No work is done because there is no movement (d = 0) · 3 4 | 18 Energy • The ability to do work. An object or system that possesses energy has the ability to do work • When work

1

3 | 10http://themalloryfamily.net

CHAPTER 4Work

http://themalloryfamily.net 4 | 11

Work

• Work - the product of the magnitude of the force (F) and the parallel distance (d) through which the object moves

• work = force x parallel distance• W = Fd• Mechanically, work involves both force and

motion

Section 4.1

http://themalloryfamily.net 4 | 12 http://themalloryfamily.net 4 | 13

No work is done because there is no movement (d = 0)

Section 4.1

•10 •11

•12 •13

2

http://themalloryfamily.net 4 | 14 http://themalloryfamily.net 4 | 15

Work Being Done Applied force (F) through a distance (d)

Section 4.1


Work - Units

• SI System– W = Fd newton x meter = Nꞏm = joule (J)

• British System– W = Fd pound x foot = foot-pound (ft-lb)

Section 4.1

Nꞏm = joule (J)N = newton = kgꞏm/s2

J = kgꞏm2/s2


Working against Something

• When work is done, we generally feel the other part of Newton’s third-law force acting against us

• Gravity and friction are common agents working against work

• In the case of gravity, we must apply force to overcome the force of gravity (weight = w = ma)

• Work = W= Fd = wd = mad – (d is the distance lifted)

Section 4.1

•14 •15

•16 •17

3


Energy

• The ability to do work. An object or system that possesses energy has the ability to do work

• When work is done by a system, the amount of energy of the system decreases ↓

• When work is done on a system, the system gains energy ↑

• Work is the process by which energy is transferred from one object to another

• Work and Energy have the same units – joules

Section 4.2 http://themalloryfamily.net 4 | 19

Kinetic Energy

• Kinetic Energy - the energy an object possesses because of its motion, the energy of motion

• kinetic energy = ½ x mass x (velocity)2

• Ek = ½mv2

• If an object is already moving• Work = change in kinetic energy• W = k = Ek2 – Ek1 = ½mv2

2 - ½mv12

Section 4.2


Potential Energy

• Potential Energy - the energy an object has because of its position or location, the energy of position

• Most potential energy is due to gravity• Remember that:

– Work = Force x distance (W = Fd)– Weight is a force (w = ma where a=9.80 m/s2)

• Therefore W = mad– Grav. potential energy = weight x height

• Ep = madSection 4.2 http://themalloryfamily.net 4 | 21

•18 •19

•20 •21

4


Gravitational Potential Energy

• The gravitational Potential Energy is equal to the work done and this is equal to the weight times the height

• W = Ep = mad• Example: How much work is done lifting a 1.0

kg book to the height of 1m?• Work = W = (1.0 kg) (9.8 m/s2) (1m) = 9.8 J• This is also the amount of Ep that the book has

at a height of 1m


Potential Energy

• Depends only on the initial and final positions (difference in height - d) and is independent of path

• If we disregard any frictional loss, it takes the same amount of work (W) to lift the mass (m), no matter the path

Section 4.2


Work = change in potential energy• Work = W = Ep = mad = mad• In the previous examples the d is actually d• Work is done when there is a change in position• Therefore the reference point for measuring

heights is arbitrary (but must be internally consistent)


Reference Point No matter which scale – d is the same

Section 4.2

•22 •23

•24 •25

5


Conservation of Energy

• Energy can neither be created nor destroyed.• In changing from one form to another, energy is

always conserved• The total energy of an isolated system remains

constant• (total energy)time1 = (total energy) time2• The total energy does not change with time


Conservation of Mechanical Energy

• To simplify we will deal with ideal systems – in which energy is only in two forms – kinetic and potential

• Total Energy = Ek + Ep

• Conservation of energy(Ek + Ep)1 = (Ek + Ep)2

(½mv2 + mad)1 = (½mv2 + mad)2

Section 4.3


Conservation of Energy Finding Kinetic and Potential Energies

• A 0.10 kg stone is dropped from a height of 10.0 m. What will be the kinetic and potential energies of the stone at the heights indicated in the figure (neglect air resistance).

• ET = Ek + Ep will be true at all heights.

• At the moment the stone is released ET= Ep (Ek = 0)

• At the moment the stone hits the ground ET = Ek (Ep = 0)


Solve for Ep and Ek at heights indicated

• At any height, the potential energy Ep = mad

• d = 10 m: Ep = (0.10 kg)(9.8 m/s2)(10.0 m) = 9.8 J• d = 7 m: Ep = (0.10 kg)(9.8 m/s2)(7.0 m) = 6.9 J• d = 3 m: Ep = (0.10 kg)(9.8 m/s2)(3.0 m) = 2.9 J• d = 0 m: Ep = (0.10 kg)(9.8 m/s2)(0 m) = 0 J• ET = Ek + Ep

• Ek = ET - Ep

Section 4.3

•26 •27

•28 •29

6


Solve for Ep and Ek at heights indicated

Height(m)

ET(Joules)

Ep(Joules)

Ek(Joules)

10.0 9.8 9.8 0

7.0 9.8 6.9 2.9

3.0 9.8 2.9 6.9

0 9.8 0 9.8

Section 4.3

ET = Ek + Ephttp://themalloryfamily.net 4 | 31

Magnitude of Velocity

• Potential Energy (Ep) converted = mad• Converted into Kinetic Energy (Ek) = ½mv2

• Since all the Ep is converted into Ek just before hitting the ground, we can use this to compute the speed or magnitude of velocity

• Therefore: ½mv2 = mad• ½v2 = ad (cancel m’s)• v2 = 2ad (solve for v)

Section 4.3

2ad• v =


Power – SI System

• Power - the time rate of doing work

• SI Units J/s = Watt (1 J/s = 1 W)• For example a 100W light bulbs uses 100

joules/second of electrical power or 100 Watts• Careful not to confuse W (work) with W (watt)

Section 4.4

worktime

Wt

Fdt

• Power = = =


Force of 1.0 N to raise a mass 1.0 m, the amount of work done is 1.0 J. If this work is done in 1.0 s, then the power is 1.0 W

Section 4.4

•30 •31

•32 •33

7


Quantity Unit SymbolEquivalent

Units

Force newton N Kgꞏm/s2

Work joule J Nꞏm

Energy joule J Nꞏm

Power watt W J/s

A Review of SI Units


Energy

• No matter what type of energy that we speak of – chemical, electrical, mechanical – the main unifying concept is the conservation of energy

• We cannot create or destroy energy, but we can change it from one form to another

Section 4.5


Forms of Energy

• Thermal (heat) Energy – related to the kinetic and potential energies on a molecular level

• Gravitational potential energy – from an object’s position, stored gravitational energy

• Electrical energy – associated with the motion of electric charges

• Chemical energy – molecular bonds• Radiant energy – sun• Nuclear energy – rearrangement of nuclei

– Fission – breaking apart of larger nuclei– Fusion - smaller nuclei are put together


Fossil Fuels

• Fossil Fuels – oil, gas, coal - from once living organisms; basically stored solar and chemical energy

• Oil – from marine organisms (U.S. imports more than 50% of our needs)

• Gas – from marine organisms (most is produced domestically)

• Coal – from terrestrial (land) plants (the U.S. has large reserves, but environmental problems in coal mining)

• Methane hydrate – crystalline form of natural gas and water (research on possible usage)

Section 4.5

•34 •35

•36 •37

8


Approximate Relative Fuel Consumption in the

U.S.Fuels for Electrical

Generation


Alternate and Renewable Energy Sources

• Alternate energy sources – energy sources not based on fossil fuels or nuclear processes.

• Renewable energy sources – energy sources that cannot be exhausted.

• In large part these types of energies overlap.

Section 4.6


Chapter 4 - Important Equations

• W = Fd (Work)

• Ek = ½mv2 (Kinetic Energy)

• Ep = mgh (Potential Energy)

• Total Energy = Ek + Ep

• P = W/t (Power)

Review

2gh• v =

Quantity Unit SymbolEquivalent Units

Force newton N Kgꞏm/s2

Work joule J Nꞏm

Energy joule J Nꞏm

Power watt W J/s


𝑚 11,000

𝑐 1100

𝑘 1,000

𝑣ΔxΔ𝑡

𝑎Δv⃑Δ𝑡

𝑑12 𝑔𝑡2

𝐹 𝑚𝑎 𝑊 𝑚𝑔 𝐸 ℎ𝑓

𝑊𝑏𝑜𝑦 𝑣𝑏𝑜𝑦 𝑊𝑔𝑖𝑟𝑙 𝑣𝑔𝑖𝑟𝑙(momentum)

𝑊 𝐹𝑑

𝐾𝐸 12 𝑚𝑣2

𝑃𝐸 𝑚𝑎𝑑

𝑣 2𝑔ℎ⃑

𝑃𝑊𝑡

𝑇𝑘 𝑇𝐶 273 𝐻𝑒𝑎𝑡 𝑆𝐻 𝑚 Δ𝑡

𝐻𝑒𝑎𝑡 𝐿𝑓 𝑚

𝐻𝑒𝑎𝑡 𝐿𝑣𝑚 𝑃1

𝑃2

𝑇1

𝑇2

𝑣 𝑓𝜆

𝑇1𝑓

𝑛𝑐

𝑐𝑚

𝑉 𝐼𝑅 𝑃 𝑉𝐼

Stuff you now know…Stuff you need for the Final

•38 •39

•40 •41

9

3 | 42http://themalloryfamily.net

Bring for the final:• Pen (or pencil)• Calculator• 3”x5” card• Ruler• Test 6 (astronomy)


Questions…4. How much work is required to lift a 4.0 kg concrete block to a

height of 2.0 m?

h = 0.0mm = 4.0 kg

h = 2.0mm = 4.0 kg


Questions…12. Which has more kinetic energy: a 0.0020 kg bullet traveling at 400

m/s or a 6.4 x 107kg ocean liner traveling at 10 m/s (20 knots)? Justify your answer.

v = 10 m/sm = 6.4 x 107 kg

v = 400 m/sm = 0.0020 kg


Questions…15. What is the potential energy of a 3.00 kg object at the bottom of a

well 10.0 m deep as measured from ground level? Explain the sign of the answer.

h = 0.00 mm = 3.00 kg

h = -10.0 mm = 3.00 kg

•42 •43

•44 •45

10


Questions…16. How much work is required to lift a 3.00 kg object from the

bottom of a 10.0 m deep well?

h = 0.00 mm = 3.00 kg

h = 10.0 mm = 3.00 kg


Questions…20. A 35.0 kg child starting from rest slides down a water slide with a

vertical height of 20.0 m. What is the child’s speed ata. Halfway down the slide’s vertical distance? b. Three quarters of the way down?



vertical height of 20.0 m. What is the child’s speed ata. Halfway down the slide’s vertical distance? b. Three quarters of the way down?



vertical height of 20.0 m. What is the child’s speed ata. Halfway down the slide’s vertical distance? b. Three quarters of the way down? h = 20.0 m

m = 35.0 kg

h = 10.0 mm = 35.0 kg

h = 5.0 mm = 35.0 kg

h = 0.0 mm = 35.0 kg

•46 •47

•48 •49

11


Questions…24. A 130 lb student races up stairs with a vertical height of 8.0 m in

5.0 s to get to a class on the second floor. How much power in watts does the student expend in doing work against gravity?


Questions…24. A 130 lb student races up stairs with a vertical height of 8.0 m in

5.0 s to get to a class on the second floor. How much power in watts does the student expend in doing work against gravity?

h = 0 mw = 130 lbst = 0 s

h = 8.0 mw = 130 lbst = 5.0 s


Don’t forget your homework!!!Test Next Week on

Chapters 3 & 4

•50 •51

•52

Documents

No work is done because there is no movement (d = 0) · 3 4 | 18 Energy • The ability to do work. An object or system that possesses energy has the ability to do work • When work