Work, Energy, and PowerWork

What is Work and Energy?

• Energy(E)- the ability to do work• Work (W)- A change in energy (ΔE) or the product of Force and

distance (d)– W=Fd– Work is only being done when components of the applied force are

parallel to the displacement• Both are scalar and are measured in joules

– 1 joule=kg m2/s2 or 1 joule=N*m

When is work being done?

• If a hold a 30 kg object at a height of 1.5 meters is work being done?

• I am exerting energy….• Work is NOT being done on the OBJECT, work is being done on

muscles, but not the object• The distance that the object has moved is zero so no work is done• W=Fd W=F0

Example

• If the same 30 kg object was pushed to the right with an acceleration of 2m/s2 for 2.0 meters, how much work is done on the object?

• W=Fd• Remember F=ma• M=30 kg• a=2 m/s2

• d=2.0 m• W=?• F=ma• F=30(2) = 60N• W=Fd• W=60(2) =120 J

Example

• If I were to lift the 30.0 kg object up off the ground to a height of 1.5 m, how much work is done on the object?

• When an object is being lifted against gravity, use g for the acceleration (9.8 m/s2)

• W=mgd• m=30 kg• g=9.8 m/s2

• d=1.5 m• W=?• W=30(9.8)(1.5) W= 440 J

Clicker Question

• A 3.0 kg pineapple is held 1.2 m above the floor for 15 s. How much work is done on the pineapple?

• A)0.25 J• B)54 J• C)35 J• D) 0 J

Clicker Question

• A 10.0 kg pumpkin is moved horizontally 5.00 m at a constant velocity across a level floor using a horizontal force of 3.00 N. How much work is done in moving the pumpkin?

• A) 30 J• B) 294 J• C) 15 J• D) 0 J

Example- Honors

• A 50.0 kg banana box is pulled 11.0 m along a level surface by a rope. If the rope makes an angle with the floor of 35o and the tension in the rope is 90.0 N, how much work is done on the box?

• Use the force component that is parallel to the displacement! • m=50.0 kg• d=11.0 m• Theta=35 degrees• Fapplied=90.0 N• W=?• W=Fd• F(x)=?

Example

• A 1385 kg car traveling at 61 km/h is brought to a stop while skidding 42 m. What is the work done on the car by frictional forces?

• m=1385 kg• vi-=61 km/hr • Vi=17 m/s • Δx=42 m• Vf=0 • W=?• W=Fd• F=?• F=ma

Nonconservative Forces

• The work produced by nonconservative forces are dependent on the paths taken

• Friction and air resistance are types of nonconservative forces• A conservative force, such as gravity, are not dependent on the

path taken

How does an angle impact work?

1.0m10 Kg A

B10

Kg

If you have a 10.0 kg object, how much work is done on the object if it is lifted 1 meter straight off the ground? On a ramp that is 30 degrees off the ground (A)? 60 degrees(B)?

How does an angle impact work?

1.0m10 Kg A

B10

Kg

Wf = Ffd

Ff = ukFN

FN gets largeras the angle getssmaller

So… Ff gets smaller,But you still need to Add the FgSo the workIncreases with a Higher angle

Continued

• Work against gravity will not change, however!• If they end at the same height the work against gravity will not

change• The amount of force needed will change according to the angle,

but the distance will change as well to get to the same height• So the work against gravity is the SAME

Work, Energy, and PowerPotential Energy

Potential Energy

• Energy can either be potential energy or kinetic energy• Potential energy is stored energy• Examples

– Chemical– Elastic (bungee cord, trampoline, bow)– Electrical (static charges)– Gravitational potential energy

Energy can be converted into different forms by doing work

Gravitational Potential Energy

• Due to an object’s position (height) measured relative to a reference point

• Gravitational Potential Energy – Ep (or GPE)

• Ep=mgh• m=mass• g=9.8 m/s2

• h=height

Example

• A 15.0 kg textbook is sitting on a 1.20 m tall table. If the book is lifted 0.80 m above the table, how much gravitational potential energy does it have:

• With respect of the table?• With respect to the ground?

Clicker Question

• A 1400 kg roller coaster is moved to the top of a track that is 100 m above the lowest part of the track. What is the gravitional potential energy of the coaster?

• A) 2000 J• B) 1.4 x 104

• C) 34000 J• D)1.4 x 106 J

Spring/Elastic Potential Energy

• The energy available for use in deformed elastic objects– Rubber bands, springs in trampolines, pole-vault poles, muscles

• For springs, the distance compressed or stretched = x• Spring constant (k) depends on stiffness of spring, measured in N/m

– Force needed to stretch the spring 1 meter

Example

• When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table

• What is the gravitational potential energy associated with the mass relative to the table?

• What is the spring’s elastic potential energy is the spring constant is 400.0 N/m?

Work, Energy and PowerKinetic Energy

Kinetic Energy

• Energy of motion• scalar• Ek=1/2 m v2

– Ek= kinetic energy– m=mass– v=speed

Example

• A 60.0 kg student is running at a uniform speed of 5.70 m/s. What is the kinetic energy of the student? • Ek=1/2 m v2

• m=60 kg• v=5.70 m/s• Ek=?

• Ek=1/2(60)(5.7)2

• Ek=975 J

Clicker Question

• The kinetic energy of a 2.1 kg rotten tomato is 1000 J. How fast is it moving?

• A) 15.4 m/s• B) 31 m/s• C) 961 m/s• D) 4000 m/s

Work Energy Theorem

• If a net force is acting on an objet then the object must be accelerating

• The change in kinetic energy is proportional to the net force• ΔEk=Fnetd• d=distance

Example

• A sprinter exerts a net force of 260 N over a distance of 35 meters. What is his change in kinetic energy?

• ΔEk=Fnetd• Fnet=260 N• d= 35 m• ΔEk=?

• ΔEk=260 (35)

• ΔEk=9100 J

Example

• A student pushes a 25 kg crate which is initially at rest with a force of 160 N over a distance of 15 meters. If there is 75 N of friction, what is the final speed of the crate?

• ΔEk=Fnetd

• Ek=1/2mv2

• m=25 kg• F applied=160 N• d=15 m• Ff=75 N

Work, Energy, and PowerConservation of Energy

Law of Conservation of Energy

• Energy cannot be created or destroyed, only converted into other forms of energy

• TOTAL energy is always conserved • Potential energy can be converted to

kinetic energy as an object moves• When only conservative forces act on

object potential energy is completely converted to kinetic energy

• When nonconservative forces like friction act on an object, some energy will be converted to heat

Mechanical Energy

• Mechanical Energy is the sum of kinetic energy and all forms of potential energy associated with an object

• ME=KE + PE• When only conservative forces act on an object then mechanical

energy is conserved

Law of Conservation of Energy (Quantitatively)

• Initial Energy= Final Energy– Ei = Ef

– GPEi + Kei = GPEf + Kef

– mghi + ½ mv2i = mghf + ½ mv2

f

• GPE=gravitational potential energy

Example

• A student falls from the building, if they reach the ground at 5.0 m/s , what height did they fall from?

• Vf=5.0 m/s• Hi=?• Vi=0• Hf=0• GPEi + KEi= GPEf + KEf

Example

• While jumping over The Great Wall of China an 82 kg skateboarder is needs to leave the ramp traveling at 22 m/s. A) How much potential energy is needed to jump over? B) What minimum height should the ramp be?

• m=82 kg• Vf=22 m/s• g=9.8 m/s2

• GPE=?• h=?• Ei=Ef

• GPEi + KEi= GPEf + KEf

• GPEi =Kef

• GPE = ½ mv2f

Clicker Question

• A 66 kg skateboarder jumps The Great Wall of China, clearly. At the peak of jump he is 18 m high and traveling at 12 m/s . Assuming he started at rest, find his initial height.

• A) 10 m• B) 19 m• C) 25 m• D) 30 m

Clicker Question

• A 75 kg snowboarder slides up a frictionless rail to a height of 1.75m and slides across it at 2.50 m/s. How much kinetic energy did he have before he went up the rail?

• A) 1520 J• B) 1380 J• C) 200 J• D) Impossible to solve

Roller Coasters

• Although not perfectly energy efficient, they are a fun way to view how work, gravitational potential and kinetic energy are exchanged

The Downhill skier

• When a nonconservative force is applied (friction) the work is negative because it is removing energy from the system

What’s this?

Work, Energy, and PowerPower

Power

• Power (P) is the rate of doing work• Measured in J/s or Watts (W)• Power= Work/time• P=W/t or P=ΔE/t

Clicker Question

• Mike performed 5 J of work in 10 seconds. Joe did 3 J of work in 5 seconds. Who produced the greater power?

• A) Mike• B) Joe• C) Both produced the same amount of power

Example

• Lover’s Leap is a 122 m vertical climb. The record time of 4 min 25 s was achieved by Dan Osman (65 kg). What was his average power output during the climb?

• h=122 m• t=4 min 25 s 265 s• m=65 kg• g=9.8 m/s2

• P=?• P=W/t or P= ΔE/t

Example

• A 1.00x103 kg car accelerates from rest to a velocity of 15.0 m/s in 4.00 s. Calculate the power output of the car. Ignore friction.

• m=1.00 x 103 kg• Vf=15 m/s • t=4.00 s• P=?• P=W/t or P=ΔE/t

Clicker Question

• A 68 kg student runs up a flight of stairs 3.2 m high in 4.8 seconds. Determine their power output while running up the stairs.

• A) 217.6 W• B) 45.33 W • C) 440 W• D) There is no work in this problem, not enough info

Clicker Question

• A 642 kg formula 1 car can reach a speed of 27.78 m/s in 1.7 seconds. What is the power output of the car during this acceleration?

• A) 300,000 W• B) 5000 W• C) 150,000 W• D) 3000 W

Another Useful Formula

• P=W/t• P=Fd/t

– V=d/t• So..• P=FV• Note this formula is only useful when the velocity is held constant

Example

• A student uses 140 N to push a block up a ramp at a constant velocity of 2.2 m/s. What is their power output?

• F=140 N• V=2.2 m/s• P=?• P=FV• P=140 (2.2)• P=310 W

Clicker Question

• An elevator motor has a power rating of 110 kW. How much force would it exert if it was lifting a load at a constant velocity of 3.0 m/s?

• A) 3700 N• B) 37 N• C) 330 N• D) 4 N

Work, Energy, PowerEfficiency

Efficiency

• A measure of how much of the energy that goes into a machine actually gets used

• Machines are useful because they allow us to use less force over a longer distance to do the same work

Efficiency of a Machine

• Eff= W out x 100 W in

• Eff= P out x 100 P in

• There are no units for efficiency because it is a percentage

Example

A lever is used to lift a 50.0 kg object 10.0 cm. To do this we must apply a force of 75 N to the end of the lever which displaces 1.00 m. Find the efficiency of the lever• What are the output variables?• m=50.0 kg• d=10.0 cm or 0.10 m• What are the input variables?• F=75 N• d=1.00 m

Work, Energy, and PowerThermal Energy

Thermal Energy Versus Temperature

• Thermal Energy or Heat (q) - the total amount of kinetic energy and potential energy of the particles in an object

• Temperature- The average kinetic energy of the particles in an object

• Temperature is an indirect measurement of heat

• Which has more heat a massive iceberg or a pot of boiling water?

Changes in States of Matter

• All particles have kinetic energy• Solids have the lowest amount of kinetic energy and gases (and

plasmas) have the highest amount of kinetic energy• If heat is added to an object the molecules will gain kinetic energy

and as a result they will generally expand

Changes in States of Matter

• If an object is heated it will either• 1) increase temperature • 2)Change state in matter

Discussion Question

• Why is it better to leave sodas to cool in an ice chest of ice rather than an ice chest of 0°C liquid water?

The Flow of Heat

• Heat always flows from high to low concentration by either– Conduction • Contact

– Convection• Movement of fluid

– Radiation• No medium required

• This transfer occurs until thermal equilibrium is achieved

Specific Heat Capacity

• Specific heat capacity is the amount of heat energy required to heat 1 gram (or kg)of a substance by 1 °C

• What does it mean when a substance has a higher specific heat capacity?

• The larger c is, the more energy required to heat the substance

Discussion Question

• Why is water a better choice to be used as a coolant instead of any of the choices below?

Measurement of Heat

• The amount of heat transferred to an object is found with• Q=mcΔt• Q=heat• m=mass• c=specific heat capacity (J/kg °C)• Δt=change in temperature (tf-ti) (°C)

Example

• Ms. K makes a cup of tea by boiling 250 g of water that is initially at 15° C. How much heat is needed?

• m= 250 g 0.250 kg• Ti=0 ° C• Tf=100 °C• c=4180 J/kg °C• q=?• Q=mcΔt• Q=(0.250)(4180)(100-15)• Q=88825 J

Conservation of Heat

• Heat lost=heat gained• If an object cools down the energy lost from this “hot” object is

gained from the surroundings

Example

• A 0.240 kg chunk of iron is heated to 215 oC and quickly placed into 0.275 kg of water that has a temperature of 12 oC. What will the final temperature of the water be?

• Metal• m=0.240 kg• Ti=215 °C• C=448 J/kg°C• Water• m=0.275 kg• Ti=12°C• C=4180 J/kg°C• Tf=?

What is entropy?

• Entropy (ΔS)- measurement of disorder • ΔS=Q/T Q=heat T= temperature• Entropy increases when heat is added to a substance, and

decreases when heat is removed• Which has more entropy, a gas or a liquid?• A gas• What happens to the entropy as water freezes?• The entropy of the water decreases since it becomes more ordered

and the entropy of the surrounding air increases

What is Internal Energy?

• Internal Energy (U) is the energy a substance has due to the motion of the particles (kinetic energy) and the position of the particles (potential energy).

Predict the appearance of the bar graphs at points c, d, and e.

Conservation of Energy

How are work and heat related?

• Energy can be converted into work or heat• ΔU = Q + W