phy115 – sault college – bazlurslide 1 energy, work and power

PHY115 – Sault College – Bazlur slide 1

Energy, Work and

Power


Energy and Matter Perhaps the concept most central to all of science

is energy.

Energy and matter makes up the universe!

• Matter: Anything that has mass and occupies space.

– matter is substance – can see, smell and feel

• Energy: Anything that can change the condition of matter; the ability to do work.

– energy is the mover of substance – cannot see, smell or feel most forms of energy


Energy• Surprisingly, the idea of energy was unknown to

Isaac Newton (1643 -1727), and its existence was still being debated in the 1850s.

• Although energy is familiar to us, it is difficult to define, because it is not only a “thing” but both a thing and a process—as if it were both a noun and a verb.


Energy• Persons, places, and things have energy, but we

usually observe energy only when it is being transferred or being transformed.

• It comes to us in the form of electromagnetic waves from the sun and we feel it as thermal energy; it is captured by plants and binds molecules of matter together; it is in the food we eat.

• Even matter itself is condensed bottled-up energy, as set forth in Einstein's famous formula, E = mc2.

• We'll begin our study of energy by considering a related concept: work.


Work


WorkWe saw that changes in an object's motion depend on

both force and how long the force acts. – “How long” means time. – We call the quantity “force × time” impulse.

But “how long” need not always mean time. – It can mean distance also. – When we consider the quantity force × distance, we are

talking about an entirely different quantity - work.


WorkWhen we lift a load against Earth's gravity, work is done. The heavier the load or the higher we lift the load, the

more work is done. Two things enter the picture whenever work is done:

(1) application of a force, and (2) the movement of something by that force.

For the simplest case, where the force is constant and the motion takes place in a straight line in the direction of the force, we define the work done on an object by an applied force as the product of the force and the distance through which the object is moved.

In shorter form:


Work


Work

A rocket blasting off from the launch pad.


WorkPam pulls a wagon in which her little brother Ken is riding.

She exerts a force of 10 N [E] to pull the wagon through a displacement of 5 m [E], as shown.

Calculate the work done by Pam on the wagon.


WorkWork must be done by one object on another object.

Work was done by Pam, and work was done on the wagon.


SI Unit of WorkFrom the equation of work, we can determine the units

of work.

W = F d= 10 N x 5 m= 50 N m = 50 joule= 50 J

In honor of English physicist James P. Joule the unit of work (N m) given the name joule (J).

One joule of work is done when a force of 1 newton is exerted over a distance of 1 meter, as in lifting an apple over your head.


English Unit of WorkFrom the equation of work, we can determine the

units of work.

W = F d= 20 lb x 10 ft= 200 ft lb


English Unit of WorkJim pushes a 350 lb cart a distance of 30 ft by

exerting a force of 40 lb. How much work does Jim do?


English Unit of WorkJim pushes a 350 lb cart a distance of 30 ft by

exerting a force of 40 lb. How much work does Jim do?

W = F d= 40 lb x 30 ft= 1200 ft lb


Work, force in the direction of motionTo determine the work when the force is not applied in

the direction of the motion, use the component of the force along the motion to calculate the amount of work.

Consider a block being pulled by a rope with a force F that makes an angle with the level ground.

The horizontal component Fx is the force in the direction of motion.

Using trigonometric relations, Fx = F cos


Work

Vertical:No motion!

Horizontal:Direction ofmotion!

• Only that component of force directed along the path of the moving object is involved in calculating work done.


Work, force in the direction of motionJim pulls a sled along level ground a distance of

10 m by exerting a force of 100 N at an angle of 30 with the ground.

How much work does he do?

W = Fx d W = F cos 30 d

= 100 N x 0.866 x 10 m= 866 N m= 866 J


Work in the direction of motionW = Fx d

W = F cos d

= Fd cos


Example of WorkPam pulls a sled along level ground a distance of

10 m by exerting a force of 100 N at an angle of 30 with the ground.

How much work does she do?

W = F d= 40 lb x 30 ft= 1200 ft lb


Work ?In science, to do work you must apply a force

that causes an object to move a distance.

W = Fd

+ 4 NFriction: - 4 N


Work ?


Work ? Space capsule drifting in space with constant velocity.


Power


PowerThe definition of work says nothing about how long it

takes to do the work.

The same amount of work is done when carrying a load up a flight of stairs, whether we walk up or run up.

So why are we more tired after running upstairs in a few seconds than after walking upstairs in a few minutes?

To understand this difference, we need to talk about a measure of how fast the work is done - power.

Power is equal to the amount of work done per time it takes to do it:


Power• Work tells us nothing about time!

• Power is the rate at which work is done or energy is transformed.

• Power equals the amount of work done per unit time.

Power = work done

time interval

P = W t


PowerAn engine of great power can do work rapidly.

A liter (L) of fuel can do a certain amount of work, but the power produced when we burn it can be any amount, depending on how fast it is burned.

– It can operate a lawn mower for a half-hour or – a jet engine at 3600 times the power for a half-

second.


PowerThe unit of power is the joule per second (J/s),

also known as the watt

(in honor of Scottish inventor James Watt 1736-1819, the developer of the steam engine).

One watt (W) of power is expended when 1 joule of work is done in 1 second.

The engines are rated in units of horsepower and electricity in kilowatts, but either may be used.

In the metric system of units, automobiles are rated in kilowatts.

One horsepower is the same as three-fourths of a kilowatt, so an engine rated at 133 horsepower is a 100-kW engine.


History of the term "horsepower"The term "horsepower" was invented by James Watt to help

market his improved steam engine.

Watt determined that a horse could turn a mill wheel 144 times in an hour (or 2.4 times a minute). The wheel was 12 feet in radius, thus in a minute the horse traveled 2.4 × 2π × 12 feet.

Watt judged that the horse could pull with a force of 180 pounds

So:

This was rounded to an even 33,000 ft·lbf/min[6].


Conversion of horsepower to wattsThe historical value of 33,000 ft·lbf/min may be converted to the

SI unit of watts by using the following conversion of units factors:

1 ft = 0.3048m

1 lbf = g × 1 lbm

= 9.80665 m/s2 × 1 lbm × 0.45359237 kg/lbm

= 4.44822 kg·m/s2

= 4.44822 N

1 minute = 60 seconds

And the watt is defined as

1 hp = 33,000 ft·lbf/min = 746 W = 0.75 kW = ¾ kW


Energy


EnergyWork is done in lifting the heavy ram of a pile driver,

and, as a result, the ram acquires the property of being able to do work on a piling when it falls.

In this case, something has been acquired.

This “something” given to the object enables the object to do work.


EnergyWhen work is done by an archer in drawing a bow, the

bent bow has the ability to do work on the arrow.

When work is done to wind a spring mechanism, the spring acquires the ability to do work on various gears to run a clock, ring a bell, or sound an alarm.

In each case, something has been acquired.

This “something” that enables an object to do work is energy.


EnergyEnergy is measured in joules.

It appears in many forms:

– Mechanical,

– Electrical,

– Thermal,

– Chemical,

– Atomic,

– Nuclear,

– Sound.


Mechanical EnergyMechanical energy - the form of energy

– due to the relative position of interacting bodies (potential energy) or,

– due to their motion (kinetic energy).

Mechanical energy may be in the form of either – potential energy or – kinetic energy, or – both.


Potential EnergyAn object may store energy because of its

position relative to some other object.

This energy is called potential energy (PE), because in the stored state it has the potential to do work.

For example, a stretched or compressed spring has the potential for doing work. When a bow is drawn, energy is stored in the bow.

A stretched rubber band has potential energy because of its position, for if it is part of a slingshot, it is capable of doing work.


Potential Energy• Potential Energy (PE) is the energy an object

has stored because of its position relative to another object.


Potential EnergyThe chemical energy in fuels is also potential

energy, due to the relative positions of atoms in molecules.

Such energy characterizes fossil fuels, electric batteries, and the food we eat.

This energy is available when atoms are rearranged, that is, when a chemical change takes place.

Any substance that can do work through chemical action possesses potential energy.


Potential EnergyWork is required to elevate objects against Earth's gravity.

The potential energy of a body due to elevated positions is called gravitational potential energy.

Water in an elevated reservoir and the ram of a pile driver have gravitational potential energy.

The amount of gravitational potential energy possessed by an elevated object is equal to the work done against gravity in lifting it.

The work done equals the force required to move it upward times the vertical distance it is moved.

W = Fd

PEgravitational = Fd


Potential Energy Once upward motion begins, the upward force to keep it moving

at constant speed equals the weight mg of the object. (There is a bit of extra work needed to get the object moving, but that is balanced by “negative work” done when it stops at the top.)

So the work done in lifting an object of weight mg through a height h is given by the product mgh.

W = Fd

PEgravitational = weight x height

= mg hNote that the height h is the distance above some reference level,

such as the ground or the floor of a building.

The potential energy mgh is relative to that reference level and depends only on mg and the height h.


Potential EnergyThe potential energy of the ball at the top of the ledge depends on

the height but does not depend on the path taken to get it there.

Gravitational Potential Energy = weight x height

PE = mgh


Potential EnergyThe potential energy of the 10-N ball is the same (30 J)

in all three cases because the work done in elevating it 3 m is the same whether it is

(a) lifted with 10 N of force vertically,

(b) pushed with 6 N of force up the 5-m incline, or

(c) lifted with 10 N up each 1-m stair.

(d) No work is done in moving it horizontally (neglecting friction).


Potential EnergyPotential energy, gravitational or otherwise, has

significance only when it changes - when it does work or transforms to energy of some other form.

For example, if the ball falls from its elevated position and does 20 joules of work when it lands, then it has lost 20 joules of potential energy.

How much total potential energy the ball had when it was elevated is relative to some reference level, and isn't important.

What's important is the amount of potential energy that is converted to some other form.

Only changes in potential energy are meaningful.

One of the kinds of energy into which potential energy can change is energy of motion, or kinetic energy.


Potential Energy to Kinetic EnergyThe potential energy of the elevated ram is

converted to kinetic energy when released.


Kinetic EnergyIf we push on an object, we can set it in motion.

More specifically, if we do work on an object, we can change the energy of motion of that object.

If an object is moving, then by virtue of that motion it is capable of doing work.

We call energy of motion kinetic energy (KE).


Kinetic Energy• The energy of motion is called kinetic energy

(KE).

• The kinetic energy of an object depends on:– Mass &– Speed

KE = ½ mass x speed2

KE = ½ mv2


Kinetic EnergyJust before hitting the pile, the KE of the ram is:

2

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1)0(

2

1)(

2

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2

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a

2mv

vvvvvvwheret

v

t

vm

vvvvvvwheretvt

vm

dt

vm

dm

Fd

W

PEKE

ffifavg

ffifavg


KE depends on the reference frameThe amount of kinetic energy, like the amount of speed,

depends on the reference frame in which it's measured.

For example, when you ride in a fast-moving car you have zero kinetic energy relative to the car, but considerable kinetic energy relative to the ground.


KE v2

Notice that speed is squared in the definition of KE, so if the speed of an object is doubled, its kinetic energy is quadrupled (22 = 4).

This means a car going 100 km/h has 4 times as much kinetic energy as when going 50 km/h.

Speed is squared for kinetic energy (this squaring of speed also means that KE can only be zero or positive, never negative).


Kinetic Energy

What is the kinetic energy of a 148 g baseball moving at 30 m/s?

KE = ½ mv2

KE = ½ 0.148 kg x (30 m/s)2

KE = 0.074 kg x 900 m2/s2

KE = 66.6 kg x m2/s2 (1kg m/s2 = 1 N)

KE = 66.6 kg x m/s2 x m

KE = 66.6 N x m

KE = 66.6 J


ForcesContact Forces

– Frictional Force – Tensional Force – Normal Force – Air Resistance Force – Applied Force – Spring Force

Action-at-a-Distance Forces – Gravitational Force – Electrical Force – Magnetic Force

http://www.physicsclassroom.com/


Internal versus External forcesCategorize forces based upon whether or not their

presence is capable of changing an object's total mechanical energy.

– We will learn that there are certain types of forces, which when present and when involved in doing work on objects will change the total mechanical energy of the object.

– And there are other types of forces which can never change the total mechanical energy of an object, but rather can only transform the energy of an object from potential energy to kinetic energy (or vice versa).

The two categories of forces are – internal versus – external forces.


Internal forcesInternal forces include:

– gravitational forces, – magnetic forces, – electrical forces, and – spring forces.

• When work is done upon an object by an internal force, the total mechanical energy (KE + PE) of that object remains constant.

• The object's energy changes form. • The total mechanical energy is said to be "conserved."

TMEi = TMEf

KEi + PEi = KEf + PEf


Conservation of Mechanical EnergyInternal forces does not cause the

change of Mechanical Energy.

The total mechanical energy is said to be "conserved."

TMEi = TMEf

KEi + PEi = KEf + PEf


External forceWhenever work is done upon an object by an

external force, there will be a change in the total mechanical energy of the object.

– In the from of KE or PE.


Work-Energy TheoremThe quantitative relationship between work and

mechanical energy is expressed by the following equation:

TMEi + Wext = TMEf

The equation states that the initial amount of total mechanical energy (TMEi) plus the work done by external forces (Wext) is equal to the final amount of total mechanical energy (TMEf).

KEi + PEi + Wext = KEf + PEf

The above equation is often said to be an expression of the work-energy theorem.


Work done by External forcesThe work done by external forces can be a

positive or a negative work term. – A positive work increases the final TME.

• Pushing a car

– A negative work decreases the final TME.• Braking a car


Work equals change in kinetic energyWhen a car speeds up, its gain in kinetic energy

comes from the work done on it.

Or when a moving car slows, work is done to reduce its kinetic energy.

We can say Work equals change in kinetic energy.

W = KE

This is the work-energy theorem.Fd = ½ mv2

Fd = ½ mv2 if the initial speed is zero


Net Work doneThe work in this equation is the net work - that is, the work

based on the net force.

If, for instance, you push on an object and friction also acts on the object, the change of kinetic energy is equal to the work done by the net force, which is your push minus friction.

In this case, only part of the total work that you do is changing the object's kinetic energy.

The rest is going into heat.

If the force of friction is equal and opposite to your push, the net force on the object is zero and no net work is done.

There is zero change in the object's kinetic energy.


Work equals change in kinetic energyThe work-energy theorem applies as well to

decreasing speed.

The more kinetic energy something has, the more work is required to stop it.

When you slam on the brakes of a car, causing it to skid, the road does work on the car.

This work is the friction force multiplied by the distance over which the friction force acts.


Stopping Distance Velocity2

Interestingly, the friction force between a skidding tire and the road is the same whether the car moves slowly or quickly.

Friction doesn't depend on speed.

The variable is the distance needed to stop.

Car1 versus Car2

v 2v

KE 4KE

Fd 4Fd

d 4d

If friction force is the same, the distance required to stop the double speed car is 4 times more.



While braking, the work is related to the kinetic energy change.

The stopping distance is proportional to the velocity squared.

When, mass and friction is constant



This means that a car moving twice as fast as another, with four times the kinetic energy of the other, takes four times as much work to stop, and therefore takes four times as much distance to stop.

Accident investigators are well aware that an automobile going 100 kilometers per hour will skid four times as far in a panic stop as it would going 50 kilometers per hour.


Work can change PE, Heat, electricalThe work-energy theorem applies to more than changes

in kinetic energy.

Work can change – the potential energy of a mechanical device, – the heat energy in a thermal system, or – the electrical energy in an electrical device.

Work is not a form of energy, but a way of transferring energy from one place to another or one form to another.


Every form of energy can be transformed into every other form

Average kinetic energy of random molecular motion is related to temperature;

potential energies of electric charges account for voltage; and

kinetic and potential energies of vibrating air define sound intensity.

Even light energy originates from the motion of electrons within atoms.


Work-Energy Theorem1. When you are driving at 90 km/h, how much

more distance do you need to stop than if you were driving at 30 km/h?


Kinetic Energy = ½ mv2 The distance needed to stop?

Car1 versus Car2

30km/h 90km/h

v 3v

KE 9KE

Fd 9Fd

d 9d

If friction force is the same, the distance required to stop the triple speed car is 9 times more.

Square of the speed ratio (1:3).


Work-Energy Theorem2. Can an object have energy?


Work-Energy TheoremYes, but in a relative sense. For example, an elevated object may possess PE

relative to the ground below, but none relative to a point at the same elevation.

Similarly, the KE that an object has is with respect to a frame of reference, usually taken to be the Earth's surface.


Work-Energy Theorem3. Can an object have work?


Work-Energy TheoremNo, unlike momentum or energy, work is not

something that an object has. Work is something that an object does to some

other object. An object can do work only if it has energy.

Force, Impulse and Work – are results of interactions, not what an object have.


Conservation of EnergyThe law of conservation of energy states:

“Energy can not be created or destroyed; it may be transformed from one form to another, but the total amount of energy never changes.”


Conservation of Energy


Conservation of mechanical energyThe principle of conservation of mechanical

energy states that, if a system is subject only to conservative forces (e.g. only to a gravitational force), its mechanical energy remains constant.

For instance, if an object with constant mass is in free fall, the total energy of position 1 will equal that of position 2.


Conservative vs. Nonconservative• Forces can be classified as conservative or

nonconservative. – Conservative forces include gravity,

electromagnetic force, and spring force. Causes conservation of mechanical energy.PE to KE or, vice versa

– Nonconservative forces include friction and drag. However, for any sufficiently detailed description, all forces are conservative.

– Transforms Mechanical energy to some other form. E.g., Heat from Friction.


Summary• Work (W = Fd)

• Power (P = W/t)

• Potential energy

• Gravitational potential energy

(PEgravitational = mgh)

• Kinetic energy (KE = ½ mv2)

• Work-Energy theorem (W = KE) or, (Fd = 1/2mv2)

• The Law of Conservation of Energy


Energy - Calorie http://en.wikipedia.org/wiki/Calorie

A calorie is a unit of measurement for energy.

The unit's name is French and derives from the Latin calor (heat).

In most fields, unit of measurement for energy is joule, the SI unit of energy.

Calorie is commonly used for the amount of energy obtained from food.


EnergyThe small calorie or gram calorie approximates the

energy needed to increase the temperature of 1 g of water by 1 °C. This is about 4.185 J.

The large calorie or kilogram calorie approximates the energy needed to increase the temperature of 1 kg of water by 1 °C. This is about 4.185 kJ, and exactly 1000 small calories.

• In scientific contexts, the name "calorie" refers strictly to the gram calorie, and this unit has the symbol cal.

• SI prefixes are used with this name and symbol, so that the kilogram calorie is known as the "kilocalorie" and has the symbol kcal.


Energy1 thermochemical calorie = 4.184 J

1 watt-hour = 3600 J (exact)

1 kWh = 1 kilowatt-hour = 3.6×106 J = 3.6 MJ

The energy released by 1 kg of gasoline is rated in mega joules (MJ).

The energy released by 1 kg of pasta is 3600 kcal = 3.6 MJ


caloriesAs a rough guideline,

recommended daily energy intake values for

– young adults are: 2500 kcal/d (10 MJ/d, 120 W) for men and

– 2000 kcal/d (8 MJ/d, 100 W) for women.

– Children and older people require less energy,

– physically active people require more energy.

phy115 – sault college – bazlurslide 1 energy, work and power

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