Energy & Work

Work involves a change in a system.

   

changing an object’s position heating or cooling a building, generating a image on the TV screen, moving a speaker cone to make sound Since different tasks require different amounts of work, some things require more energy than others.

Work is…

 F  d     W  F  d  cos(  )

F = force in Newtons d = displacement in meters The angle



between F & d Joule is the unit of WORK

Work is…

   

Work- A quantity that measures the effects of a force acting over a distance.

Work is a result of motion in the direction of the force. There is no work without motion (d=0).

Distance-means distance in the direction of the force. If a force is vertical and motion is horizontal, No work is done.

Work is…

  

MAXIMUM when



= 0º MAXIMUM when Force // Displacement MINIMUM when



= 90º



MINIMUM when Force ┴ Displacement

Question #2

If you push vigorously against a brick wall, how much work do you do on the wall? a) A lot b) None c) Without numbers, how can we know?

d) No idea

Answer #2: (b) None

 There is no work done on the wall as there is no displacement of the wall .

W  F  d  cos( W  F  0  cos( W=0  )  )

What are the

units

of WORK?

 

Work is measured in Newton-meters (N•m) or foot pounds (ft•lb) A Newton-meter is called a “JOULE” (sounds like ‘jewel’)

– –

Named after James Prescott Joule (1818-1889) British physicist who established the mechanical equivalence of heat and discovered the first law of thermodynamics.

Find the work done by gravity when a 2.0 kg rock falls 1.5 m.

     

w = F (d) cos(



) What is the formula for Force (F) F = m (g) or F = m (9.8 m/s 2 ) w = (m · g) (d) cos(



) w = (2.0kg · 9.8m/s 2 )(1.5m) cos(0°) w = 29 J

Negative Work...

  

= 0° Cos(0°) = 1

  

= 180° Cos(180°) = -1

Question #3

How much work is done when a man pushes a car with an 800 N constant force over a distance of 20 m?

a) 0 J b) 40 J c) 800 J d) 16000 J e) I’m lost…

Answer #3: (d) 16000 J

How much work is done when a man pushes a car with an 800 N constant force over a distance of 20 m?

w = F (d) cos(



) w = (800 N)(20 m) cos(0°) w = 16 000 J

Question #4

How much work is done by a woman pulling a loaded dolly 100 ft with a force of 150 lb at an angle of 45°?

a) 0 ft-lb b) 7879.8 ft-lb c) 10606.6 ft-lb d) 15000 ft-lb e) I’m lost…

Answer #4: (c) 10606.6 ft-lb

How much work is done by a woman pulling a loaded dolly 100 ft with a force of 150 lb at an angle of 45°?

w = F (d) cos(  ) w = (150 lb)(100 ft) cos(45 °) w = 10606.6 ft-lb

Power & Work

   

Work

can be done at different rates. Since work involves the transfer of energy, the faster work is done, the quicker energy needs to be transferred.

Power

done. i s the measure of how fast work can be In other words, power is the

rate

at which energy is transferred.

Power is…

Power  Work Time  Force  Displaceme nt  cos(  ) Time   

W = work in Joules t = time in seconds WATT is the unit of power

Question #5

A woman exerts 100 N of force pushing a grocery cart 5 meters in 2.5 seconds. How much power did she exert?

a) 0 watt b) 40 watt c) 200 watt d) 1250 watt e) I’m lost…

Answer #5: (c) 200 watt

A woman exerts 100 N of force pushing a grocery cart 5 meters in 2.5 seconds. How much power did she exert?

Power Power Power   Work Time 100 N  5 meters 2.5sec

 200 watts 

Horsepower



Horsepower (hp) is a commonly used unit of power.



1hp = 746 watts(W)

For example…

• • • • • Let's carry a box of books up a set of stairs.

From experience, we know that running the books up the stairs takes more energy than walking the same distance (you would be more tired if you ran). But the amount of work done is the same since the books weighed the same and moved the same distance each trip. However, the work is done much faster if we run, so energy must be converted

faster

.

Therefore, more power is required.

For example #2…

   Think of a racecar versus an economy car.

They both can travel the same distance, but the race car does it much faster since it is capable of expending much more energy in much less time. This is because the more powerful car can convert energy quicker.

For example #3…

    Think of an 18-wheeler versus an economy car.

They both can travel the same distance, but the economy car does it much faster since it is capable of expending much more energy in much less time. BUT… The truck can carry more weight (exert a greater force) and is more powerful…

Electrical Power

• • • • • Electrical Power is defined the same way. Work must be done to move electrons through the electrical devices (i.e.,resistance). More resistance means more work must be done to allow the device to operate. More electrical power means more energy is being converted. This electrical energy is supplied by the source of the electrical current, like a battery or generator.

Energy



The ability to do work.



An object has energy if it is able to produce change in itself or its surroundings.

Energy lets us do work

    

“Energy is the ability to do Work” Energy is important to all living things in order to maintain life functions.

Humans use energy to modify their environment and perform work. Energy is measured by the amount of work it is able to do. The units of energy are joules (J).

Energy exists in different forms

1.

2.

3.

4.

5.

6.

Mechanical energy (moving objects and their positions) Radiant energy (light and solar energy) Chemical energy (including the food you eat and fuels we burn) Thermal or heat energy (molecules moving faster means more heat) Electrical energy (electrons moving through a wire) Nuclear energy (energy locked in the nucleus of an atom)

Energy can be transferred…

 Fossil fuels like coal and oil can be burned to heat water that boils into steam that turns a turbine to generate electricity that you use to operate a stereo.    Chemical energy  Thermal energy  Kinetic energy  Thermal energy Kinetic energy Electrical energy

Energy cannot be

created

or

destroyed

.

  In the example of riding a bicycle down a steep hill, you begin with a lot of

potential energy

at the top of the hill and gain

kinetic energy

as you coast down the hill. If you are not making the kinetic energy (movement down the hill), where does it come from? The answer is simple: your potential energy at the top is transformed into kinetic energy as you speed along.

Mechanical Energy

  Kinetic & Potential Kinetic is the energy of moving objects. KE  1 2 mv 2   Potential Energy is

stored

energy. Gravitational PE is energy due to

position

.

PE  mgh 

Mechanical Energy - II

    As you speed down a steep hill on a bicycle, you are moving and therefore have kinetic energy. But where did this energy come from? You probably already know that it came from your position at the top of the hill. At the top of the hill, you had the ability to do work (move the bicycle) purely because of where you were. You had the

potential

to perform the work of moving the bicycle.

Whenever you work with mechanical energy, you probably are dealing with both forms together in the same system.

Potential Energy

 Energy that is a result of an object’s position or condition.

 All potential energy is Stored Energy.

– Pull back on a bow string and bend the bow. The object then possesses potential energy.

Potential Energy

  

A rock on a table top has more potential energy than when it is on the ground due to its position.

This is a form of gravitational potential energy.

Fuel is an example of chemical potential energy, due to its ability to burn.

Gravitational Potential Energy

 

Depends on mass and height.

GPE = m(g)h m = mass g = acceleration due to gravity h = height -What are the Units of GPE?

SI units?

   

m = kg g = m/s 2 h = m PE = (kg · m/s 2 ) * m = N*m = J

Question #6

A man lifts a 2 kilogram book from the floor to the top of a 1.25 meter tall table. What is the change in the book’s gravitational potential energy?

a) 0 joules b) +2.50 joules c) -2.50 joules d) +24.525 joules e) -24.525 joules



Answer #6: (d) +24.525 J

A man lifts a 2 kilogram book from the floor to the top of a 1.25 meter tall table. What is the change in the book’s gravitational potential energy?

GPE  mgh GPE GPE  (2kg)    9.81

m s 2    24.525 joules (1.25m) (ADDING energy to the book)

Question #7

A mouse now pushes a book (2 kg) off the table (1.25m). What is the change in the book’s gravitational potential energy?

a) 0 joules b) +2.50 joules c) -2.50 joules d) +24.525 joules e) -24.525 joules



Answer #7: (e) -24.525 J

A man lifts a 2 kilogram book from the floor to the top of a 1.25 meter tall table. What is the change in the book’s gravitational potential energy?

GPE  mgh GPE GPE  (2kg)    9.81

m s 2    24.525 joules (-1.25m) (REMOVING energy from the book)

Kinetic Energy



Energy that appears in the form of motion.



Depends on the mass and speed of the object in motion.

Kinetic Energy

  

KE = (1/2)mv 2 m = mass v = velocity Unit for energy is Joule (J) it is defined as a Newton Meter.



SI units?

KE mass   1

mv

2 2 kilograms (

velocity

) 2  

meters

sec

ond

 2 

KE



ki

log

ram



meter

 sec

ond

2 

meter



Newton



meter



Joule

Kinetic Energy



Energy due to motion.



A brick falling at the same speed as a ping pong ball will do more damage.



KE is dependent on mass.



KE also depends on speed (v)

Kinetic Energy

Which would affect the kinetic energy of an object more, doubling its mass or its velocity?

 

doubling the mass would result in a doubling of the KE.

doubling the velocity would quadruple the KE.

Question #8

What is the KE of a 1140 kg (2513 lb) car driving at 8.95 m/s (20 mph)?

a) 0 joules b) 5101.5 joules c) 10203 joules d) 4.57x10

4 e) I’m lost… joules

 Answer #8: (d) 45658.4 J What is the KE of a 1140 kg (2513 lb) car driving at 8.95 m/s (20 mph)?

KE

 1 2

mv

2

KE

 1 2  1140

kg

  8.95

m

 2

s



KE

 4.57

x

10 4

J

Question #9

What is the KE of 11 pound rabbit running at 302.6 mph? Note: 1 ton = 907.185 kg and 1 mph = 0.447 m/s.

a) 0 joules b) 5101.5 joules c) 10203 joules d) 4.57x10

4 e) I’m lost… joules

Answer #9

What is the KE of 11 pound rabbit running at 302.6 mph? Note: 1 pound = 0.454 kg and 1 mph = 0.447 m/s.

KE KE

  1 2

mv

2 1 2  4.99

kg

  135.26

m

 2

s



KE

 4.57

x

10 4

J



Recall, Law of Conservation of Energy   

Energy can not be created nor destroyed.

Energy can change from one form to another.

The total energy in the universe is constant.

Conservation of Energy



In a roller coaster all of the energy for the entire ride comes from the conveyor belt that takes the cars up the first hill.

Examples

 A 400 kg roller coaster car sits at the top of the first hill of the Magnum XL200. If the hill is 151 ft (46 m) tall, what is the potential energy of the cart?

 What is the speed of the cart at the bottom (what do you need to ignore?)  How much KE and PE does the car have half way down the hill?

Answers

      Energy at Top = Energy at Bottom Ignoring friction – assume 100% energy conversion Energy at Top – – GPE = 400 kg x 9.8 m/s 2 x 46 m = 180 320 Joules KE = 0 Energy at Bottom – – GPE = 0 KE = 1/2 x 400 kg x v 2 180 320 = 200 v 2 Velocity at Bottom = 30 m/s = 67 mph

Answers

    Energy at Top = Energy at Bottom Energy at Halfway point?

– – 1/2 PE = 90 160 J 1/2 KE = 90 160 J Speed at Halfway point = ?

– 1/2 of 30 m/s = 15 m/s = 33.5 mph NO !!!!!!

– 1/2 mv 2 = 90 160 – Velocity = 21.2 m/s = 47.5 mph

The End

