WorkWork& &

EnergyEnergy

Introductory Physics – Kinematics and Mechanics

Distance and displacementSpeed and VelocityAccelerationKinematic formulasForces – Contact and Non-contactNewton’s laws of motionGravity and Friction

Forces Do WorkForces Do Work

x

Here, the force is exerted on the car to get it to move from rest. In physics, we say that the force F did work on the car.

Kinetic Frictional Force Does WorkKinetic Frictional Force Does Work

x

Here, the frictional force was exerted on the sled to slow it to a stop. In physics, we say that the frictional force did work on the sled.

Work Done by a Constant Work Done by a Constant ForceForceDefinition: Work Done by a Constant Force

The work done on an object by a constant force F is

where F is the magnitude of the force, x is the magnitude of the displacement, and is the angle between the force and the displacement.The SI Unit for work is newton · meter = joule (J).

( cos )W F x cos 0 1

cos 90 0

cos180 1

Accelerating a Crate

The truck is accelerating ata rate of +1.50 m/s2. The massof the crate is 120-kg and itdoes not slip. The magnitude ofthe displacement is 65 m.

What is the total work done on the crate by all of the forces acting on it?

The angle between the displacement and the normal force is 90 degrees.

The angle between the displacement and the weight is also 90 degrees.

cos90 0W F x

The angle between the displacementand the friction force is 0 degrees.

4

cos0

180N cos0 65 m

1.2 10 J

sW f x

2120 kg 1.5m s

180N

sf ma

x x

Find the work done if the force is 45.0-N, the angle is 50.0 degrees, and the displacement is 75.0 m.

cos

45.0 N cos50.0 75.0 m

2170 J

W F x

If you do some work, you expect to get something for it.

In physics, when a net force does some work on an object, the result is a change in the kinetic energy of the object.

Kinetic EnergyKinetic Energy

Definition: Kinetic Energy

The kinetic energy of an object with mass m and speed v is

The SI Unit for Kinetic Energy is joule (J).

221 mvKE

Work – Energy TheoremWork – Energy Theorem

When a net external force does work W on an object, the kinetic energy of the object changes from its initial value of KE0 to a final value KEF, the difference between the two values is equal to the work:

202

12F2

1

0F KEKE

mvmv

W

x

Find the distance x the sled slides, if the magnitude of the kinetic frictional force is 35 N and the combined mass of the sled and rider is 70.0 kg.

Using Energy - ExampleUsing Energy - Example

Accelerating a Car

A car is waiting for a traffic light to change. How much energy do you need to accelerate the 1500-kg car from 0 to 22 m/s?

J 106.3

m/s) kg)(22 1500(5

221

202

12F2

1

mvmvKEW

J 106.3

m/s) kg)(22 1500(5

221

202

12F2

1

mvmvKEWGasoline Used?Each liter of gas has an energy equivalent of 3.3 107 J.

liter 0.01

J 103.3

liter 1J 106.3

75

V

liter 0.01

J 103.3

liter 1J 106.3

75

V

Using EnergyUsing Energy

Accelerating a Car

A certain amount of energy is used to accelerate a car from 0 m/s to a speed v. How much more energy is required to accelerate from v to 2v?

Gravitational Potential Gravitational Potential EnergyEnergy• The work done by the force of gravity on an object is:

• This is equal to the gravitational potential energy PE that an object has by virtue of its position relative to the surface of the earth.

• That position is measured by the height h of the object relative to an arbitrary zero level.

PE = mgh

0 F( cos )( )W mg h h

A dam blocks the passage of a river and generates electricity. Approximately, 57 000 kg of water fall each second through a height of 19 m. How much potential energy is converted to kinetic energy each second?

Conservation of Mechanical Conservation of Mechanical EnergyEnergy

Conservative Forces

Gravitational ForceElastic Spring ForceElectric Force

Conservative Forces

Gravitational ForceElastic Spring ForceElectric Force

Non-Conservative Forces

FrictionNormal ForcePropulsion Force of a

Rocket or a Motor

Non-Conservative Forces

FrictionNormal ForcePropulsion Force of a

Rocket or a Motor

Principle of Conservation of Mechanical Energy

The total mechanical energyE = KE + PE

of an object remains constant as the object moves, provided that the net work done by non-conservative forces is zero.

Conservation of Mechanical Conservation of Mechanical EnergyEnergy

Conservation of Mechanical Energy - Conservation of Mechanical Energy - ExampleExample

Daredevil Jumping

A motorcyclist attempts to leap a canyon by driving horizontally off a cliff.When it leaves the cliff, the cycle has a speed of 38.0 m/s.

Ignoring air resistance, find the speed with which the cycle hits the ground on the other side.

Conservation of Mechanical Energy - Conservation of Mechanical Energy - ExampleExample

J 0NC W J 0NC W

0F

0202

1F

2F2

1

EE

mghmvmghmv 0F

0202

1F

2F2

1

EE

mghmvmghmv

A quarter is dropped from rest from the fifth A quarter is dropped from rest from the fifth floor of a very tall building. The speed of the floor of a very tall building. The speed of the quarter is quarter is vv just before striking the ground. just before striking the ground. From what floor would the quarter have to be From what floor would the quarter have to be dropped from rest for the speed just before dropped from rest for the speed just before striking the ground to be approximately 2striking the ground to be approximately 2vv? ? Ignore all air resistance effects to determine Ignore all air resistance effects to determine your answer.your answer.

0F

2 21 12 2f f 0 0

212 f 0

f 02

EE

mv mgh mv mgh

mv mgh

v gh

0F

2 21 12 2f f 0 0

212 f 0

f 02

EE

mv mgh mv mgh

mv mgh

v gh

For fall from 5th story…

f 0 0 02 2 2 (4)2 2 (4 )

Comparing, this with the first case,

you can see that the height is 4 times the initial height.

v gh gh g h f 0 0 02 2 2 (4)2 2 (4 )

Comparing, this with the first case,

you can see that the height is 4 times the initial height.

v gh gh g h

For 2vf multiply both side by 2 and find the new initial height.

Principle of Conservation of Energy

Energy can neither be created nor destroyed, but can only be converted from one form to another.

Forms of Energy:Chemical – Nuclear – Radiant – Thermal – Sound – Electrical - Mechanical

Each liter of gas has an energy equivalent of 3.3 107 J.

This is equivalent to…

one kilogram of coalone Burger King value meal is 5 441 800 J.

So, 6 such meals equals one liter of gasoline.

a 100 W computer monitor on for 90 hours

Food CaloriesFood CaloriesUsually, the energy content of food is expressed in Calories. The energy stored in food is a form of chemical energy that is released as we digest it.

• 1 cup of lettuce = 10 Calories = 42 000 J• 1 cup of carrots = 45 Calories = 188 000 J• 12 ounce light beer = 95 Calories = 398 000 J• plain baked potato = 145 Calories = 607 000 J• piece of apple pie = 405 Calories = 1.7 million J• 1 cup of rice = 670 Calories = 2.8 million J• double cheeseburger = 1050 Calories = 4.4 million J

One Calorie = 1000 calories = 4186 J.

If this were all (100 %) converted into potential energy mg(hF h0), we can find the equivalent change in height.

Suppose a 65-kg hiker eats a 250 C snack. So the snack contains…

Food CaloriesFood Calories

m 1600)m/s kg)(9.80 (65

J 100.12

6

0F

mg

PEhh

0( )fPE mg h h

EfficiencyEfficiency• Not all of the energy is converted to usable work, some goes to other things such as producing an increase in body temperature.

• A more realistic estimate would be that 25% of the food calories would be used up in climbing, the rest goes to other things.

• The net result of all of this is that the climber could only climb a quarter of the way, about 400 m on that 250-Calorie snack.

Similarly, in a moving car the chemical energy of the gasoline is converted into kinetic energy, electrical energy, and heat.

PowerPower

Average Power

Average power Pave is the average rate of work W is done; and it’s obtained by dividing W by the time required to perform the work:

t

WP

time

workave

The SI unit for power is: joule/s = watt (W)

PowerPower

A dam blocks the passage of a river and generates electricity. Approximately, 57 000 kg of water fall each second through a height of 19 m. If one half of the gravitational potential energy of the water were converted to electrical energy, how much power would be generated?

P = E / t = ½ mgh / t = ½ (57 000 kg)(9.8 m/s2)(19 m) / (1 s) = 5.3 x 106 J / s = 5300 kW

kilowatt - hour

One kilowatt-hour is the amount of work or energy generated when one kilowatt of power is supplied for a time of one hour.

PowerPower

A television is rated at 150 watts. (a) What is the cost of operating the TV for 5 hours if the utility charges $0.11 per kilowatt-hour? (b) How many joules of energy are purchased?

(a)E = Pt = (150 W)(5 h) = 750 W-h = 0.75 kW-hCost = (0.75 kW-h)($0.11/kW-h) = $0.08

(b) 61000 W 1 J/s 3600 s0.75 kW-h 2.7 10 J

1 kW 1 W 1 h

PowerPowerClock radio = 10 W Hair dryer = 1200 – 1875 WCoffee maker = 900 – 1200 W Microwave oven = 750 – 1100 WClothes washer = 350 – 500 W Laptop = 50 – 100 WClothes dryer = 1800 – 5000 WDishwasher = 1200 – 2400 W (using the drying feature greatly increases energy consumption)Fans Heater (portable) = 750 – 1500

Ceiling = 65–175 W Clothes iron = 1000 - 1800 WWindow = 55–250 W Toaster = 800 – 1400 WFurnace = 750 W VCR/DVD = 17–21 / 20–25 WWhole house = 240 – 750

Refrigerator (frost-free, 16 cubic feet) = 725 WTelevisions (color) Water heater = 4500 – 5500 W

19" = 65 – 110 W27" = 113 W36" = 133 W53“ - 61" Projection = 170 WFlat screen = 120 W