topic 5: work, energy & power. work definition of work: definition of work: when a force causes...

TOPIC 5:TOPIC 5:

Work, Energy & Work, Energy & PowerPower

WORKWORK

Definition of Work:Definition of Work: When a force causes a displacement of When a force causes a displacement of

an objectan object Components of the force need to be in Components of the force need to be in

the direction of the displacementthe direction of the displacement

Net Work done by a Net Work done by a Constant Net ForceConstant Net Force

Work = Force (F) x Displacement (x)Work = Force (F) x Displacement (x)

W = FxW = Fx

W = Fx = (FcosW = Fx = (Fcosθ)x θ)x ** Only the component of the force in the direction of the ** Only the component of the force in the direction of the

displacement, contributes to work displacement, contributes to work

Units of WorkUnits of Work

Work = Force x DisplacementWork = Force x Displacement

= Newtons x meters= Newtons x meters

Newton x meter Newton x meter Joule (J)Joule (J)

* Joule is named after James Prescott Joule (1818-1889) who * Joule is named after James Prescott Joule (1818-1889) who made major contributions to the understanding of energy, made major contributions to the understanding of energy, heat, and electricityheat, and electricity

==

WorkWork

Work:Work: Scalar quantityScalar quantity Can be positive or negativeCan be positive or negative Positive work Positive work Exists when the force & Exists when the force &

displacement vectors point in the same displacement vectors point in the same directiondirection

Negative work Negative work Exists when the force Exists when the force & displacement vectors point in opposite & displacement vectors point in opposite directionsdirections

ProblemProblem

How much work is done on a vacuum How much work is done on a vacuum cleaner pulled 3 m by a force of 50 N at cleaner pulled 3 m by a force of 50 N at an angle of 30° above the horizontal?an angle of 30° above the horizontal?

W = (FcosW = (Fcosθ)xθ)x W = ?W = ? F = 50NF = 50N

d = 3md = 3m θ = 30°θ = 30°

W W = (50N)(cos30°)(3m) = (50N)(cos30°)(3m)

= 130 J= 130 J

ENERGYENERGY

Kinetic Energy:Kinetic Energy:

* * Energy associated with an object in Energy associated with an object in motionmotion

* Depends on speed and mass* Depends on speed and mass

* Scalar quantity * Scalar quantity

* SI unit for all forms of energy = * SI unit for all forms of energy = Joule (J)Joule (J)

KE = ½ mvKE = ½ mv22

KE = ½ x mass x (velocity)KE = ½ x mass x (velocity)22

Kinetic EnergyKinetic Energy

If a bowling ball and a soccer ball are If a bowling ball and a soccer ball are traveling at the same speed, which do traveling at the same speed, which do you think has more kinetic energy?you think has more kinetic energy?


* Both are moving with identical speeds* Both are moving with identical speeds

* Bowling ball has more mass than the soccer ball * Bowling ball has more mass than the soccer ball Bowling ball has more kinetic energy Bowling ball has more kinetic energy

Kinetic Energy ProblemKinetic Energy Problem

A 7 kg bowling ball moves at 3 m/s. How A 7 kg bowling ball moves at 3 m/s. How fast must a 2.45 g tennis ball move in fast must a 2.45 g tennis ball move in order to have the same kinetic energy order to have the same kinetic energy as the bowling ball?as the bowling ball?

Velocity of tennis ball = 160 m/sVelocity of tennis ball = 160 m/s

Work-Kinetic Energy Work-Kinetic Energy TheoremTheorem

Work-kinetic Energy Theorem:Work-kinetic Energy Theorem:• Net work done on a particle equals the Net work done on a particle equals the

change in its kinetic energy (KE)change in its kinetic energy (KE)

W = W = ΔKEΔKE

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PROBLEMPROBLEM

What is the soccer ball’s speed What is the soccer ball’s speed immediately after being kicked? immediately after being kicked? Its mass is 0.42 kg.Its mass is 0.42 kg.

PROBLEMPROBLEM

What is the soccer ball’s speed What is the soccer ball’s speed immediately after being kicked? immediately after being kicked? Its mass is 0.42 kg.Its mass is 0.42 kg.

W = F ∙ ΔxW = F ∙ Δx

W = (240 N) (0.20 m) = 48 JW = (240 N) (0.20 m) = 48 J

W = ΔKE = 48 JW = ΔKE = 48 J

KE = ½ mvKE = ½ mv22 = 48 J = 48 J

vv22 = 2(48 J)/0.42 kg = 2(48 J)/0.42 kg

v = 15 m/sv = 15 m/s

On a frozen pond, a person kicks a 10 kg On a frozen pond, a person kicks a 10 kg sled, giving it an initial speed of 2.2 m/s. sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the How far does the sled move if the coefficient of kinetic friction between the coefficient of kinetic friction between the sled and the ice is 0.10?sled and the ice is 0.10?

m = 10 kg vm = 10 kg vii = 2.2 m/s v = 2.2 m/s vff = 0 m/s = 0 m/s μμkk = = 0.100.10

d = ?d = ?


WWnetnet = F = Fnetnetdcosdcosθθ

* Net work done of the sled is provided by the * Net work done of the sled is provided by the force of kinetic frictionforce of kinetic friction

WWnetnet = F = Fkkdcosθ dcosθ F Fkk = μ = μkkN N N = mg N = mg

WWnetnet = μ = μkkmgdcosθmgdcosθ

* The force of kinetic friction is in the direction * The force of kinetic friction is in the direction opposite of d opposite of d θ = 180° θ = 180°

* Sled comes to rest * Sled comes to rest So, final KE = 0 So, final KE = 0

WWnetnet = Δ KE = ½ mv = Δ KE = ½ mv22ff – ½ mv – ½ mv22

ii

WWnetnet = -1/2 mv = -1/2 mv22ii


Use the work-kinetic energy Use the work-kinetic energy theorem, and solve for dtheorem, and solve for d

WWnetnet = = ΔKEΔKE

- ½ mv- ½ mv22i i == μ μkkmgdcosθmgdcosθ

d = 2.5 md = 2.5 m


POWERPOWER

POWER:POWER:

* A quantity that measures the rate at * A quantity that measures the rate at which work is done or energy is which work is done or energy is transformedtransformed

* Power = work / time interval* Power = work / time interval

P = W/P = W/ΔtΔt((W = Fx W = Fx P = Fx/Δt P = Fx/Δt v = x/Δt) v = x/Δt)

* Power = Force x speed* Power = Force x speed

P = FvP = Fv

POWERPOWER

SI Unit for Power:SI Unit for Power:Watt (W) Watt (W) Defined as 1 joule per second Defined as 1 joule per second (J/s)(J/s)

Horsepower = Another unit of powerHorsepower = Another unit of power

1 hp = 746 watts1 hp = 746 watts

POWER PROBLEMPOWER PROBLEM

A 193 kg curtain needs to be raised A 193 kg curtain needs to be raised 7.5 m, in as close to 5 s as possible. 7.5 m, in as close to 5 s as possible. The power ratings for three motors The power ratings for three motors are listed as 1 kW, 3.5 kW, and 5.5 are listed as 1 kW, 3.5 kW, and 5.5 kW. What motor is best for the job? kW. What motor is best for the job?


m = 193 kgm = 193 kg Δt = 5s Δt = 5s d =7.5md =7.5m

P = ?P = ?

P = W/ΔtP = W/Δt

= Fx/Δt= Fx/Δt

= mgx/Δt= mgx/Δt

= (193kg)(9.8m/s= (193kg)(9.8m/s22)(7.5m)/5s)(7.5m)/5s

= 280 W = 280 W 2.8 kW 2.8 kW**** Best motor to use = 3.5 kW motor. The 1 kW motor will not lift the Best motor to use = 3.5 kW motor. The 1 kW motor will not lift the

curtain fast enough, and the 5.5 kW motor will lift the curtain too fastcurtain fast enough, and the 5.5 kW motor will lift the curtain too fast

POTENTIAL ENERGYPOTENTIAL ENERGY

Potential Energy:Potential Energy:

* Stored energy* Stored energy

* Associated with an object that has the * Associated with an object that has the potential to move because of its position potential to move because of its position relative to some other locationrelative to some other location

Example:Example:

Balancing rock- Arches National Park, UtahBalancing rock- Arches National Park, Utah

Delicate Arch- Arches National Park, UtahDelicate Arch- Arches National Park, Utah

GRAVITATIONAL POTENTIAL ENERGY- Definition

Gravitational potential energy PEg is the energy anobject of mass m has by virtue of its position relative to the surface of the earth. That position is measured by the height h of the object relative to an arbitrary zero level:

PEg = mgh

SI Unit = Joule (J)

ProblemProblem

What is the bucket’s What is the bucket’s gravitational potential energy?gravitational potential energy?

ProblemProblem

What is the bucket’s What is the bucket’s gravitational potential energy?gravitational potential energy?

PE = mghPE = mgh

PE = (2.00 kg)(9.80 m/s2)(4.00 m)PE = (2.00 kg)(9.80 m/s2)(4.00 m)

PE = 78.4 JPE = 78.4 J

Gravitational Potential EnergyGravitational Potential Energy

Example: A Gymnast on a Trampoline

The gymnast leaves the trampoline at an initial height of 1.20 mand reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the gymnast?

Gravitational Potential EnergyGravitational Potential Energy

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Elastic Potential EnergyElastic Potential Energy

* Energy stored in any compressed or * Energy stored in any compressed or stretched objectstretched object

Spring, stretched strings of a tennis racket or guitar, Spring, stretched strings of a tennis racket or guitar, rubber bands, bungee cords, trampolines, an arrow rubber bands, bungee cords, trampolines, an arrow drawn into a bow, etc.drawn into a bow, etc.

SpringsSprings

When an external force compresses or When an external force compresses or stretches a spring stretches a spring Elastic potential Elastic potential energy is stored in the springenergy is stored in the spring

The more stretch, the more stored energyThe more stretch, the more stored energy

For certain springs, the amount of force is directly For certain springs, the amount of force is directly proportional to the amount of stretch or proportional to the amount of stretch or compression (x); compression (x); Constant of proportionality is known as the spring constant (k)Constant of proportionality is known as the spring constant (k)

FFspringspring = k * x = k * x

Hooke’s LawHooke’s Law

If a spring is not stretched or If a spring is not stretched or compressed compressed no potential energy is no potential energy is being stored being stored Spring is in an Spring is in an Equilibrium positionEquilibrium position

Equilibrium positionEquilibrium position: : Position spring Position spring naturally assumes when there is no force naturally assumes when there is no force applied to itapplied to it

Zero potential energy positionZero potential energy position

Hooke’s LawHooke’s Law

Special equation for springsSpecial equation for springs Relates the amount of elastic potential Relates the amount of elastic potential

energy to the amount of stretch (or energy to the amount of stretch (or compression) and the spring constantcompression) and the spring constant

PEPE elastic elastic = ½kx = ½kx22

k = Spring constant (N/m)k = Spring constant (N/m)

Stiffer the spring Stiffer the spring Larger the spring constant Larger the spring constant

x = Amount of compression relative to the equilibrium x = Amount of compression relative to the equilibrium position position

Potential Energy Potential Energy ProblemProblem

A 70 kg stuntman is attached to a bungee cord A 70 kg stuntman is attached to a bungee cord with an unstretched length of 15 m. He jumps off with an unstretched length of 15 m. He jumps off the bridge spanning a river from a height of 50m. the bridge spanning a river from a height of 50m. When he finally stops, the cord has a stretched When he finally stops, the cord has a stretched length of 44 m. Treat the stuntman as a point length of 44 m. Treat the stuntman as a point mass, and disregard the weight of the bungee mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops energy relative to the water when the man stops falling? falling?

* Zero level for gravitational potential energy is * Zero level for gravitational potential energy is chosen to be the surface of the waterchosen to be the surface of the water

* Total potential energy * Total potential energy sum of the gravitational sum of the gravitational & elastic potential energy& elastic potential energy

PEPEtotaltotal = PE = PEgg + PE + PEelasticelastic

= mgh + ½ kx= mgh + ½ kx22

* Substitute the values into the equation* Substitute the values into the equation

PEPEtotaltotal = 3.43 x 10 = 3.43 x 1044 J J

Potential Energy Potential Energy ProblemProblem

Potential EnergyPotential Energy

The energy stored in an object due to The energy stored in an object due to its position relative to some zero its position relative to some zero positionposition An object possesses gravitational An object possesses gravitational

potential energy if it is positioned at a potential energy if it is positioned at a height above (or below) the zero height height above (or below) the zero height

An object possesses elastic potential An object possesses elastic potential energy if it is at a position on an elastic energy if it is at a position on an elastic medium other than the equilibrium medium other than the equilibrium position position

Linking Work to Linking Work to Mechanical EnergyMechanical Energy

WORKWORK is a force acting upon an is a force acting upon an object to cause a displacement object to cause a displacement

When work is done upon an object, When work is done upon an object, that object gains energythat object gains energy

Energy acquired by the objects upon Energy acquired by the objects upon which work is done is known as which work is done is known as MECHANICAL ENERGYMECHANICAL ENERGY

Mechanical EnergyMechanical Energy

Objects have mechanical energy if Objects have mechanical energy if they are in motion and/or if they are they are in motion and/or if they are at some position relative to a at some position relative to a zero zero potential energy positionpotential energy position

Total Mechanical EnergyTotal Mechanical Energy

*Total Mechanical Energy*Total Mechanical Energy: : The sum of The sum of kinetic energy & all forms of potential energykinetic energy & all forms of potential energy

1. Kinetic Energy (Energy of motion)1. Kinetic Energy (Energy of motion)


2. Potential Energy 2. Potential Energy (Stored energy of position)(Stored energy of position)

a. Gravitational a. Gravitational

PEPEgg = mgh = mgh

b. Elastic b. Elastic

PEPEelastic elastic = ½ kx= ½ kx22


CONSERVATION OF MECHANICAL ENERGY:CONSERVATION OF MECHANICAL ENERGY:* In the absence of friction, mechanical energy is * In the absence of friction, mechanical energy is conserved, so the amount of mechanical energy conserved, so the amount of mechanical energy remains constantremains constant

MEMEii = ME = MEffInitial mechanical energy = final mechanical energyInitial mechanical energy = final mechanical energy

(in the absence of friction)(in the absence of friction)

PEPEi i + KE+ KEii = PE = PEf f + KE+ KEff

mghmghii + ½ mv + ½ mvii2 2 = mgh = mghff + ½ mv + ½ mvff

22

Conservation of Energy Conservation of Energy ProblemProblem

Starting from rest, a child zooms Starting from rest, a child zooms down a frictionless slide from an down a frictionless slide from an initial height of 3 m. What is her initial height of 3 m. What is her speed at the bottom of the slide? speed at the bottom of the slide? (Assume she has a mass of 25 kg)(Assume she has a mass of 25 kg)


hhii = 3m = 3m m = 25kgm = 25kg vvii = 0 m/s = 0 m/s

hhff = 0m = 0m vvff = ? = ?• Slide is frictionless Slide is frictionless Mechanical energy is conserved Mechanical energy is conserved• Kinetic energy & potential energy = only forms of energy Kinetic energy & potential energy = only forms of energy

presentpresent• KE = ½ mvKE = ½ mv22 PEPEgg = mgh = mgh

• Final gravitational potential energy = zero (Bottom of the Final gravitational potential energy = zero (Bottom of the slide) slide) PE PEgfgf = 0 = 0

• Initial gravitational potential energy Initial gravitational potential energy Top of the slide Top of the slide PEPEgigi = mgh = mghii (25kg)(9.8m/s (25kg)(9.8m/s22)(3m) = 736 J)(3m) = 736 J


hhii = 3m = 3m m = 25kgm = 25kg vvii = 0 m/s = 0 m/s

hhff = 0m = 0m vvff = ? = ?• Initial Kinetic Energy = 0, because child starts at restInitial Kinetic Energy = 0, because child starts at rest

• KEKEii = 0 = 0

• Final Kinetic EnergyFinal Kinetic Energy• KEKEff = ½ mv = ½ mv2 2 ½ (25kg)v ½ (25kg)v22

ff

• MEMEii = ME = MEff

PEPEii + KE + KEi i = PE= PEff + Ke + Keff

736 J + 0 J = 0 J + (1/2)(25kg)(v736 J + 0 J = 0 J + (1/2)(25kg)(v22ff))

vvff = 7.67 m/s = 7.67 m/s

Mechanical Energy Mechanical Energy Ability to do WorkAbility to do Work

An object that possesses mechanical An object that possesses mechanical energy is able to do workenergy is able to do work

Its mechanical energy enables that object to Its mechanical energy enables that object to apply a force to another object in order to apply a force to another object in order to cause it to be displacedcause it to be displaced

Classic Example Classic Example Massive wrecking ball of Massive wrecking ball of a demolition machinea demolition machine

Mechanical Energy is the Mechanical Energy is the ability to do work…ability to do work…

An object that possesses mechanical An object that possesses mechanical energy (whether it be kinetic energy energy (whether it be kinetic energy or potential energy) has the ability to or potential energy) has the ability to do workdo work

That is… its mechanical energy That is… its mechanical energy enables that object to apply a force enables that object to apply a force to another object in order to cause it to another object in order to cause it to be displacedto be displaced


Work is a force acting on an object to Work is a force acting on an object to cause a displacementcause a displacement

In the process of doing work In the process of doing work the the object which is doing the work object which is doing the work exchanges energy with the object exchanges energy with the object upon which the work is doneupon which the work is done

When work is done up the object When work is done up the object that object gains energythat object gains energy


A weightlifter applies a force to A weightlifter applies a force to cause a barbell to be displacedcause a barbell to be displaced Barbell now possesses mechanical Barbell now possesses mechanical

energy- all in the form of potential energy- all in the form of potential energyenergy

** The energy acquired by the objects ** The energy acquired by the objects upon which work is done is known as upon which work is done is known as mechanical energymechanical energy

Mechanical Energy is the Mechanical Energy is the ability to do work…ability to do work…

Examples on website:Examples on website:

Massive wrecking ball of a demolition Massive wrecking ball of a demolition machinemachine

The wrecking ball is a massive object which is The wrecking ball is a massive object which is swung backwards to a high position and allowed to swung backwards to a high position and allowed to swing forward into a building structure or other swing forward into a building structure or other object in order to demolish itobject in order to demolish it

Upon hitting the structure, the wrecking ball Upon hitting the structure, the wrecking ball applies a force to it in order to cause the wall of the applies a force to it in order to cause the wall of the structure to be displacedstructure to be displaced

Mechanical energy = ability to do work

Work- Energy TheoremWork- Energy Theorem

Categorize forces based upon whether or not Categorize forces based upon whether or not their presence is capable of changing an their presence is capable of changing an object’s total mechanical energyobject’s total mechanical energy

* Certain types of forces, which when present * Certain types of forces, which when present and when involved in doing work on objects, will and when involved in doing work on objects, will change the total mechanical energy of the objectchange the total mechanical energy of the object

* Other types of forces can never change the * Other types of forces can never change the total mechanical energy of an object, but rather only total mechanical energy of an object, but rather only transform the energy of an object from PE to KE or transform the energy of an object from PE to KE or vice versavice versa

** Two categories of forces ** Two categories of forces Internal & External Internal & External


External Forces:External Forces:Applied force, normal force, tension force, Applied force, normal force, tension force,

friction force and air resistance forcefriction force and air resistance force

Internal Forces:Internal Forces:Gravity forces, spring forces, electrical Gravity forces, spring forces, electrical

forces and magnetic forcesforces and magnetic forces


THE BIG CONCEPT!!THE BIG CONCEPT!!

* * When the only type of force doing net work upon When the only type of force doing net work upon an object is an internal force (gravitational and an object is an internal force (gravitational and spring forces) spring forces)

Total mechanical energy (KE + PE) of that Total mechanical energy (KE + PE) of that object remains constantobject remains constant

Object’s energy simply changes form Object’s energy simply changes form Conservation of EnergyConservation of Energy

** Ex) As an object is “forced” from a high elevation to a lower ** Ex) As an object is “forced” from a high elevation to a lower elevation by gravity elevation by gravity Some of the PE is transformed into KE Some of the PE is transformed into KE (Yet, the sum of KE + PE = remains constant) (Yet, the sum of KE + PE = remains constant)



* If only internal forces are doing work * If only internal forces are doing work energy energy changes forms (KE to PE or vice versa) changes forms (KE to PE or vice versa) total total mechanical energy is therefore conservedmechanical energy is therefore conserved

* Internal forces – referred to as conservative forces * Internal forces – referred to as conservative forces

Quick Quiz

Work-Energy Work-Energy RelationshipRelationship

Analysis of situations in which work is conserved Analysis of situations in which work is conserved only only internal forces are involvedinternal forces are involved

TMETMEi i + W+ WEXTEXT = TME = TMEff

(Initial amount of total mechanical energy (TME(Initial amount of total mechanical energy (TMEii) plus the work done by external forces ) plus the work done by external forces (W(WEXTEXT) ) equals the final amount of total mechanical energy (TME equals the final amount of total mechanical energy (TMEff))))

KEKEii + PE + PEii + W + Wextext = KE = KEff + PE + PEff

KEKEii + PE + PEii = KE = KEff + Pe + Peff

Website



* Forces are categorized as being either internal * Forces are categorized as being either internal or external based upon the ability of that type of or external based upon the ability of that type of force to change an object’s total mechanical force to change an object’s total mechanical energy when it does work upon an objectenergy when it does work upon an object

* Net work done upon an object by an * Net work done upon an object by an external force external force Changes the total mechanical Changes the total mechanical energy (KE + PE) of the objectenergy (KE + PE) of the object

Positive work = object gained Positive work = object gained energyenergy

Negative work = object lost energy Negative work = object lost energy



* Gain or loss in energy can be in the form of* Gain or loss in energy can be in the form of

PE, KE, or bothPE, KE, or both

Under such circumstances, the work which Under such circumstances, the work which is done is equal to the change in mechanical is done is equal to the change in mechanical energy of the objectenergy of the object

** External forces ** External forces capable of changing the total capable of changing the total mechanical energy of an object (Nonconservative mechanical energy of an object (Nonconservative forces)forces)

Work-Energy Work-Energy RelationshipRelationship

Analysis of situations involving external Analysis of situations involving external forcesforces

TMETMEi i + W+ WEXTEXT = TME = TMEff

(Initial amount of total mechanical energy (TME(Initial amount of total mechanical energy (TMEii) plus the work ) plus the work done by external forces (Wdone by external forces (WEXTEXT) ) equals the final amount of total equals the final amount of total mechanical energy (TMEmechanical energy (TMEff))))

KEKEii + PE + PEii + W + Wextext = KE = KEff + PE + PEff

Practice Problems

DEFINITION OF A CONSERVATIVE FORCE

Version 1 A force is conservative when the work it does on a moving object is independent of the path between the object’s initial and final positions.

Version 2 A force is conservative when it does no work on an object moving around a closed path, starting and finishing at the same point.

Conservative Versus Nonconservative ForcesConservative Versus Nonconservative Forces


Version 1 A force is conservative when the work it does on a moving object is independent of the path between the object’s initial and final positions.

fo hhmgW gravity


Version 2 A force is conservative when it does no work on an object moving around a closed path, starting andfinishing at the same point.

fo hh fo hhmgW gravity


An example of a nonconservative force is the kinetic frictional force.

dfdfdFW kk 180coscos

The work done by the kinetic frictional force is always negative. Thus, it is impossible for the work it does on an object that moves around a closed path to be zero.

The concept of potential energy is not defined for a nonconservative force.


In normal situations both conservative and nonconservativeforces act simultaneously on an object, so the work done bythe net external force can be written as

ncc WWW

KEKEKE of W

PEPEPE fogravity foc mghmghWW


ncc WWW

ncW PEKE

THE WORK-ENERGY THEOREM

PEKE ncW

The Conservation of Mechanical EnergyThe Conservation of Mechanical Energy

ofof PEPEKEKEPEKE ncW

ooff PEKEPEKE ncW

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If the net work on an object by nonconservative forcesis zero, then its energy does not change:

of EE


THE PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGY

The total mechanical energy (E = KE + PE) of an objectremains constant as the object moves, provided that the network done by external nonconservative forces is zero.


Example A Daredevil Motorcyclist

A motorcyclist is trying to leap across the canyon by driving horizontally off a cliff at 38.0 m/s. Ignoring air resistance, findthe speed with which the cycle strikes the ground on the otherside.


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Nonconservative Forces and the Work-Energy Nonconservative Forces and the Work-Energy TheoremTheorem

THE WORK-ENERGY THEOREM

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Example Fireworks

Assuming that the nonconservative forcegenerated by the burning propellant does425 J of work, what is the final speedof the rocket. Ignore air resistance. The massof the rocket is 0.2kg.

2

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POWERPOWER

POWER:POWER:

* A quantity that measures the rate at * A quantity that measures the rate at which work is done or energy is which work is done or energy is transformedtransformed

* Power = work / time interval* Power = work / time interval

P = W/P = W/ΔtΔtW = Fd W = Fd P = Fd/Δt P = Fd/Δt v = d/Δt v = d/Δt

* Power = Force x speed* Power = Force x speed

P = FvP = Fv

POWERPOWER

SI Unit for Power:SI Unit for Power:Watt (W) Watt (W) Defined as 1 joule per second Defined as 1 joule per second (J/s)(J/s)

Horsepower = Another unit of powerHorsepower = Another unit of power

1 hp = 746 watts1 hp = 746 watts


A 193 kg curtain needs to be raised A 193 kg curtain needs to be raised 7.5 m, in as close to 5 s as possible. 7.5 m, in as close to 5 s as possible. The power ratings for three motors The power ratings for three motors are listed as 1 kW, 3.5 kW, and 5.5 are listed as 1 kW, 3.5 kW, and 5.5 kW. What motor is best for the job? kW. What motor is best for the job?


m = 193 kgm = 193 kg Δt = 5s Δt = 5s d =7.5md =7.5m

P = ?P = ?

P = W/ΔtP = W/Δt

= Fd/Δt= Fd/Δt

= mgd/Δt= mgd/Δt

= (193kg)(9.8m/s= (193kg)(9.8m/s22)(7.5m)/5s)(7.5m)/5s

= 280 W = 280 W 2.8 kW 2.8 kW**** Best motor to use = 3.5 kW motor. The 1 kW motor will not lift the Best motor to use = 3.5 kW motor. The 1 kW motor will not lift the

curtain fast enough, and the 5.5 kW motor will lift the curtain too fastcurtain fast enough, and the 5.5 kW motor will lift the curtain too fast

THE PRINCIPLE OF CONSERVATION OF ENERGY

Energy can neither be created nor destroyed, but can only be converted from one form to another.

* Disclaimer: This powerpoint presentation is a compilation of various works.

QuestionQuestion

A cart is loaded with a brick and pulled at A cart is loaded with a brick and pulled at constant speed along an inclined plane to the constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?of the loaded cart at the height of the seat-top?

PE = m*g*hPE = m*g*h

PE = (3 kg ) * (9.8 m/s/s) * (0.45m) PE = (3 kg ) * (9.8 m/s/s) * (0.45m) PE = 13.2 JPE = 13.2 J

QuestionQuestion

If a force of 14.7 N is used to drag the loaded If a force of 14.7 N is used to drag the loaded cart (from previous question) along the incline cart (from previous question) along the incline for a distance of 0.90 meters, then how much for a distance of 0.90 meters, then how much work is done on the loaded cart?work is done on the loaded cart?

W = F * d * cos ThetaW = F * d * cos Theta

W = 14.7 N * 0.9 m * cos (0 degrees)W = 14.7 N * 0.9 m * cos (0 degrees)

W = 13.2 J W = 13.2 J (Note: The angle between F and d is 0 degrees because the F (Note: The angle between F and d is 0 degrees because the F and d are in the same direction)and d are in the same direction)

topic 5: work, energy & power. work definition of work: definition of work: when a force causes...

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