distance w = (20)(10) = 200 joules

2. Joe balances a stationary coin on the tip of his finger 0.20m from the top of the table. How much work is Joe doing?

No work, since no movement

3. Frank does 2400J of work in climbing a set of stairs. If he does the work in 6 seconds, what is his power output?

Power = Work/time

Power = 2400J/ 6 sec = 400 watts

4. How much work is required to pull a sled if you use 60J of work in 5 seconds?

Power = Work/time

Power = 60J/ 5 sec = 12 watts

5. How much work does an elephant do while moving a circus wagon 20meters with a pulling force of 200N?

Work = force x distance w = (200N)(10m) = 2000 joules

6. If it takes 5 seconds for you to do 1000J of work, what is your power output?

Power = Work/time

Power = 1000J/ 5 sec = 200 watts

7. A 900N mountain climber scales a 100m cliff. How much work is done by the mountain climber?

Work = force x distance w = (900)(100) = 90000 joules

8. A small motor does 4000J of work in 20 seconds. What is the power of the motor in watts?

Power = Work/time

Power = 4000/ 20 sec = 20 watts

9. A woman runs a kilometer using a force of 210N and a power output of 500W. How long in minutes does it take this woman to complete 1000 meters?

Work = force x distance W=210x1000=210000J

Power = Work/time 210000/t = 500W

|Free-Body |Forces Doing Work |Amount of Work Done |

|Diagram |on the Object |by Each Force |

|A 10-N forces is applied to push a block across a friction free surface for a |10N right does the work|W = Fxd |

|displacement of 5.0 m to the right. |since object moves | |

|[pic] |right | |

|A 10-N frictional force slows a moving block to a stop after a displacement of 5.0 m|skip |skip |

|to the right. | | |

|[pic] | | |

|A 10-N force is applied to push a block across a frictional surface at constant |No net force |W = Fxd |

|speed for a displacement of 5.0 m to the right. | |W = 0 N |

|[pic] | |(no work) |

|A 2-kg object is sliding at constant speed across a friction free surface for a |No net force |W = Fxd |

|displacement of 5 m to the right. | |W = 0 N |

|[pic] | |(no work) |

|A 2-kg object is pulled upward at constant speed by a 20-N force for a vertical |No net force |W = Fxd |

|displacement of 5 m. | |W = 0 N |

|[pic] | |(no work) |

Work and Power

What is work?

(W = F x d) Work is done when force moves an object a certain distance.

(No work is done if there is a force with no distance moved)

The amount of work done depends on:

1) the amount of force

2) the distance that the object is moved

Units of Work:

Formula: W = F x d

***The force must act over a distance in the direction of an object’s motion!***

Practice Problems:

1. A student’s backpack weighs 30N. She lifts it from the floor to a shelf 1.5m high. How much work was done?

W = F x d W = (30N)(1.5m) = 45 joules

2. A carpenter pushes a 45 kg beam 1.2 m across a flat surface. How much work was done?

3. Bobby carries a 5 kg box up a two-story staircase. If each story is 5 m high, how much work did Bobby do?

4. A man pushes against a car stuck in a snow bank while his date sits nervously behind the steering wheel trying not to make the tires spin. However, the car does not move. How much work did he do on the car?

5. While performing a chin-up, Carlos raises himself 0.8m. How much work does Carlos, who weighs 600N, accomplish doing a chin-up?

What is power?

The speed (rate) at which ___work_______is done.

Power tells us:

Work and time

Units of power:

watts

Formula:

Power = work / time P = W/t

Practice Problems:

1. How much power is required to do 300J of work in 30 seconds?

Power = work / time P = W/t

P = 300 J / 30 seconds = 10 watts

2.. A skater lifts his 450N partner 1.0m in 3.0s. How much power is required for this?

W = F x d W = (450N)(1.0m) = 450 joules

P = W/t P = 450 J / 3.0s = 150 watts

3. A mother lifts her 200N suitcase 1.2m in 2 minutes. How much power is required for this?

4. An elevator with a mass of 2550 kg rises 30m in 1 minute. How much power is required?

5. An elevator with a mass of 2,550,000 g rises 3000 cm in 1 minute. How much power is required?

6. Joe needs a pump that can provide 35000 Nm every hour. What power is required for this pump?

-----------------------

Mechanical Energy

[pic][pic]

KE PE

Radiant Energy

(Solar)

(electromagnetic spectrum)

N

(joules) (kg) (m/s2) (m)

kg

At the bottom.

No height

Velocity = 20 m/s

At the bottom.

No height

Velocity = 20 m/s

At the top,

Maximum height

Velocity = 0 m/s

Which is

0 joules?

PE or KE

Which is

0 joules?

PE or KE

Total mechanical energy (PE + KE)

64 j

0 j

44j

3

1

2

Include units.

Object is moved in the same direction as the force!!!!

Force – 20N

Distance –10 meters

Work – ?

Power -

Force –

Distance –

Work –

Power -

time –6 seconds

Work – 2400J

Power - ?

time –5 seconds

Work – 60J

Power - ?

Force – 200N

Distance –20 meters

Work –

Power -

Work –1000J

time - 5 seconds

Power -

Force – 900N

Distance –100m

Work – ?

Work – 4000J

time - 20 seconds

Power -?

Force – 210N

Distance –1000m

Work –

time -

Power -500W

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