<< Chapter < Page Chapter >> Page >
W net = W nc + W c , size 12{W rSub { size 8{"net"} } =W rSub { size 8{"nc"} } +W rSub { size 8{c} } } {}

so that

W nc + W c = Δ KE , size 12{W rSub { size 8{"nc"} } +W rSub { size 8{c} } =Δ"KE"} {}

where W nc size 12{W rSub { size 8{"nc"} } } {} is the total work done by all nonconservative forces and W c size 12{W rSub { size 8{c} } } {} is the total work done by all conservative forces.

A person pushing a heavy box up an incline. A force F p applied by the person is shown by a vector pointing up the incline. And frictional force f is shown by a vector pointing down the incline, acting on the box.
A person pushes a crate up a ramp, doing work on the crate. Friction and gravitational force (not shown) also do work on the crate; both forces oppose the person’s push. As the crate is pushed up the ramp, it gains mechanical energy, implying that the work done by the person is greater than the work done by friction.

Consider [link] , in which a person pushes a crate up a ramp and is opposed by friction. As in the previous section, we note that work done by a conservative force comes from a loss of gravitational potential energy, so that W c = Δ PE size 12{W rSub { size 8{c} } = - Δ"PE"} {} . Substituting this equation into the previous one and solving for W nc size 12{W rSub { size 8{"nc"} } } {} gives

W nc = Δ KE + Δ PE. size 12{W rSub { size 8{"nc"} } =Δ"KE"+Δ"PE"} {}

This equation means that the total mechanical energy ( KE + PE ) size 12{ \( "KE + PE" \) } {} changes by exactly the amount of work done by nonconservative forces. In [link] , this is the work done by the person minus the work done by friction. So even if energy is not conserved for the system of interest (such as the crate), we know that an equal amount of work was done to cause the change in total mechanical energy.

We rearrange W nc = Δ KE + Δ PE size 12{W rSub { size 8{"nc"} } =D"KE"+D"PE"} {} to obtain

KE i + PE i + W nc = KE f + PE f . size 12{"KE""" lSub { size 8{i} } +"PE" rSub { size 8{i} } +W rSub { size 8{"nc"} } ="KE""" lSub { size 8{f} } +"PE" rSub { size 8{f} } } {}

This means that the amount of work done by nonconservative forces adds to the mechanical energy of a system. If W nc size 12{W rSub { size 8{"nc"} } } {} is positive, then mechanical energy is increased, such as when the person pushes the crate up the ramp in [link] . If W nc size 12{W rSub { size 8{"nc"} } } {} is negative, then mechanical energy is decreased, such as when the rock hits the ground in [link] (b). If W nc size 12{W rSub { size 8{"nc"} } } {} is zero, then mechanical energy is conserved, and nonconservative forces are balanced. For example, when you push a lawn mower at constant speed on level ground, your work done is removed by the work of friction, and the mower has a constant energy.

Applying energy conservation with nonconservative forces

When no change in potential energy occurs, applying KE i + PE i + W nc = KE f + PE f size 12{"KE""" lSub { size 8{i} } +"PE" rSub { size 8{i} } +W rSub { size 8{"nc"} } ="KE""" lSub { size 8{f} } +"PE" rSub { size 8{f} } } {} amounts to applying the work-energy theorem by setting the change in kinetic energy to be equal to the net work done on the system, which in the most general case includes both conservative and nonconservative forces. But when seeking instead to find a change in total mechanical energy in situations that involve changes in both potential and kinetic energy, the previous equation KE i + PE i + W nc = KE f + PE f size 12{"KE""" lSub { size 8{i} } +"PE" rSub { size 8{i} } +W rSub { size 8{"nc"} } ="KE""" lSub { size 8{f} } +"PE" rSub { size 8{f} } } {} says that you can start by finding the change in mechanical energy that would have resulted from just the conservative forces, including the potential energy changes, and add to it the work done, with the proper sign, by any nonconservative forces involved.

Calculating distance traveled: how far a baseball player slides

Consider the situation shown in [link] , where a baseball player slides to a stop on level ground. Using energy considerations, calculate the distance the 65.0-kg baseball player slides, given that his initial speed is 6.00 m/s and the force of friction against him is a constant 450 N.

A baseball player slides to stop in a distance d. the displacement d is shown by a vector towards the left and frictional force f on the player is shown by a small vector pointing towards the right equal to four hundred and fifty newtons. K E is equal to half m v squared, which is equal to f times d.
The baseball player slides to a stop in a distance d size 12{d} {} . In the process, friction removes the player’s kinetic energy by doing an amount of work fd size 12{ ital "fd"} {} equal to the initial kinetic energy.

Strategy

Friction stops the player by converting his kinetic energy into other forms, including thermal energy. In terms of the work-energy theorem, the work done by friction, which is negative, is added to the initial kinetic energy to reduce it to zero. The work done by friction is negative, because f size 12{f} {} is in the opposite direction of the motion (that is, θ = 180º size 12{q="180"°} {} , and so cos θ = 1 size 12{"cos"θ= - 1} {} ). Thus W nc = fd size 12{W rSub { size 8{"nc"} } = - ital "fd"} {} . The equation simplifies to

1 2 mv i 2 fd = 0 size 12{ { {1} over {2} }  ital "mv" rSub { size 8{i} rSup { size 8{2} } } - ital "fd"=0} {}

or

fd = 1 2 mv i 2 . size 12{ ital "fd"= { {1} over {2} }  ital "mv" rSub { size 8{i} rSup { size 8{2} } } "." } {}

This equation can now be solved for the distance d size 12{d} {} .

Solution

Solving the previous equation for d size 12{d} {} and substituting known values yields

d = mv i 2 2 f = ( 65.0 kg ) ( 6 . 00 m/s ) 2 ( 2 ) ( 450 N ) = 2.60 m. alignl { stack { size 12{d= { { ital "mv" rSub { size 8{i} rSup { size 8{2} } } } over {2f} } } {} #= { { \( "65" "." 0" kg" \) \( 6 "." "00"" m/s" \) rSup { size 8{2} } } over { \( 2 \) \( "450"" N" \) } } {} # " "=" 2" "." "60 m" "." {}} } {}

Discussion

The most important point of this example is that the amount of nonconservative work equals the change in mechanical energy. For example, you must work harder to stop a truck, with its large mechanical energy, than to stop a mosquito.

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply
Practice Key Terms 2

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Une: physics for the health professions. OpenStax CNX. Aug 20, 2014 Download for free at http://legacy.cnx.org/content/col11697/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Une: physics for the health professions' conversation and receive update notifications?

Ask