Work, Energy, and

Power Forces in doing work, rate of doing

work, and in energy transformation

Work

defined as the product of the force magnitude F and the displacement magnitude d

Work is done Work is done

Work is done

displacement

displacement

No work is done

No work is done

+ Work is done by the man

+ Work is done by gravity

lifting

falling

Work

Is done when the Force (Fnet) applied to an

object causes that object to be displaced (d)

in the same direction as the force applied.

Is a method of transferring energy

How can we

The ground is doing

+ work on us.

http://2.bp.blogspot.com/-EsjHgHyE0Xo/VU-Mz9UejGI/AAAAAAAALq4/MOdF14vdUv8/s1600/walk1.jpg

Work

𝑊 = 𝐹𝑑𝑐𝑜𝑠𝜃

Example

Suppose a woman is pushing a grocery cart with a

500 Newton force along the 7 meter aisle, how much

work is done in pushing the cart from one of the aisle

to the other?

http://www.google.com.ph/imgres?imgurl=http://vectortoons.com/wp-content/uploads/2015/02/shopping-collection-sarah-004.jpg&imgrefurl=http://vectortoons.com/product/a-woman-pushing-a-shopping-cart-inside-the-supermarket/&h=904&w=1024&tbnid=lU4J2cTaNdNsnM:&zoom=1&docid=i94W7CJRHFiiOM&ei=4IN1VbmxJ5H3oAT-v4OwCQ&tbm=isch&ved=0CC4QMygqMCo4ZA

Example

The librarian found a book of mass 1kg is on the floor.

If the book is lifted by the librarian from the floor to the

top shelf which is 2 meters from the floor, how much

work is done on the book?

http://bloximages.chicago2.vip.townnews.com/nwitimes.com/content/tncms/assets/v3/editorial/9/bb/9bbd9852-8a43-5056-8293-3e2c919deff5/506d0316cf7a7.preview-620.jpg

Kinetic Energy (KE)

Is the energy of a moving object

Quantifies the amount of work an object can do

because of its motion

Kinetic Energy (KE)

𝐾𝐸 =1

2𝑚𝑣2

Work-energy principle

The net work done on an object is equal to the

change in the objects kinetic energy.

𝑊 = 𝐾𝐸𝑓 − 𝐾𝐸𝑖 = ∆𝐾𝐸

Concept Check

What will happen to the KE of an object if its mass is

doubled but the velocity remains the same?

How about if the velocity is doubled but the mass

remains the same?

Example

A 1000kg jeepney has a velocity of

17 m/s. What is its kinetic energy?

A 2000kg jeepney has a velocity of

17 m/s. What is its kinetic energy?

A 1000kg jeepney has a velocity of

34 m/s. What is its kinetic energy? http://www.paulancheta.com/weblog/images/07-04-2-jeepney.jpg

Example

A 145-g baseball is thrown so that

it acquires a speed of 25m/s. a)

What is its KE? b) What was the

net work done on the ball to make

it reach this speed, if it started from

rest?

http://www.nextlevelballplayer.com/wp-content/uploads/2012/10/baseball-hitting-tips.jpeg

Example

How much net work is

required to accelerate a

1000kg car from 20m/s to

30m/s?

http://www.gannett-cdn.com/-mm-/79af5a7336b66a51e8927d539cedabfd7085a349/c=72-0-1209-853&r=x404&c=534x401/local/-/media/2015/05/14/DetroitNews/B99270515Z.1_20150514165000_000_G47GNCQ1.1-0.jpg

Potential Energy

Is energy gained in raising an object from the ground

or lost when made to fall

Also known as gravitational potential energy

Potential Energy

𝑃𝐸 = 𝑚𝑔ℎ

Highest PE PE decreases as KE increases

http://scienceblogs.com/startswithabang/files/2011/12/kinetic_energy_c_la_784.jpeg

Example

What is the potential energy of a 1

kg book lifted to a 0.5m height

above a table?

What is the potential energy of a 1

kg book lifted to a 1.5m height

above a table? http://etc.usf.edu/clipart/63200/63282/63282_books_table_lg.gif

Elastic Potential Energy

depends on an elastic material’s elasticity and

how much the material is stretched or

compressed

http://images.wisegeek.com/spring.jpg

Elastic Potential Energy

𝐸𝑃𝐸 =1

2𝑘𝑥2

Rest position EPE stored Work done to

release

energy

Power

rate of doing work or the rate of using energy

𝑃 =𝑤𝑜𝑟𝑘

𝑡𝑖𝑚𝑒=

𝑒𝑛𝑒𝑟𝑔𝑦

𝑡𝑖𝑚𝑒

Power

rate of doing work or the rate of using energy

𝑃 =1 𝐽𝑜𝑢𝑙𝑒

1 𝑠𝑒𝑐𝑜𝑛𝑑= 1Watt

Example

A 50.0kg marathon runner runs up the

stairs to the top of the approximately

350m-tall MSHS building. To lift herself

to the top in 15.0minutes, what must be

her average power output?

Mechanical Energy

∆𝐾𝐸 + ∆𝑃𝐸 = 0

𝐾𝐸2 − 𝐾𝐸1 + 𝑃𝐸2 − 𝑃𝐸1 = 0

𝐾𝐸2 + 𝑃𝐸2 = 𝐾𝐸1 + 𝑃𝐸1

Example

A 50 kg member of your group jumped straight

up in the air with an initial speed of 2.94 m/s.

Ignoring air resistance, a) how high (in m) did he

go? b) What is the amount of work done? c)

How much force was exerted by the floor on that

member?

Example

c) How much force was exerted by the floor on

that member? d) how long (in sec) did it take the

member to reach that height? e) what is the

power of this member of your group?

http://www.ws-corp.com/wsc08/wsc14/LiveEditor/images/SLIDES/13/1.jpg

http://www.daviddarling.info/images/hydroelectric_power_plant.gif