Work Energy Power

Force• Force is a push or pull. Force is measured in newtons (N)

Definition of Work• Work is a force applied over a distance in the same direction

as the motion. W (work) = f (force) x d (distance) W = f x d Work is measured in Nm. 1 Nm = 1 J (joule) The units of work are joules (J). James Prescott Joule determined the relationship between mechanical work and energy forms.

Objects moving steadily in a straight line have balanced forces on them.

The force needed to steadily lift an object.• The force needed to steadily lift an object is equal to its

weight (but in the opposite direction).

The Work in lifting an object• The work needed to lift an object is equal to the lifting

force times the distance the lifting force acts (W = f x d).

The work needed to horizontally move an object.• If an object is moved through air, the force acting in the

direction of motion is essentially zero so the work done is also zero (W = 0 x distance = 0).

Work to slide an object• The work to slide an object is equal to the effort force

(equals friction) time the distance the object slides.

Work to go up a stairs• A

Energy Definition• Energy is the ability to do work. The amount of energy

present depends on the amount of work it can do. Energy is measured in joules (J). The farther back a bow string is pulled, the more potential energy (stored energy) it has.

Potential and Kinetic Energy• Kinetic energy is the energy moving objects have because

of their motion (the work they can do because of their motion).

• Potential energy is the energy stored in an object (the work that can be done when the stored energy is released).

Gravity Potential Energy• The gravitational potential energy an object has is equal to

the force times the distance that the object can exert its force over (PE = mgh)

Potential Energy of a SkierThe potential energy that a skier has is mgh, the work that gravity can do on the skier.

Kinetic Energy: The Energy of Motion• The kinetic energy of an object (KE) = ½ mv2 . This formula

is derived as follows:KE is work, W or KE = fd but f = ma

So, KE = mad but a = v2 2 – v1

2/2d from v2 2 = v1

2 + 2ad

So, KE = m(v2 2 – v1

2/2d)d which simplifies to

KE = m(v2 2 – v1

2/2) which simplifies to KE = ½m(v2 2 – v1

2)

If v1 = 0, then the KE of a moving object, KE = ½mv2 where v is the v2 or speed of the object as compared to rest (V1 = 0)

Energy is Conserved but Changes FormsEnergy can change from one form to another. Eventually all forms of energy change into heat which is lost to space. 4.18 J of any energy (work) will become 1 cal of heat (the amount of heat that raises the temperature of 1 g of water 1 celsius degree). Conservation of energy means that energy can not be created or destroyed.

Conversion of Potential to Kinetic EnergyWhen an object is dropped, the potential energy the object has at the top of its drop (mgh) is converted to kinetic energy (energy of motion) as it falls. Neglecting air resistance, the sum of the PE and KE throughout the fall remains constant.

Sample ProblemDetermine the velocity of a 5.00 kg object which was dropped from a height of 25.0 m, when this object is 5.00 m from the ground. Neglect air resistance.

The potential energy of the object (mgh) at the top of its drop is 1225 J. At 5.00 m from the ground, the PEobject is 245 J (mgh). The object has lost 1225 J - 245 J = 980 J of energy. This potential energy lost has been converted into kinetic energy. From KE = ½ mv2, v2 = 2KE/m, so that v = √(2KE/m).V = √(2*980 kgm2/s2/5.00 kg) = 19.8 m/s

25.0 m

5.00 m

PE = 1225 JKE = 0 J

Mass = 5.00 kg

PE = 245 JKE = 980 J

Sample ProblemDetermine the PE, KE, ME (Mechanical Energy = sum of KE and PE) and v, given the skateboarder’s initial v and mass. At position 3, the boarder is at his maximum height.

Sample Problem Answers

At 1 the boarder has 0 J PE, 1920 J KE and ME = 1920J

At 2 the boarder has 588 J PE, 1332 J KE, 1920 J ME, v = 6.7 m/s (√(2KE/m).

At 3 (maximum height), the boarder has 1920 J PE, 0 J KE, 1920 J ME, v= 0 m/s, and height = 3.27 m

Energy Conversion and Conservation in a PendulumWhen a pendulum bob is brought from rest position (M) to position E1, it is at a height h above its rest position which gives it a potential energy of mgh. When released, the pendulum bob converts all its potential energy at E1 into kinetic energy at M and then back into potential energy at E2.

Energy Conversion and Conservation in a PendulumEnergy just changes forms as a pendulum swings. If there were no friction or wind resistance, a pendulum would swing to exactly the same height on both sides.

Demonstrating Conservation of EnergyWhen a ball is given potential energy by lifting it to a side, it transforms this potential energy into kinetic as it falls and then passes this energy through the balls to the other side where the kinetic energy moves the ball upward until it has converted all kinetic into potential energy.

Requirement for Energy Conservation?To conserve energy (PE = mgh) with balls 1&2, what must

happen?

Another Demonstration of Energy Conservation• The bob is lifted to the height of the second horizontal

stripe. Its swing is interrupted midway by a protruding peg. Note that the bob continues to rise to the level of the second horizontal stripe.

The Energy of a Roller CoasterA roller coaster continuously demonstrated conversion of

potential to kinetic to potential energy as it rises and falls.

Harnessing Water’s Potential EnergyA waterwheel converts water’s potential energy (mgh) into

kinetic energy in the moving wheel which can do work.

The Law of Conservation of EnergyEnergy cannot be created or destroyed. It just changes

forms.

The Law of Conservation of EnergyUltimately all energy on earth becomes heat which is radiated

out into space. The sun provides a constant input of energy which provides the basis for motion on earth and for life on earth.

PowerPower is defined as the rate of doing work. The power

formula is P = W/t or P = fd/t. Power equals work done divided by the time it takes to do this work. If a device does the same work as another device but does it quicker (in less time), then it is more powerful.

If a conditioned person lifts a 300N weight 1 m in 2 seconds, the work rate or power is 150J/s. If another person lifts 300 N 1m in 3 seconds, the work rate or power is 100 J/s.

1 m lift

300 NWeight

The Power Unit: The WattThe base power unit is called a watt. One watt is the power

when 1 J of work is done per 1 second. 1 W = 1J/s

The power formula can be rearranged to compute work or time given power. For example, if a pump has a power of 4000.0 watts, how much time will it take to lift 5,000 L of water a distance of 10.0 m from the bottom of a well, given that 1 L of water has 1 kg of mass?

t = W/P = fd/P

t = (5,000 kg)(9.8 N/kg)(10 m)/4000 W = 122.5 s = 2.04 min.

Power as Energy per TimeSince energy is measured by the work it does, power can be

expressed as energy produced per time (for power generated) or as energy consumed/used per time (for power consumption) .

A 60 W stereo consumes 60 J/s of electrical energy.

A 100 W bulb consumes 100 J/s of electrical energy.

The Work of James WattJames Watt improved the steam engine so that it could replace

animal power in England. To sell his steam engine to prospective clients, Watt needed to show them how many animals (usually horses) his new steam engine could replace.

The English Power Unit: HorsepowerWatt measured how much work a horse could do per second and

called this 1 horsepower. He then measured the amount of work his steam engines could do and rated his steam engines in horsepower, indicating how many horses one of his engines could replace. The metric power unit is named in honour of James Watt. 1 H.P. = 746 W. (1 H.P. = 550 ftpd/s – English)

Thermal EnergyThermal energy is the total kinetic energy of all the molecules

inside a substance (their colliding, spinning and vibrating) and their potential energy as they move closer or farther apart.

Temperature vs Thermal EnergyTemperature is a measure of the average energy per molecule.

Thermal energy is a measure of the total energy of all molecules.

V = 1

V = 2

V = 3

Molecules at various speeds

V = 4

V = 5 Temperature or Vav = (1+2+3+4+5)/5 = 3

V = 1

V = 2

V = 3

Molecules at various speeds

V = 4

V = 5 Thermal Energy or Vt = 1+2+3+4+5 = 15

Thermal Energy and Temperature Measure Different Things!

Temperature measures the average kinetic energy (movement energy) of a substance’s particles.

Thermal Energy measures the total kinetic energy (sum) of all the particles of a substance.

• A spoon of water at 100 celsius

• A bucket of water at 100 celsius. Equal temperatures! But not equal thermal energy!

HeatHeat is the thermal energy that gets passed from warmer to

cooler objects when they are in contact.

SummaryAs the diagram to the

right shows, heat moves from objects with higher temperatures to objects with lower temperatures. It can move from an object with less thermal energy to an object with higher thermal energy provided that the object with greater thermal energy has a lower temperature.

Measuring Heat by CaloriesA calorie is the amount of heat required to raise the

temperature of 1 g of water by 1 celsius degree. For example, the heat required to raise 1 g of water from 23 C to 24 C would be 1 calorie.

1 g water

1 g water

Temp = 23o C

Temp = 24o C

1 calorie of heat added

A Formula for Calculating Heat (For Water)If 2 g of water were raised 3 celsius degrees in temperature,

the amount of heat required would be 6 calories. To calculate heat (Q for quantity of heat),

Q = m(Δt) where Q is heat, m is mass and Δt is the temperature change

1 g water

1 g water

43 oC

46 oC

1 J heat/gCo

1 g water

1 g water

43 oC

46 oC

1 J heat/gCo

Food Calories (kilocalories or kcal)A food calorie is actually a kilocalorie or Calorie (capital C)

which is 1,000 calories, the energy (heat) needed to raise 1 kg of water by 1 celsius degree.

Lean Ground Beef: Snickers Bar: Apple:

The Mechanical Equivalent of HeatJames Prescott Joule conducted experiments where he

measured how much heat a given quantity of work would generate. He found that 4.18 J of work would raise 1 g of water by 1 celsius degree.

Thus 1 calorie heat energy = 4.18 J heat energy or ME.

The SI or Metric System Unit of Heat: JHeat in the SI is measured in joules since it is a form of

energy like all other forms of energy that are also measured in joules. The calorie unit is not a metric unit.

A Formula for Calculating Heat (For Water)If 2 g of water were raised 3 celsius degrees in temperature,

the amount of heat required would be 24.72 joules. To calculate heat (Q for quantity of heat),

Q = m(Δt)(c) where Q is heat, m is mass, Δt is the temperature change, and c is the specific heat capacity

1 g water

1 g water

43 oC

46 oC

4.12 Jheat/gCo

1 g water

1 g water

43 oC

46 oC

4.12 Jheat/gCo

The Heat Capacity of a SubstanceDifferent substances have different heat cpacities. If 5 balls

of equal mass are allowed to sit in boiling water (100 oC) for several minutes, these balls will have equal masses and equal temperatures (100 oC). When placed in a wax pan these balls melt different amounts of paraffin which shows that they gained different amounts of heat even though they had the same mass and initial temperature.

Boiling water 100 oC

Different metal balls

Specific Heat Capacity (Specific Heat)The specific heat capacity (c) or specific heat of a substance

is the amount of heat (J) to raise a given mass by a celsius degree. The units of specific heat are J/kgCo or J/gCo or cal/gCo . For any substance the heat gained, Q = mΔtc

2 g Lead at 22 oC

2 g lead at 25 oC

CPb = .130 J/gCo

2 g Al at 22 oC

2 g Al at 25 oC

CAl = .900 J/gCo

QAl = mΔtc= 2(3)(.900)= 5.4 J

QLead = mΔtc= 2(3)(.130)= .78 J

Explanation of Ball Expt.Since each ball stores different

amounts of heat (different specific heats), some balls release more heat as they change the same temp.

Paraffin Wax

Lead BallSpH = .130 J/gCo

AluminumBall SpH =.900 J/gCo

100 g balls at initial temperature of 100 oC. Final temperature is 20 oC (room temperature). Change in temperature = 80 Co .

The Lead ball lost 1,040 J of heat. Q=mΔtc

The Al ball lost 7,200 J of heat (6.9X heat)Q=mΔtc

Heat stored in Lead ball

Relative amount of heat stored in Al ball

Relation of Specific Heat to Temperature ChangeWhen given the same amount of heat, substances with low

specific heats will change their temperatures much more than substances with high specific heats.

4,186 J of heat added to the equal masses of sand and water.

.1 kg of sand at 10 oC

.1 kg of water at 10 oC

Δt = Q/mc =50.43 Co

C = 830 J/kgCo

C = 4,186 J/kgCo

Final Temp = 60.43 oC

Δt = Q/mc =10 Co

Final Temp. =20 oC

Climate Implications Related to Specific HeatRegions at the same latitude (Vancouver BC and Weyburn

Saskatchewan) differ in their yearly high and low temperatures (Vancouver: -1 C to 20 C, Weyburn: -20 C to 27 C) because the ocean near Vancouver changes temperature very little due to its high specific heat (From 6 C in winter to 12 C in Summer. At 10 m depth, the water is a constant 9 C). The water cools the surrounding land in summer and warms the surrounding land in winter.

Why are Beaches Always Warmer Than the Water?Since sand has a low specific heat (830 J/kgC), it raises its

temperature more quickly than water whose high specific heat (4,128 J/kgC) means it will absorb more heat before it changes temperature.

4,128 J/kgC

830 J/kgC

Solar Heat Storage SystemsThe high heat capacity of water makes it a suitable substance

to store energy in although its weight can be a negative factor. Rock bed storage systems with lower heat capacities use forced air to add and extract heat.

Energy EfficiencyEnergy efficiency for a device or situation is defined as the

useful energy output per total energy input times 100%.

Efficiency = useful energy output x 100%

energy input

In an incandescent bulb if 100 J of electricity convert to 3 J of light, its efficiency as a light producer is 2.5 % (97.5 % efficient as a heat producer).

Comparing the Efficiency of Kinds of Lights

Incandescent CFL (Compact Fluorescent LED (Light-

fluorescent lite) tube emitting diode)

2.5 % 7.8% 10% 9%

Sample ProblemFrom 1,000 J of gasoline a car’s engine produces 750 J of heat, the transmission and drive train produce 150 J of heat and 100 J becomes kinetic energy of motion. What is the

car’s efficiency?

Efficiency = 100J/1000 J x 100% = 10%

Car Efficiencies

Gasoline Engine Diesel Engine Electric Engine

10-25% 16-40% 75% Emissions Emissions No Emissions

Battery Replacement

Infrastructure Needed

Petroleum-Generated Electricity?

Cost – Rebate?

AA