Chapter 5 “Work and Energy” Chapter 5 “Work and Energy”

Honors PhysicsHonors Physics

TermsTerms

In science, certain terms In science, certain terms have meanings that are have meanings that are different from common different from common usage.usage.

Work, Energy and Power are Work, Energy and Power are three of them.three of them.

WorkWork– Objectives:Objectives:– 1. Recognize the difference between 1. Recognize the difference between

the scientific and ordinary definitions of the scientific and ordinary definitions of work.work.

– 2. Define work by relating it to force 2. Define work by relating it to force and displacement.and displacement.

– 3. Identify where work is being 3. Identify where work is being performed in a variety of situations.performed in a variety of situations.

– 4. Calculate the net work done when 4. Calculate the net work done when many forces are applied to an object.many forces are applied to an object.

WorkWork

For the purposes of this class:For the purposes of this class:

Work is not where you go to Work is not where you go to after school. Work doesn’t after school. Work doesn’t mean sweat. Work doesn’t mean sweat. Work doesn’t equal a paycheck.equal a paycheck.

Scientific WorkScientific Work

Work is force x distance x cos Work is force x distance x cos W = F·d·cos W = F·d·cos Note that no Work is done by a Note that no Work is done by a force at 90° to the direction of force at 90° to the direction of motion, cos motion, cos = 0. = 0.If work is done in the direction of If work is done in the direction of motion then cos motion then cos = 1. = 1.Work requires some movement.Work requires some movement.

Signs of WorkSigns of WorkUnits are N·m or Joules, J.Units are N·m or Joules, J.

Force applied on the object Force applied on the object that results in a that results in a displacement in the same displacement in the same direction is positive, +W.direction is positive, +W.

The opposite results in –W.The opposite results in –W.The area under a Force vs The area under a Force vs Displacement graph = Work.Displacement graph = Work.

When is work done?When is work done?– Work is not done on an object unless the Work is not done on an object unless the

object is moved through the application object is moved through the application of a force.of a force.

– If you balance your Physics book above If you balance your Physics book above on your head for 5 hours, not only will on your head for 5 hours, not only will you not learn any Physics through you not learn any Physics through osmosis, but no work will be done on the osmosis, but no work will be done on the book because it does not move.book because it does not move.

When is work done?When is work done?– If more than one force is acting on an If more than one force is acting on an

object, the net work can be found by object, the net work can be found by first finding the net force.first finding the net force.

– WWnetnet=F=Fnetnetd cosd cosθθ

– Work has SI units of N times meters Work has SI units of N times meters (N▪m) or joules (J).(N▪m) or joules (J).

ExampleExampleA 20.0 kg suitcase is raised 3.0 m above a A 20.0 kg suitcase is raised 3.0 m above a platform by a conveyor belt. How much platform by a conveyor belt. How much work is done on the suitcase?work is done on the suitcase?

ExampleExample5.9 x 105.9 x 102 J2 J

A tugboat pulls a ship with a constant net A tugboat pulls a ship with a constant net horizontal force of 5.00 x 10horizontal force of 5.00 x 103 3 N and N and causes the ship to move through a causes the ship to move through a harbor. How much work is done on the harbor. How much work is done on the ship as it moves a distance of 3.00 km?ship as it moves a distance of 3.00 km?

ExampleExample

1.5 x 101.5 x 107 J7 J

ExampleExampleA weight lifter lifts a set of weights a A weight lifter lifts a set of weights a vertical distance of 2.00 m. If a constant vertical distance of 2.00 m. If a constant net force of 350 N is exerted on the net force of 350 N is exerted on the weights, what is the net work done on the weights, what is the net work done on the weights?weights?

ExampleExample7.0 x 107.0 x 102 J2 J

ExampleExampleA shopper in a supermarket pushes a cart A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of with a force of 35 N directed at an angle of 25˚ downward from the horizontal. Find 25˚ downward from the horizontal. Find the work done by the shopper on the cart the work done by the shopper on the cart as the shopper moves along a 50.0 m as the shopper moves along a 50.0 m length of aisle.length of aisle.

ExampleExample1.6 x 101.6 x 103 J3 J

ExampleExampleIf 2.0 J of work is done in raising a 180 g If 2.0 J of work is done in raising a 180 g apple, how far is it lifted?apple, how far is it lifted?

ExampleExample1.1 m1.1 m

EnergyEnergyObjectives:Objectives:

1. Identify several forms of energy.1. Identify several forms of energy.

2.2.Calculate kinetic energy for an object.Calculate kinetic energy for an object.

3.3.Apply the work-kinetic energy theorem to Apply the work-kinetic energy theorem to solve problems.solve problems.

4. Distinguish between kinetic and potential 4. Distinguish between kinetic and potential energy.energy.

5. Classify different types of potential energy.5. Classify different types of potential energy.

6. Calculate the potential energy associated 6. Calculate the potential energy associated with an object's position.with an object's position.

EnergyEnergy

Energy comes in many forms. Energy comes in many forms. Electrical, chemical, heat, Electrical, chemical, heat, and atomic are just a few and atomic are just a few examples.examples.

A good definition of Energy is A good definition of Energy is the ability to do the ability to do workwork..

Categories of EnergiesCategories of Energies

Scientists divide energy into Scientists divide energy into two basic categories: two basic categories: mechanical and non-mechanical and non-mechanical. All those mechanical. All those energies listed on the energies listed on the previous slide and more can previous slide and more can be classified as mechanical be classified as mechanical or non-mechanical. or non-mechanical.

Kinetic EnergyKinetic Energy

The kinetic energy (KE) of an The kinetic energy (KE) of an object is the amount of object is the amount of “work” stored by that object “work” stored by that object due to its motion. The due to its motion. The velocity of the object is the velocity of the object is the most influential component.most influential component.

KE = ½ mvKE = ½ mv22

ExampleExampleA 6.0 kg cat runs after a mouse at 10.0 A 6.0 kg cat runs after a mouse at 10.0 m/s. What is the cat's kinetic energy?m/s. What is the cat's kinetic energy?

ExampleExample3.0 x 103.0 x 102 J2 J

Calculate the speed of an 8.0 x 10Calculate the speed of an 8.0 x 104 4 kg kg airliner with a kinetic energy of 1.1 x 109 airliner with a kinetic energy of 1.1 x 109 J.J.

ExampleExample1.7 x 101.7 x 102 m/s2 m/s

ExampleExampleTwo bullets have masses of 3.0 g and 6.0 Two bullets have masses of 3.0 g and 6.0 g, respectively. Both are fired with a g, respectively. Both are fired with a speed of 40.0 m/s. Which bullet has more speed of 40.0 m/s. Which bullet has more kinetic energy? What is the ratio of their kinetic energy? What is the ratio of their kinetic energies?kinetic energies?

ExampleExampleThe bullet with the greater mass; 2 to 1The bullet with the greater mass; 2 to 1

Work-Kinetic Energy TheoremWork-Kinetic Energy Theorem

The The netnet work done by a work done by a netnet force acting on an object is force acting on an object is equal to the change in kinetic equal to the change in kinetic energy.energy.

W W netnet = = KE = KEKE = KEff- KE- KEii

ExampleExampleA student wearing frictionless in-line A student wearing frictionless in-line skates on a horizontal surface is pushed skates on a horizontal surface is pushed by a friend with a constant force of 45 N. by a friend with a constant force of 45 N. How far must the student be pushed, How far must the student be pushed, starting from rest, so that her final kinetic starting from rest, so that her final kinetic energy is 352 J?energy is 352 J?

ExampleExample7.8 m7.8 m

ExampleExampleA 2.0 x 10A 2.0 x 103 3 kg car accelerates from rest kg car accelerates from rest under the actions of two forces. One is a under the actions of two forces. One is a forward force of 1140 N provided by the forward force of 1140 N provided by the traction between the wheels and the road. traction between the wheels and the road. The other is a 950 N resistive force due The other is a 950 N resistive force due to various frictional forces. Use the work-to various frictional forces. Use the work-kinetic energy theorem to determine how kinetic energy theorem to determine how far the car must travel for its speed to far the car must travel for its speed to reach 2.0 m/s.reach 2.0 m/s.

ExampleExample21 m21 m

ExampleExample– A 2.1 x 10A 2.1 x 103 3 kg car starts from rest at the kg car starts from rest at the

top of a driveway that is sloped at an top of a driveway that is sloped at an angle of 20.0° with the horizontal. An angle of 20.0° with the horizontal. An average frictional force of 4.0 x 10average frictional force of 4.0 x 103 3 N N impedes the car's motion so that the impedes the car's motion so that the car's speed at the bottom of the car's speed at the bottom of the driveway is 3.8 m/s. What is the length driveway is 3.8 m/s. What is the length of the driveway?of the driveway?

ExampleExample5.0 m5.0 m

Potential EnergyPotential Energy

The potential energy (PE) of The potential energy (PE) of an object is the amount of an object is the amount of “work” stored by that object “work” stored by that object due to its position. The due to its position. The “height” of the object is the “height” of the object is the most influential component.most influential component.

Types of Potential EnergyTypes of Potential Energy

For gravitational potential For gravitational potential energy:energy:

PEPEgg = mgh = mghFor elastic potential energy:For elastic potential energy:

PEPEelasticelastic= ½ kx= ½ kx22

k is the spring constant and x k is the spring constant and x is the distance the spring is is the distance the spring is compressed or stretched.compressed or stretched.

Elastic Potential EnergyElastic Potential EnergyElastic potential energy is the energy stored Elastic potential energy is the energy stored

in any compressed or stretched object.in any compressed or stretched object.

The kinetic energy of an object moved by a The kinetic energy of an object moved by a spring comes from the potential energy spring comes from the potential energy stored in the spring.stored in the spring.

The length of the spring when no external The length of the spring when no external forces are acting on it is called the forces are acting on it is called the relaxed relaxed length.length.

When an external force compresses or When an external force compresses or stretches the spring, elastic potential stretches the spring, elastic potential energy is stored.energy is stored.

ExampleExampleWhen a 2.00 kg mass is attached to a vertical When a 2.00 kg mass is attached to a vertical

spring, the spring is stretched 10.0 cm such spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table.that the mass is 50.0 cm above the table.

a. What is the gravitational potential a. What is the gravitational potential energy associated with this mass energy associated with this mass relative to the table?relative to the table?

b. What is the spring's elastic potential b. What is the spring's elastic potential energy if the spring constant is 400.0 energy if the spring constant is 400.0 N/m?N/m?

c. What is the total potential energy?c. What is the total potential energy?

ExampleExample– a. 9.81 Ja. 9.81 J– b. 2.00 Jb. 2.00 J– c. 11.81 Jc. 11.81 J

ExampleExampleA spring with a force constant of 5.2 N/m A spring with a force constant of 5.2 N/m has a relaxed length of 2.45 m. When a has a relaxed length of 2.45 m. When a mass is attached to the end of the spring mass is attached to the end of the spring and allowed to come to rest, the vertical and allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate length of the spring is 3.57 m. Calculate the elastic potential energy stored in the the elastic potential energy stored in the spring.spring.

ExampleExample3.3 J3.3 J

ExampleExample– A 40.0 kg child is in a swing that is A 40.0 kg child is in a swing that is

attached to ropes 2.00 m long. Find the attached to ropes 2.00 m long. Find the gravitational potential energy gravitational potential energy associated with the child relative to the associated with the child relative to the child's lowest position under the child's lowest position under the following conditions:following conditions:

– a. when the ropes are horizontal.a. when the ropes are horizontal.– b. when the ropes make a 30.0° b. when the ropes make a 30.0°

angle with the vertical.angle with the vertical.– c. at the bottom of the circular arc.c. at the bottom of the circular arc.

ExampleExample– a. 785 Ja. 785 J– b. 106 Jb. 106 J– c. 0.00 Jc. 0.00 J

Conservation of EnergyConservation of Energy– Objectives:Objectives:– 1. Identify situations in which 1. Identify situations in which

conservation of mechanical energy is conservation of mechanical energy is valid.valid.

– 2. Recognize the forms that conserved 2. Recognize the forms that conserved energy can take.energy can take.

– 3. Solve problems using conservation of 3. Solve problems using conservation of mechanical energy.mechanical energy.

The Law of Conservation of EnergyThe Law of Conservation of Energy

Energy can’t be created or Energy can’t be created or destroyed, however, it can destroyed, however, it can be transferred. When you be transferred. When you burn gasoline in your car the burn gasoline in your car the chemical energy is chemical energy is transferred to heat energy, transferred to heat energy, etc.. Total energy is always etc.. Total energy is always conserved.conserved.

Mechanical EnergyMechanical Energy

Mechanical energy is the sum Mechanical energy is the sum of the kinetic energy and all of the kinetic energy and all forms of potential energy forms of potential energy that are assoicated with an that are assoicated with an object or system.object or system.

ME = KE + ME = KE + PEPE

Conservation of Mechanical EnergyConservation of Mechanical Energy

In the absence of friction, In the absence of friction, mechanical energy is mechanical energy is conserved. Remember that conserved. Remember that friction produces heat and friction produces heat and heat is not a mechanical heat is not a mechanical energy.energy.

MEMEii = ME = MEff

Conservation of Mechanical Conservation of Mechanical EnergyEnergy

– In the absence of friction, the total In the absence of friction, the total mechanical energy remains the same.mechanical energy remains the same.

– Conservation of mechanical energyConservation of mechanical energy

– MeMeii=ME=MEff

– If the only force acting on an object is the If the only force acting on an object is the force due to gravity, thenforce due to gravity, then

– ½ ½ mvmvii22 + mgh + mghii = ½ mv = ½ mvff

22 + mgh + mghff

– If other forces (besides friction) are acting If other forces (besides friction) are acting on an object, add the appropriate potential on an object, add the appropriate potential energy formulae.energy formulae.

ExampleExample– A small 10.0 g ball is held to a slingshot A small 10.0 g ball is held to a slingshot

that is stretched 6.0 cm. The spring that is stretched 6.0 cm. The spring constant is 2.0 x 10constant is 2.0 x 102 N/m.2 N/m.

– a. What is the elastic potential energy of a. What is the elastic potential energy of the slingshot before it is released?the slingshot before it is released?

– b. What is the kinetic energy of the ball b. What is the kinetic energy of the ball just after the slingshot is released?just after the slingshot is released?

– c. What is the ball's speed at that c. What is the ball's speed at that instant?instant?

– d. How high does the ball rise if it is shot d. How high does the ball rise if it is shot directly upward?directly upward?

ExampleExample– a. 0.36 Ja. 0.36 J– b. 0.36 Jb. 0.36 J– c. 8.5 m/sc. 8.5 m/s– d. 3.7 md. 3.7 m

ExampleExampleA bird is flying with a speed of 18.0 m/s A bird is flying with a speed of 18.0 m/s over water when it accidentally drops a over water when it accidentally drops a 2.00 kg fish. If the altitude of the bird is 2.00 kg fish. If the altitude of the bird is 5.40 m and friction is disregarded, what is 5.40 m and friction is disregarded, what is the speed of the fish when it hits the the speed of the fish when it hits the water?water?

ExampleExample20.7 m/s20.7 m/s

ExampleExampleA 755 N diver drops from a board 10.0 m A 755 N diver drops from a board 10.0 m above the water's surface. Find the diver's above the water's surface. Find the diver's speed 5.00 m above the water's surface. speed 5.00 m above the water's surface. Then find the diver's speed just before Then find the diver's speed just before striking the water.striking the water.

ExampleExample9.9 m/s; 14.0 m/s9.9 m/s; 14.0 m/s

ExampleExample– An Olympic runner leaps over a hurdle. An Olympic runner leaps over a hurdle.

If the runner's initial vertical speed is 2.2 If the runner's initial vertical speed is 2.2 m/s, how much will the runner's center m/s, how much will the runner's center of mass be raised during the jump?of mass be raised during the jump?

ExampleExample0.25 m0.25 m

PowerPower– Objectives:Objectives:– 1. Relate the concepts of energy, time, 1. Relate the concepts of energy, time,

and power.and power.– 2. Calculate power in two different 2. Calculate power in two different

ways.ways.– 3. Explain the effects of machines on 3. Explain the effects of machines on

work and power.work and power.

Simple MachinesSimple Machines

Simple machines change the Simple machines change the direction or magnitude of the direction or magnitude of the exerted force but do not exerted force but do not change the work done. The change the work done. The usually trade distance for usually trade distance for effort.effort.

POWERPOWER

Power is the rate at which Power is the rate at which work is done. It also work is done. It also describes the rate of energy describes the rate of energy transfer.transfer.

P =P = WW//t t or F or F dd//t t or F (speed)or F (speed)

The unit is Watt (W)The unit is Watt (W)

1 horsepower = 746 W1 horsepower = 746 W

ExampleExample– Two horses pull a cart. Each exerts a Two horses pull a cart. Each exerts a

force of 250.0 N at a speed of 2.0 m/s force of 250.0 N at a speed of 2.0 m/s for 10.0 min.for 10.0 min.

– a. Calculate the power delivered by a. Calculate the power delivered by the horses.the horses.

– b. How much work is done by the b. How much work is done by the two horses?two horses?

ExampleExample– a. 1.0 x 10a. 1.0 x 103 W3 W

– b. 6.0 x 10b. 6.0 x 1055 J J

Mechanical AdvantageMechanical Advantage

Mechanical Advantage (MA) is Mechanical Advantage (MA) is the ratio of the effort force the ratio of the effort force compared to the resistance compared to the resistance force.force.

MA = FMA = Frr/F/Fee or W or Woutout = W = Winin

FFrrddrr = F = Feeddee

FFrr/F/Fee = d = dee/d/drr

Ideal Mechanical AdvantageIdeal Mechanical Advantage

IMA = dIMA = dee/d/drr

Efficiency = WEfficiency = Woo/W/Wii x 100% x 100%

= MA/IMA x 100%= MA/IMA x 100%