energylchs. work forms of energy power conservation of energy kepler’s laws of motion simple...

EnergyEnergyLCHSLCHS

WorkWork Forms of EnergyForms of Energy

PowerPowerConservation of Conservation of

EnergyEnergy Kepler’s Laws of Kepler’s Laws of

Motion Motion Simple Simple Machines Machines

Mechanical Mechanical AdvantageAdvantage

WorkWork can be done by you, as well as on youAre you the pusher or the pusheeWork is a measure of expended energyWork makes you tiredMachines make work easy (ramps, levers, etc.)Apply less force over larger distance for same work

Now instead of a force for how long in time we consider a force for how long in distance.

The unit for work is the Newton-meter which is also called a Joule.

WorkThe simplest definition for the amount of work a force does on an object is

magnitude of the force times the distance over which it’s applied:

W = F xThis formula applies when:

• the force is constant

• the force is in the same direction as the displacement of the object

F

x

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•If you push a box with a force of one Newton for a distance of one meter, you have done exactly one joule of work.

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•In Physics, work has a very specific meaning.

•In Physics, work represents a measurable change in a system, caused by a force.

Question

How much work is required to push a desk 15 m across a floor with a force of 100 N?A) 6.7 JB) 115 JC) 85 JD) 1500 J

Question

Pushing a crate 10 m across a floor with a force of 250 N requires _____ J of work?A) 2500 JB) 25 JC) 250 JD) .25 J

Questions:

How much work is done when a weight lifter lifts a barbell weighing 1000 Newtons 1.5 meters above the ground?

Questions:

How much work is done when a weight lifter pushes on a stationary wall with a force of 1000 Newtons for 15 seconds?

QuestionA 10 N weight is lifted 5 m. A 20 N weight is lifted 2.5 m. Which lifting required the most work?

(a) 10 N weight(b) 20 N weight(c) same work for each lifting(d) not enough information is given to work the

problem

Two cars, A and B, travel as fast as they can to the top of a hill. If their masses are equal and they start at the same time, which one does the most work if A gets to the top first?

(a) A(b) B(c) they do the same amount of work

Question

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Do Work Problems

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Forms of EnergyForms of EnergyWhen work is done on an object the amount of energy the object has as well as the types of energy it possesses could change. Here are some types of energy you should know:

• Kinetic energy

• Rotational Kinetic Energy

• Gravitational Potential Energy

• Elastic Potential Energy

• Chemical Potential Energy

• Work

• Electrical energy

• Light

• Sound

• Other waves

• Thermal energy

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Kinetic EnergyKinetic energy is the energy of motion. By definition,

kinetic energy is given by:

K = ½ m v 2

The equation shows that . . .

. . . the more kinetic energy it’s got.

• the more mass a body has

• or the faster it’s moving

K is proportional to v 2, so doubling the speed quadruples kinetic

energy, and tripling the speed makes it nine times greater.

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Energy Units

The formula for kinetic energy, K = ½ m v 2, shows that its units are:

kg · (m/s)2 = kg · m 2 / s

2 = (kg · m / s 2

) m = N · m = J

So the SI unit for kinetic energy is the Joule, just as it is for work. The Joule is the SI unit for all types of energy.

One common non-SI unit for energy is the calorie. 1 cal = 4.186 J. A calorie is the amount of energy needed to raise the temperature of 1 gram of water 1 C.

A food calorie is really a kilocalorie. 1 Cal = 1000 cal = 4186 J.

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Kinetic EnergyKinetic Energy

•Energy of motion is called kinetic energy.

•The kinetic energy of a moving object depends on two things: mass and speed.

•Kinetic energy is proportional to mass.

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•Mathematically, kinetic energy increases as the square of speed.

•If the speed of an object doubles, its kinetic energy increases four times. (mass is constant)

Kinetic EnergyKinetic Energy

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Kinetic Energy Example

A 55 kg toy sailboat is cruising at 3 m/s. What is its kinetic energy?

K = ½ m v 2

K = 0.5 (55) (3) 2 = 247.5 J

Note: Kinetic energy (along with every other type of energy) is a scalar, not a vector!

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Calculate Kinetic EnergyCalculate Kinetic Energy

A car with a mass of 1,300 kg is going straight ahead at a speed of 30 m/sec (67 mph).

The brakes can supply a force of 9,500 N.

Calculate:

a) The kinetic energy of the car.

b) The distance it takes to stop.

Kinetic Energy CalculationA 1000 kg car is traveling at 20 m/s. What is its kinetic energy?

200,000 J

The same car is traveling at 40 m/s. What is its kinetic energy?

800,000 J

The same car is traveling at 60 m/s. What is its kinetic energy?

1,800,000

Kinetic energy becomes important in calculating braking distance

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Determine the kinetic energy Determine the kinetic energy of a 100-kg car that is of a 100-kg car that is moving with a speed of 5 moving with a speed of 5 m/s. m/s.

A) 20 JoulesA) 20 JoulesB) 480 JoulesB) 480 JoulesC) 1250 JoulesC) 1250 JoulesD) 500 JoulesD) 500 Joules

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Determine the kinetic energy Determine the kinetic energy of a 90-kg person that is of a 90-kg person that is running with a speed of 10 m/s. running with a speed of 10 m/s.

A) 900 JoulesA) 900 JoulesB) 100 JoulesB) 100 JoulesC) 9 JoulesC) 9 JoulesD) 4500 JoulesD) 4500 Joules

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The kinetic energy of a 204-The kinetic energy of a 204-kg roller coaster car that is kg roller coaster car that is 34,159 Joules. What is the 34,159 Joules. What is the speed of the roller coaster in speed of the roller coaster in m/s?m/s?

Kinetic Energy CalculationIf the brakes supply 7000-N of stopping force, calculate how far it takes to stop the car when it is going 15 m/s (KE = 200,000 J).

28 m

Calculate how far it takes to stop the car when it is going 40 m/s (KE = 800,000 J).

114 m

Calculate how far it takes to stop the car when it is going 60 m/s (KE = 1,800,000 J).

257 m

An object of mass 6 kg is traveling at a velocity of 30 m/s. How much total work was required to obtain this velocity starting from a position of rest?

(a) 180 Joules(b) 2700 Joules(c) 36 Joules(d) 5 Joules(e) 180 Joules

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At what point is the At what point is the

kinetic energy the kinetic energy the

highest for a highest for a

satellite motion?satellite motion?

A) Kinetic energy is unrelated to satellite A) Kinetic energy is unrelated to satellite motionmotion

B) At the closest point of its path B) At the closest point of its path (Penthelion)(Penthelion)

C) At the middle of its pathC) At the middle of its path

D) At the Farthest point of its path D) At the Farthest point of its path (Aphelion)(Aphelion)

E) Kinetic energy is constantE) Kinetic energy is constant

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At what point is the kinetic At what point is the kinetic energy the highest for a energy the highest for a pendulum?pendulum?

A) Kinetic energy is unrelated to A) Kinetic energy is unrelated to heightheightB) At the end of its path (1 & 5)B) At the end of its path (1 & 5)C) At the middle of its path (2 & 4)C) At the middle of its path (2 & 4)D) At the bottom of its path (3)D) At the bottom of its path (3)E) Kinetic energy is constantE) Kinetic energy is constant

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Do KE Do KE ProblemsProblems

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Gravitational Potential Gravitational Potential EnergyEnergy

• Gravitational potential energy is the energy stored in an object as the result of its vertical position or height.

• The energy is stored as the result of the gravitational attraction of the Earth for the object.

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Gravitational potential energy is given by:

U = m g h

The equation shows that . . .

. . . the moremore gravitational potential energy it’s got.

• the moremore mass a body has

• or the strongerstronger the gravitational field it’s in

• or the higherhigher up it is

Gravitational Potential Gravitational Potential EnergyEnergy

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SI Potential Energy UnitsSI Potential Energy Units

From the equation U = m g h the units of gravitational potential energy must be:

kg · (m/s2) · m = (kg · m/s2) · m = N · m = J

This shows the SI unit for potential energy is the Joule, as it is for work and all other types of energy.

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Path doesn't matterPath doesn't matter

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Reference point for UThe amount of gravitation potential energy the mini-watermelon has depends on our reference point. It can be positive, negative, or zero.

10 N

D

C

B

A

6 m

3 m

8 m

Note: the weight of the object is given here, not the mass.

A 20 Newton weight is lifted 4 A 20 Newton weight is lifted 4 meters. The change in potential meters. The change in potential energy of the weight in Joules isenergy of the weight in Joules is

(a) 20(a) 20(b) 24(b) 24(c) 16(c) 16(d) 80(d) 80(e) 5(e) 5

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A 3.0 kg cart is loaded with a brick and pulled at constant speed along an inclined plane such that there is an increase in potential energy of 150 Joules. What is the height of the top?

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At what point is the potential energy the highest for a pendulum?A) Potential energy is unrelated to heightB) At the end of its path (1 & 5)C) At the middle of its path (2 & 4)D) At the bottom of its path (3)E) Potential energy is constant

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At what point is the At what point is the potential energy thepotential energy the highest for a highest for a satellite motion?satellite motion?

A) Potential energy is unrelated to satellite A) Potential energy is unrelated to satellite motionmotion

B) At the closest point of its path (Penthelion)B) At the closest point of its path (Penthelion)

C) At the middle of its pathC) At the middle of its path

D) At the Farthest point of its path (Aphelion)D) At the Farthest point of its path (Aphelion)

E) Potential energy is constantE) Potential energy is constant

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Do PE Do PE ProblemsProblems

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Hooke’s LawPrinciple that states the Force needed to extend or compress a spring to distance x is proportional to that distance

F = kx

k is a constant characteristic of the spring’s stiffness

k = F/x k = F/x therefore unit is N/mN/m42

A vertical spring 0.100 meters long is elongated to a length of 0.119 meters when a 1.00-kilogram mass is attached to the bottom of the spring. The spring constant of this springA. 9.8 N/mB. 82 N/mC. 98 N/mD. 520 N/m 43

Spring Potential EnergySpring Potential Energy

• Result of deformation of an elastic object, such as the stretching of a spring

• Equal to the work done to stretch the spring

• Units (N/m)(m2) = (N/m)(m×m) = Nm = Joule

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A spring with a spring constant of 80. Newtons per meter is displaced 0.30 meter from its equilibrium position. The potential energy stored in the spring is

Work = PE =1/2 kx2

PE =1/2 (80. N/m) (0.30m)2

= (40. N/m) (0. 09m2)

= 3.6 Nm = 3.6 Joules46

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As a spring is stretched, its elastic As a spring is stretched, its elastic potential energypotential energy

A. decreasesA. decreases

B. increasesB. increases

C. remains the sameC. remains the same

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A. 3.6 J

B. 7.2 J

C. 12 J

D. 24 J

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When a mass is placed on a spring with a When a mass is placed on a spring with a spring constant of 15 newtons per meter, spring constant of 15 newtons per meter, the spring is compressed 0.25 meter. How the spring is compressed 0.25 meter. How much elastic potential energy is stored in much elastic potential energy is stored in the spring?the spring?

A. 0.47 JA. 0.47 J

B. 0.94 JB. 0.94 J

C. 1.9 JC. 1.9 J

D. 3.8 JD. 3.8 J

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When a 1.53-kilogram mass is placed on a When a 1.53-kilogram mass is placed on a spring with a spring constant of 30.0 newtons spring with a spring constant of 30.0 newtons per meter, the spring is compressed 0.500 per meter, the spring is compressed 0.500 meter. How much energy is stored in the meter. How much energy is stored in the spring?spring?

A. 3.75 JA. 3.75 J

B. 7.50 JB. 7.50 J

C. 15.0 JC. 15.0 J

D. 30.0 JD. 30.0 J

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A 3.0-kilogram mass is attached to a spring A 3.0-kilogram mass is attached to a spring having a spring constant of 30. Newtons per having a spring constant of 30. Newtons per meter. The mass is pulled 0.20 meter from the meter. The mass is pulled 0.20 meter from the spring's equilibrium position and released. spring's equilibrium position and released. What is the maximum kinetic energy achieved What is the maximum kinetic energy achieved by the mass spring system?by the mass spring system?

A. 2.4 JA. 2.4 J

B. 1.5 JB. 1.5 J

C. 1.2 JC. 1.2 J

D. 0.60 JD. 0.60 J

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Do Spring PE Do Spring PE ProblemsProblems

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PowerPower is defined as the rate at which work is done. It can also refer to the rate at which energy is expended or absorbed. Mathematically, power is given by:

P = Wt

= Fdt

= ΔPEt

= Fdt

= ΔKEt

= Fv

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How long would it take a machine to How long would it take a machine to do 5,000 joules of work if the power do 5,000 joules of work if the power rating of the machine is 100 watts?rating of the machine is 100 watts?

A. 5,000 secA. 5,000 sec

B. 50 secB. 50 sec

C. 10 secC. 10 sec

D. 0.2 secD. 0.2 sec

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A 40.-kilogram student runs up a A 40.-kilogram student runs up a staircase to a floor that is 5.0 meters staircase to a floor that is 5.0 meters higher than her starting point in 7.0 higher than her starting point in 7.0 seconds. The student’s power output isseconds. The student’s power output is

A. 29 WA. 29 W

B. 280 WB. 280 W

C. 1.4 × 10C. 1.4 × 1033 W W

D. 1.4 × 10D. 1.4 × 1044 W W

55

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A 3.0-kilogram mass being moved at a A 3.0-kilogram mass being moved at a constant speed by a force of 6.0 constant speed by a force of 6.0 Newtons. If energy is supplied at the Newtons. If energy is supplied at the rate of 10 watts, how much work is rate of 10 watts, how much work is done during 2 seconds?done during 2 seconds?

A. 20 JA. 20 J

B. 15 JB. 15 J

C. 10 JC. 10 J

D. 5 JD. 5 J56

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What is the average power What is the average power required to raise a 1.81 × 10required to raise a 1.81 × 1044-N -N elevator 12.0 m in 22.5 s?elevator 12.0 m in 22.5 s?

A. 8.04 × 10A. 8.04 × 1022 W W

B. 9.65 × 10B. 9.65 × 1033 W W

C. 2.17 × 10C. 2.17 × 1055 W W

D. 4.89 × 10D. 4.89 × 1066 W W

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A machine does work at the A machine does work at the rate of 600 watts. How much rate of 600 watts. How much weight will be lifted 10 meters weight will be lifted 10 meters in 10 seconds?in 10 seconds?

A. 6 NA. 6 N

B. 60 NB. 60 N

C. 600 NC. 600 N

D. 6,000 ND. 6,000 N 58

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An electrical heater raises the An electrical heater raises the temperature of a measured temperature of a measured

quantity of water. The water quantity of water. The water absorbs 6,000 joules of energy absorbs 6,000 joules of energy

from the heater in 30.0 seconds. from the heater in 30.0 seconds. What is the minimum power What is the minimum power

supplied to the heater?supplied to the heater?

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60


A. 3.6 JB. 7.2 JC. 12 JD. 24 J

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A spring with a spring constant of 80. Newtons per meter is displaced 0.30 meter from its equilibrium position. The potential energy stored in the spring is 3.6 J. How fast will a 0.10 kg ball go when released?

PowerPower is defined as the rate at which work is done. It can also refer to the rate at which energy is expended or absorbed. Mathematically, power is given by:

P = Wt

Power BillsPower BillsA family has twelve 100 watt light bulbs A family has twelve 100 watt light bulbs and keep them on 8 hours per day seven and keep them on 8 hours per day seven days a week. The cost of electricity is $.22 / days a week. The cost of electricity is $.22 / kwh. kwh. How many watts does the family use?How many watts does the family use?1200 watts1200 wattsHow many kilowatts is that?How many kilowatts is that?1.2 kw1.2 kwHow much energy consumption is that in How much energy consumption is that in kwh per week?kwh per week?67.2 kwh 67.2 kwh How much will that cost the family?How much will that cost the family?$14.784$14.784

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A family has fifteen 100 watt light bulbs A family has fifteen 100 watt light bulbs and keep them on 12 hours per day seven and keep them on 12 hours per day seven days a week. The cost of electricity is days a week. The cost of electricity is $.22 / kwh. $.22 / kwh. How many watts are used per week?How many watts are used per week?1500 watts1500 watts

How many kilowatts is that?How many kilowatts is that?1.5 kw1.5 kw

How much energy consumption is that in How much energy consumption is that in kwh per week?kwh per week?126 kwh 126 kwh

How much will that cost the family?How much will that cost the family?$27.72$27.72

6644

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Do Power Do Power ProblemsProblems

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Potential Energy Converted to Kinetic Potential Energy Converted to Kinetic EnergyEnergy

Potential energy converts to kinetic energy when stored energy begins to move.

100 kg

100 kg

100 kg

1 meter

nail

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Forms of EnergyForms of Energy

•Mechanical energy is the energy possessed by an object due to its motion or its position.

•Radiant energy includes light, microwaves, radio waves, x-rays, and other forms of electromagnetic waves.

•Nuclear energy is released when heavy atoms in matter are split up or light atoms are put together.

•The Electrical energy we use is derived from other sources of energy such as chemical reactions

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Law of Conservation of Law of Conservation of EnergyEnergy

•As energy takes different forms and changes As energy takes different forms and changes things by doing work, nature keeps perfect track things by doing work, nature keeps perfect track of the total. of the total.

•No new energy is created and no existing energy No new energy is created and no existing energy is destroyed.is destroyed.

•How many energy How many energy transformationstransformations have you have you been involved with so far today?been involved with so far today?

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Conservation of EnergyConservation of Energy

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Conversion of PE Conversion of PE KE KE• PE + KE = PE + KE

• or• mgh + ½mv2 = mgh + ½mv2

• All masses are the same…

• mgh + ½mv2 = mgh + ½mv2

m m m m

• Therefore• gh + ½v2 = gh + ½v2

Acceleration due to gravity is independent of Acceleration due to gravity is independent of massmass

•The electrical power output of the power plant is 800MW (800 million watts). But the chemical energy input of the station was 2025 MW…..

•Calculate the efficiency of the power plant as a percentage.

•The Solution

•Efficiency = useful power output/total power

input •= 800,000,000 W/2,025,000,000 W •= 0.395 x 100% to create a percentage

•= 39.5%

•The electrical power output of the power plant is 800MW (800 million watts). But the chemical energy input of the station was 2025 MW…..So, What has happened to the rest of the energy?

•The Answer•Most of the rest of the energy is

wasted as heat - up the chimney of the power station, in the cooling towers, and because of friction in the machinery.

Example ProblemExample Problem

•A 100 kg mass is dropped from rest from a height of 1 meter.•How much potential energy does it have when it is released?•How much kinetic energy does it have just before it hits the ground?•What is its speed just before impact?•How much work could it do if it were to strike a nail before hitting the ground?

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Goliath QuestionGoliath Question• Goliath the ride at Six Flags Magic Mountain takes Goliath the ride at Six Flags Magic Mountain takes

5.2 seconds to go down the first incline.5.2 seconds to go down the first incline.

• What is the height of the first incline?What is the height of the first incline?

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5.2 seconds to go down the first incline (135.2 m)5.2 seconds to go down the first incline (135.2 m)

• If each cart that holds four people and weighs a If each cart that holds four people and weighs a total of 2000-kg. What is the potential energy for total of 2000-kg. What is the potential energy for that cart at the top of the first hill?that cart at the top of the first hill?

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5.2 seconds to go down the first incline (135.2 m) 5.2 seconds to go down the first incline (135.2 m) and each cart has a PE = 2.97 x 10and each cart has a PE = 2.97 x 106 6 at the top of the at the top of the hill.hill.

• How much work is done if the chain pulls with a How much work is done if the chain pulls with a force of 30,000 N for the 200 m incline to the top?force of 30,000 N for the 200 m incline to the top?

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5.2 seconds to go down the first incline (135.2 m) 5.2 seconds to go down the first incline (135.2 m) and each cart has a PE = 2.97 x 10and each cart has a PE = 2.97 x 106 6 J at the top of J at the top of the hill. Work = 6.00 x 10the hill. Work = 6.00 x 106 6 J J

• What is the efficiency of the chain?What is the efficiency of the chain?

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• What is the PE half way down the first hill?What is the PE half way down the first hill?

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• What is the KE half way down the first hill?What is the KE half way down the first hill?

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• What is the speed of the cart (2000-kg) half way What is the speed of the cart (2000-kg) half way down the first hill?down the first hill?

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• What is the PE at the bottom of the first hill?What is the PE at the bottom of the first hill?

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• What is the KE at the bottom of the first hill?What is the KE at the bottom of the first hill?

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5.2 seconds to go down the first incline (132.5 m) 5.2 seconds to go down the first incline (132.5 m) and each cart has a PE = 2.97 x 10and each cart has a PE = 2.97 x 1066 at the top of the at the top of the hill.hill.

• What is the speed of the cart (2000-kg) at the What is the speed of the cart (2000-kg) at the bottom of the first hill?bottom of the first hill?

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A child does 0.20 joule of work to compress the A child does 0.20 joule of work to compress the spring in a pop-up toy. If the mass of the toy is spring in a pop-up toy. If the mass of the toy is 0.010 kilogram, what is the maximum vertical 0.010 kilogram, what is the maximum vertical height that the toy can reach after the spring is height that the toy can reach after the spring is released?released?

A. 20. mA. 20. m

B. 2.0 mB. 2.0 m

C. 0.20 mC. 0.20 m

D. 0.020 mD. 0.020 m

SpringsSprings

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A machine with 75% efficiency A machine with 75% efficiency has an output of 3,300 J of has an output of 3,300 J of

energy. How much work would energy. How much work would you have to put into the you have to put into the

machine?machine?

A machine with 75% efficiency A machine with 75% efficiency has an output of 3,300 J of has an output of 3,300 J of

energy. How much work would energy. How much work would you have to put into the you have to put into the

machine?machine?

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91

Do Do Conservation Conservation

of Energy of Energy ProblemsProblems

73

92

•How do simple machines work?

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Machines•The ability of humans to build buildings and move mountains began with our invention of machines.

•In physics the term “simple machine” means a machine that uses only the forces directly applied and accomplishes its task with a single motion.

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Machines• The best way to analyze what a machine does is to think about the machine in terms of input and output

Machines - An Application Machines - An Application of Energy Conservationof Energy Conservation

•If there is no mechanical energy losses then for a simple machine...

•work input = work output

•(F d)input = (F d)output

•Examples - levers and tire jacks

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Mechanical Advantage•Mechanical advantage is the ratio of output force to input force.

•For a typical automotive jack the mechanical advantage is 30 or more.

•A force of 100 newtons (22.5 pounds) applied to the input arm of the jack produces an output force of 3,000 newtons (675 pounds)— enough to lift one corner of an automobile.

Introducing… The Lever

A lever includes a stiff structure (the lever) that rotates around a fixed point called the fulcrum.

fulcrum

Anatomy of the LeverAnatomy of the LeverFulcrum – point around which the lever rotates

Input Force – Force exerted ON the lever

Output Force – Force exerted BY the lever

Levers and the Human BodyYour body

contains muscles attached to bones in ways that act as levers.

Here the biceps muscle attached in front of the elbow opposes the muscles in the forearm. Can you think of other

muscle levers in your body?

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Mechanical Advantage

MA = Fo

Fi

Output force (N)

Input force (N)

Mechanicaladvantage

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Mechanical Advantage of a Mechanical Advantage of a LeverLever

MAlever = Li

Lo

Length of input arm (m)

Length of output arm(m)

Mechanicaladvantage

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Calculate positionCalculate position

•Where should the fulcrum of a lever be placed so one person weighing 700 N can lift the edge of a stone block with a mass of 500 kg?

•The lever is a steel bar three meters long.

•Assume a person can produce an input force equal to their own weight.

•Assume that the output force of the lever must equal half the weight of the block to lift one edge.

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•What force must be applied to the end of a 2.0 meter long crowbar in order to lift a 500 Newton rock if the fulcrum of the bar is 0.5 meters from the rock?

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105

• With what force must Megan With what force must Megan raise a wheelbarrow handle in raise a wheelbarrow handle in order to carry away a bush order to carry away a bush whose weight is 410 newtons. whose weight is 410 newtons. The bush is 40 cm from the The bush is 40 cm from the wheel of the wheelbarrow, and wheel of the wheelbarrow, and the total length of the the total length of the wheelbarrow is 100 cm.wheelbarrow is 100 cm.

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106

•How much force is needed to How much force is needed to lift a 10.0 kg mass from a lift a 10.0 kg mass from a horizontal position using the horizontal position using the human arm if the forearm is human arm if the forearm is 25 cm long and the lifting 25 cm long and the lifting muscle is 2.0 cm from the muscle is 2.0 cm from the elbow?elbow?

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107

•A nutcracker 12.5 cm long is used to open a nut placed .85 cm from the hinged edge. A force of 82.5 newtons is required to break the nut. What force must be applied to the handle of the nutcracker?

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108

•Suppose the efficiency of a 1.65 m long crowbar is 60%. What force will be needed to remove a tree stump that resists with a force of 15,500 newtons if the fulcrum of the crowbar is 8.0 cm from the tree stump?

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Do Lever Do Lever ProblemsProblems

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Ramp Example•Ramp 10 m long and 1 m high•Push 100 kg all the way up ramp•Would require mg = 980 N (220 lb) of force

to lift directly (brute strength)•Work done is (980 N)(1 m) = 980 N·m in

direct lift

•Extend over 10 m, and only 98 N (22 lb) is needed– Something we can actually provide– Excludes frictional forces/losses

1 m10 m

Work Examples “Worked” Out

•How much work does it take to lift a 30 kg suitcase onto the table, 1 meter high?

– W = (30 kg) (9.8 m/s2) (1 m) = 294 J

•Unit of work (energy) is the N·m, or Joule (J)– One Joule is 0.239 calories, or 0.000239

Calories (food)

•Pushing a crate 10 m across a floor with a force of 250 N requires 2,500 J (2.5 kJ) of work

•Gravity does 20 J of work on a 1 kg (10 N) book that it has pulled off a 2 meter shelf

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Do Ramp Do Ramp ProblemsProblems

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PulleysPulleys Like levers, ramps, and screws…. Sacrifices displacement to achieve a greater force

By pulling a greater displacement you have to apply less force

MA is shown by how many ropes are supporting the load in this case there are two

Like levers, ramps, and screws…. Sacrifices displacement to achieve a greater force

By pulling a greater displacement you have to apply less force

MA is shown by how many ropes are supporting the load in this case there are two

http://upload.wikimedia.org/wikipedia/commons/6/62/Polispasto2.jpg

Another PulleyAnother PulleyMA = 4 4 ropes supporting loadForce applied is 4 times

less than 100 NSo rope must be pulled

with 25 N of force with a distance 4 times greater than the upward distance the load moves

MA = 4 4 ropes supporting loadForce applied is 4 times

less than 100 NSo rope must be pulled

with 25 N of force with a distance 4 times greater than the upward distance the load moves

http://upload.wikimedia.org/wikipedia/commons/2/2a/Polispasto4.jpg

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• A pulley system consisting of six A pulley system consisting of six pulleys as shown to the right has pulleys as shown to the right has an input force of 220 N applied to an input force of 220 N applied to it. As a result of this input force it. As a result of this input force the mass M is lifted a distance of the mass M is lifted a distance of 25.0 cm. This machine has a 25.0 cm. This machine has a mechanical efficiency of 88%.mechanical efficiency of 88%.

• What is the ideal mechanical What is the ideal mechanical advantage of the systemadvantage of the system

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• A pulley system consisting of six pulleys as shown to the right has an input force of 220 N applied to it. As a result of this input force the mass M is lifted a distance of 25.0 cm. This machine has a mechanical efficiency of 88%.

• What is the mass of the load M?

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• How much work was done on the mass M?

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• Through what distance was the input force applied?

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• What is the actual mechanical advantage of this machine?

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Do Pulley Do Pulley ProblemsProblems

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Efficiency of MachinesEfficiency of MachinesC of E says that energy in must equal energy outHowever, often a lot of energy is lost

Heat, friction, sound, etc.

Efficiency equals (Useful energy out) *100% (Energy in)Higher the percentage….the more efficient

C of E says that energy in must equal energy outHowever, often a lot of energy is lost

Heat, friction, sound, etc.

Efficiency equals (Useful energy out) *100% (Energy in)Higher the percentage….the more efficient

A power plant burns 75kg of coal every second. Each kg of coal contains 27 MJ (27 million joules) of chemical energy.

What is the power of the power station, in watts? The Solution

Power in watts = energy transferred in one sec= 75 x 27 million J per sec= 2025 million J per sec

= 2025 million watts (2025 megawatts)

A power plant burns 75kg of coal every second. Each kg of coal contains 27 MJ (27 million joules) of chemical energy.

What is the power of the power station, in watts? The Solution

Power in watts = energy transferred in one sec= 75 x 27 million J per sec= 2025 million J per sec

= 2025 million watts (2025 megawatts)

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A box weighing 100 newtons is pushed up an inclined plane that is 5 meters long. It takes a force of 75 newtons to push it to the top, which has a height of 3 meters. What is the efficiency?

A box weighing 100 newtons is pushed up an inclined plane that is 5 meters long. It takes a force of 75 newtons to push it to the top, which has a height of 3 meters. What is the efficiency?

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Suppose the efficiency of a 1.65 m long crowbar is 60%. What force will be needed to remove a tree stump that resists with a force of 15,500 Newtons if the fulcrum of the crowbar is 8.0 cm from the tree stump?

Suppose the efficiency of a 1.65 m long crowbar is 60%. What force will be needed to remove a tree stump that resists with a force of 15,500 Newtons if the fulcrum of the crowbar is 8.0 cm from the tree stump?

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Do Efficiency Do Efficiency ProblemsProblems

104

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Momentum

• Often misused word, though most have the right idea

• Momentum, denoted p, is mass times velocity– p = m·v

• Momentum is a conserved quantity (and a vector)– Often relevant in collisions (watch out for linebackers!)

• News headline: Wad of Clay Hits Unsuspecting Sled– 1 kg clay ball strikes 5 kg sled at 12 m/s and sticks– Momentum before collision: (1 kg)(12 m/s) + (5 kg)(0 m/s)– Momentum after:12 kg·m/s (6 kg)·(2 m/s)

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Collisions• A collision is an event where

momentum or kinetic energy is transferred from one object to another.

• Two types of collisions– Elastic: Energy not dissipated out

of kinetic energy• Bouncy

– Inelastic: Some energy dissipated to other forms• Sticky

• Perfect elasticity unattainable (perpetual motion)

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Elastic Collision

•An elastic collision can be defined as a collision where both the momentum and the total kinetic energy before the collision are the same as the momentum and total kinetic energy after the collision.

•Both momentum and kinetic energy are conserved in the collision. This means that there was no wasting force during the collision.

•Only in elastic collisions are both momentum and kinetic energy conserved.

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Newton’s Cradle

• Newton’s cradle knows how many balls you let go because of the conservation of kinetic energy and momentum

• The only way to simultaneously satisfy energy and momentum conservation

• Relies on balls to all have same mass

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Inelastic Collision

•In an inelastic collision, two or more objects collide and stick together.

•Some of the kinetic energy is converted into sound, heat, and deformation of the objects.

•In an inelastic collision, Kinetic Energy is not conserved. Momentum is conserved.

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Superball Physics

• Superballs rebound proportionally to the amount of force used when thrown at a hard surface

• Superballs often behave contrary to intuition• back-and-forth motion• boomerang effect

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