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Work and Energy Work: The word looks the same, it spells the same but has different meaning in physics from the way it is normally used in the everyday language

Work and Energy

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Work and Energy. Work: The word looks the same, it spells the same but has different meaning in physics from the way it is normally used in the everyday language. F. F. F. F. d. d. θ. θ. d. - PowerPoint PPT Presentation

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Page 1: Work and Energy

Work and Energy

Work: The word looks the same, it spells the same but has different meaning in physics from the way it is normally used in the everyday language

Page 2: Work and Energy

Definition of work W done by a constant force F exerted on an object through distance d

work = force along distance × the distance moved

Only the component that acts in the same direction as the motion is doing work on the box.

Vertical component is just trying to lift the object up.

d

Fθ Fd

Fθ Fd

dW = F d = Fd cosθwork = force × distance moved × cos of the angle between them

Page 3: Work and Energy

The SI unit for work is the newton–metre and is called the joule named after the 19th Century physicist James Prescott Joule.

1 J (Joule) = 1N x 1 m

Work is a scalar (add like ordinary numbers)

Units

Page 4: Work and Energy

According to the physics definition, you are NOT doing work if you are just holding the weight above your head

(no distance moved)

Work - like studying very hard, trying to lift up the car and get completely exausted, holding weights above head for half an hour is

no work worth mentioning in physics.

you are doing work only while you are lifting the weight above your head

(force in the direction of distance moved)

A force is applied. Question: Is the work done by that force?

Page 5: Work and Energy

Who’s doing the work around here?

NO WORK WORK

If I carry a box across the room I do not do work on it because the force is not in the direction of the motion (cos 900 = 0)

Page 6: Work and Energy

θ = 00 00< θ <900 θ = 900 900< θ <1800 θ = 1800

cos θ = 1 cos θ = + cos θ = 0 cos θ = – cos θ = –1

Work done by a force F is zero if:

F

motion

normal force

F

d d

F

force is exerted but no motion is involved: no distance moved, no work

force is perpendicular to the direction of motion (cos 900 = 0)

gravitational force

tension in the string

Page 7: Work and Energy

when the force and direction of motion are generally in the same directions (the force helps the motion – can increase kinetic energy by increasing speed)

when the force and direction of motion are generally in the opposite directions(force opposes the motion – decreases kinetic energy by decreasing speed)

00< θ < 900 → cos θ = + cos 00 = 1

Work done by force F is:

W = Fd

W = - Fd

(the work done by friction force is always negative)

positive

negative

900< θ < 1800 → cos θ = – cos 1800 = –1

Page 8: Work and Energy

Mike is cutting the grass using a human-powered lawn mower. He pushes the mower with a force of 45 N directed at an angle of 41° below the horizontal direction. Calculate the work that Mike does on the mower in pushing it 9.1 m across the yard.

F410

dF = 45 N

d = 9.1 m

θ = 410

W = Fd cos θ = 310 J

Page 9: Work and Energy

Forward force is 200 N. Friction force is 200 N. The distance moved is 200 km. Find a. the work done by forward force F on the car.b. the work done by friction force Ffr on the car.c. the net work done on the car.

F = 200 N

Ffr = 200 N

d = 2x105 m

a. WF = Fd cos 00 = 4x107 J

b. Wfr = Ffr d cos 1800 = - 4x107 J

c. the net work done on the car means the work done by net force on the car.

It can be found as:

W = WF + Wfr = 0

or

W = Fnet d cos θ = 0 (Fnet = 0)

Page 10: Work and Energy

Work done by a varying force - graphically

W = Fd cos θ applies only when the force is constant.

Force can vary in magnitude or direction during the action.

Examples: 1) rocket moving away from the Earth – force of gravity decreases 2.) varying force of the golf club on a golf ball

Work done is determined graphically.

Page 11: Work and Energy

The lady from the first slide is pulling the car for 2 m with force of 160 N at the angle of 60o , then she gets tired and lowers her arms behind her at an angle of 45o pulling it now with 170 N for next 2 m. Finally seeing the end of the journey she pulls it horizontally with the force of 40 N for 1 m.

Work done by her on the car is:

W = (160 N)(cos 60o)(2m) +(170 N)(cos 45o)(2m) + (40 N)(cos 0o)(1m)

W = 80x2 + 120x2 + 40x1 = pink area + green area + blue area = 440 J

http://www.kcvs.ca/map/java/applets/workEnergy/applethelp/lesson/lesson.html#1

In general: The area under a Force - distance graph equals

the work done by that force

Page 12: Work and Energy

Energy, E

In physics energy and work are very closed linked; in some senses they are the same thing. If an object has energy it can do a work. On the other hand the work done on an object is converted into energy.

work done = change in energy

W = ∆ E

Page 13: Work and Energy

Gravitational potential energy, PE = mg h

Imagine a mass m lifted a vertical distance h following two different paths.

1. straight up: – minimum force needed is F1 = mg. – the work done against gravitational force is: W = F1 h cos 00

W = mg h

2. along a ramp a distance d (no friction) – minimum force needed is F2 = mg sinθ. – the work done against gravitational force is: W = F2 d cos 00 = mg sinθ d

W = mg h

hF1d

mg

F2

θ

the work W = mg h is stored as potential energy of the object.

PE = mg hIt depends on VERTICAL distance from initial position not on the path taken.

Page 14: Work and Energy

A ramp can reduce the force – can make life easier

1. W = F h = mg h

2. W = F d = mg sinθ h/sinθ = mg h

θ

hhd

W = F h or F d (along the ramp)

Page 15: Work and Energy

Kinetic energy, KE = ½ m v2

A moving object possesses the capacity to do work. A hammer by virtue of its motion can be used to do work in driving a nail into a piece of wood.How much work a moving object is capable of doing? Let’s find out.

Imagine an object of mass m accelerated from rest by a resultant force, F. After traveling a distance d the mass has velocity v.

The work done is: W = Fd cos 00 = Fd = mad

From v2 = u2 + 2ad → ad = v2/2 and W = ½ mv2

The work done (Fd) by the force F in moving the object adistance d is now expressed in terms of the properties of the body and its motion. The quantity ½ mv2 is called the kinetic energy (KE) of the body and is the energy that a body possesses by virtue of its motion. The kinetic energy of a body essentially tells us how much work the body is capable of doing.

Page 16: Work and Energy

Summary:

Work done on an object by applied force against gravitational force (when the net force is zero, so there is no acceleration) is stored as gravitational potential energy.

PE depends on the reference frame in which it is measured, so we keep in mind some reference level, like desk, lower reservoir of water, ground,…. PE = mg ∆h

If the net force acting on a body is not zero, then: The work done by net force on a body is equal (results) to the change in the kinetic energy of the body:

W = ∆KE = KEf – KEi

Page 17: Work and Energy

Units

W = Fd (W) = (1N)(1m) = 1 kg m2 s-2 = 1 J

PE = mgh (PE) = (1kg)(1 m s-2 )(1m) = 1 kg m2 s-2 = 1 J

Even in units we see that the work and energy are equivalent.

KE = ½ mv2 (KE) = (1kg)(1m/s)2 = 1 kg m2 s-2 = 1 J

Page 18: Work and Energy

(1) A father pushes his child on a sled on level ice, a distance 5 m from rest, giving a final speed of 2 m/s. If the mass of the child and sled is 30 kg, how much work did he do?

W = ∆ KE = ½ m v2 – 0 = ½ (30 kg)(2)2 = 60 J other way: W = Fd cosθ = Fd F = ma

F = 12 N W = 60 J

(2) What is the average force he exerted on the child?

W = Fd = 60 J, and d = 5 m, so F = 60/5 = 12 N

2 22v -ua = = 0.4 m/s

2d

Page 19: Work and Energy

(3)A 1000-kg car going at 45 km/h. When the driver slams on the brakes, the road does work on the car through a backward-directed friction force.

How much work must this friction force do in order to stop the car?

W = ∆ KE = 0 – ½ m u2 = – ½ (1000 kg) (45 x1000 m/3600 s)2

W = – 78125 J = – 78 kJ (the – sign just means the work leads to a decrease in KE)

d

u

Ffr

(work done by friction force)

v = 0

Page 20: Work and Energy

(4) Instead of slamming on the brakes the work required to stop the car is provided by a tree!!! What average force is required to stop a 1000-kg car going at 45 km/h if the

car collapses one foot (0.3 m) upon impact?

corresponds to 29 tons hitting you OUCH

Do you see why the cars should not be rigid. Smaller collapse distance, greater force, greater acceleration. For half the distance force would double!!!! OUCH, OUCH

The net force acting on the car is F

W = – 78125 J

W = – F d

F = 260 x 103 N

a = (v2 - u2 )/2d = - 520 m/s2 HUGE!!!!

- W 78125F = = d 0.3

Page 21: Work and Energy

The principle of energy conservation !!!!!!

An object of mass 4.0 kg slides from rest without friction down an inclined plane. The plane makes an angle of 30° with the horizontal and the object starts from a vertical height of 0.5 m. Determine the speed of the object when it reaches the bottom of the plane.

we shall see in nuclear physics that this should actually be the principle of mass-energy conservation

To demonstrate the so-called principle of energy conservation we will solve a dynamics problem in two different ways, one using Newton’s laws and the kinematics equations and

the other using the principle of energy conservation.

Page 22: Work and Energy

point A: h = 0.5 m, KE = 0 (u = 0) point B: h = 0 , object has gained KE

h=0

N

300B

A

h=0.5mv=?

u=0

Method 1: Newton’s law Method 2: Energy conservationAs the object slides down the plane its PE becomes transformed into KE. If we assume that no energy is ‘lost’ we can write

F mgsinθa = = = gsinθm m

v2 = u2 + 2ad = 2gsinθ

hd = sinθ

d

hsinθ

v = 2gh v = 3.2 m/s

PEA = KEB

mgh = ½ mv2

v = 2gh v = 3.2 m/s

Note that the mass of the object does not come into the question, nor does the distance travelled down the plane, only vertical height.

Page 23: Work and Energy

The second solution involves making the assumption that potential energy is transformed into kinetic energy and that no energy is converted into other forms of energy (heat, sound,…).

This is ‘Law of conservation of energy’, this means the energy is conserved. Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

When using the energy principle we are only concerned with the initial and final conditions and not with what happens in between.

No time included in energy principle.

Very powerful tool of enormous importance.

Clearly in this example it is much quicker to use the energy principle. This is often the case with many problems and in fact with some problems the solution can only be achieved using energy considerations.

Page 24: Work and Energy

If it is transformed into thermal energy, we say it is dissipated. The object can’t keep that energy. It is shared with environment.

and now problems and examples. Some of them would be very, very hard to solve using kinematic equations and Newton’s laws.

Page 25: Work and Energy

Dropping down from a pole. As he dives, PE becomes KE. Total energy is always constant, equal to initial energy.

In presence of air, some energy gets transformed to heat (which is random motion of the air molecules). Total energy at any height would be PE + KE + heat, so at a given height, the KE would be less than in vacuum.

What happens when he hits the ground?

Just before he hits ground, he has large KE (large speed). This gets transformed into heat energy of his hands and the ground on impact, sound energy, and energy associated with deformation .

If accounted for air resistance, then how would the numbers change?

Page 26: Work and Energy

Amusement park physics

the roller coaster is an excellent example of the conversion of energy from one form into another

work must first be done in lifting the cars to the top of the first hill.

the work is stored as gravitational potential energy

you are then on your way!

PE is being transformed into KE and vice versa

Page 27: Work and Energy

Up and down the track

PE

PE + KE

PE

If friction is negligible the ball will getup to the same height on the right side.

Page 28: Work and Energy

Three balls are thrown from the top of the cliff along paths A, B, and C with the same initial speed (air resistance is negligible). Which ball strikes the ground below with the greatest speed?

a. A b. B c. C d. All strike with the same speed

h

The initial PE + KE of each ball is: mgh + ½ mu2.This amount of energy becomes KE before impact ½ mv2.

mgh + ½ mu2 = ½ mv2 m cancels

The speed of impact for each ball is the same: It depends ONLY on HEIGHT and initial SPEED, not mass, not path !!!!!

2v = 2gh + u

Page 29: Work and Energy

A child of mass m is released from rest at the top of a water slide, at height h = 8.5 m above the bottom of the slide. Assuming that the slide is frictionless because of the water on it, find the child’s speed at the bottom of the slide.

m cancels on both sides

Do you think you could use kinematics equations and Newton’s laws? Try it. Good luck !

v = 2gh = 13 m/s

mgh = ½ mv2

a baby, an elephant and you would reach the bottom at the same speed !!!!!

And, by the way, it is the same speed as you were to fall straight down from the same height.

v2 = u2 + 2gh = 2gh

Page 30: Work and Energy

Work is a way of transferring energy from one form to another, but itself is not a form of energy. All types of energies and work have the same units. Everything can be transformed into each other.

When work is done on an object, energy is transferred to that object.

Example: A spring at the bottom of a slide is compressed by an external force. A parent releases the spring when a child sits on it. EPE is transferred to the child by spring force doing the work which is transformed into KE of the child. On the way up, KE is being transformed into PE.

This energy is what enables that child to then do work. How? First that PE has to be transformed back into KE – child slides down a slide – KE of the child can do work on the waiting parent – it can knock him over.

Parent does the work on the ground.

Page 31: Work and Energy

A car (toy car – no engine) is at the top of a hill on a frictionless track. What must the car’s speed be at the top of the first hill if it can just make it to the top of the second hill?

m cancels out ; v2 = 0

40m

v1mgh1 + ½ mv1

2 = mgh2 + ½ mv22

gh1 + ½ v12 = gh2

v1 = 22 m/s

v2 = 0PE1 + KE1 = PE2 + KE2

20m v12 = 2g( h2 – h1)

Page 32: Work and Energy

A simple pendulum consists of a 2.0 kg mass attached to a string. It is released from rest at A as shown. Its speed at the lowest point B is:

2 2A A B B

1 1mv + mgh = mv + mgh2 2

2B Av = 2gh = 2×9.80m/s ×1.85m = 6m/s

1.85 m

A

B

PEA + KEA = PEB + KEB

2A B

10 + gh = mv + 02

Page 33: Work and Energy

● Conservation of energy law AGAIN – WITH FRICTION INCLUDED

All previous examples were neglecting friction force, air resistance … What happens if the friction force acts?

Can we still use conservation of energy principle?

YES, WE CAN

Page 34: Work and Energy

● Example: An object of mass 4.0 kg slides 1.0 m down an inclined plane starting from rest. Determine the speed of the object when it reaches the bottom of the plane if

a. friction is neglected b. constant friction force of 16 N acts on the object as it slides down.

all PE was transformed into KE Friction converts part of KE of the object into heat energy. This energy equals to the work done by the friction. We say that the frictional force has dissipated energy.

initial energy = final energy initial energy – Ffr d = final energy

Wfr = – Ffr d decreases KE of the object

PEA = KEB PEA – Ffr d = KEB mgh = ½ mv2 mgh – Ffr d = ½ mv2

20 – 16 = 2.5 v2 v = 1.4 m/s

v = 2gh = 3.2 m/s

Page 35: Work and Energy

Types of energy and energy transformations

We usually classify energy as the following forms: 1 Kinetic energy 2 Gravitational potential energy 3 Elastic potential energy 4 Thermal or heat energy 5 Light energy 6 Sound energy 7 Chemical energy 8 Electrical energy 9 Magnetic energy 10 Nuclear energy

There are energy changes happening all around us all of the time. Here are a few examples to think about.

Page 36: Work and Energy

In any given transformation, some of the energy is almost inevitably changed to heat.

• A bouncing ball The gravitational potential energy is changed to kinetic energy and back again with each bounce losing energy due to work done by air friction and nonelastic contact with the ground . Eventually the ball comes to rest and all the energy has become low grade heat.

• An aeroplane taking off As fuel is burned in the engines, chemical energy is converted to heat, light and sound. The plane accelerates down the runway and its kinetic energy increases. There will be heat energy due to friction between the tyres and the runway. As the plane takes off and climbs into the sky, its gravitational potential energy increases.

Page 37: Work and Energy

• A laptop computer The electrical energy form the mains or chemtcal energy from the battery is changed to light on the screen and sound through the speakers. There is kinetic energy in the fan, magnetic energy in the motors, and plenty of heat is generated.

• A human body Most of the chemical energy from our food is changed to heat to keep us alive. Some is changed to kinetic energy as we move, or gravitational potential energy if we climb stairs. There is also elastic potential energy in our muscles, sound energy when we talk and electrical energy in our nerves and brain.

• A nuclear power station Nuclear energy from the uranium fuel changes to thermal energy that is used to boil water. The kinetic energy of the steam molecules drives turbines, and as the kinetic energy of the turbines increases, it interacts with magnetic energy to give electrical energy.

Page 38: Work and Energy

Power

Power is the work done in unit time or energy converted in unit time

measures how fast work is done or how quickly energy is converted. Power is a scalar quantity.

Units: ◘1J(joule)1 W(Watt) =

1s

A 100 W light bulb converts electrical energy to heat and light at the rate of 100 J every second.

Sometimes you’ll see power given in kW or even MW.

orW EP = P = t t

Page 39: Work and Energy

Calculate the power of a worker in a supermarket who stacks shelves 1.5 m high with cartons of orange juice, each of mass 6.0 kg, at the rate of 30 cartons per minute.

0W Fdcos0 (30×60N)×1.5mP = = = t t 60s P = 45 W

There is another way to calculate power

0W Fdcos0 dP = = = F t t t P = Fv

Power is equal to force times velocity, providing that both force and velocity are constant and in the same direction.

Constant velocity with a force applied ??????

That’s because we are interested in one force only. Net force is obviously zero. Like power of the engine of the car.

Page 40: Work and Energy

Efficiency

Efficiency is the ratio of how much work, energy or power we get out of a system compared to how much is put in.

useful outputefficiency = total input

No units◘

Efficiency can be expressed as percentage by multiplying by 100%.◘

out out out

in in in

W E Peff = = = W E P

No real machine or sysem can ever be 100% efficient, because there will always be some energy changed to heat due to friction, air resistance or other causes.

Page 41: Work and Energy

A car engine has an efficiency of 20 % and produces an average of 25 kJ of useful work per second.How much energy is converted into heat per second.

out

in

Eeff = E

in

25000J0.2 = E

Ein = 125000 J

heat = 125 kJ – 25 kJ = 100 kJ