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More precisely, we define the change in gravitational potential energy Δ PE g size 12{Δ"PE" rSub { size 8{g} } } {} to be

Δ P E g = P E g f P E g i = m g h f m g h i = m g ( h f h i ) = m g Δ h

Note that Δ h is positive when the final height is greater than the initial height, and vice versa. For example, if a 0.500-kg mass hung from a cuckoo clock is raised 1.00 m, then its change in gravitational potential energy is

mgΔh = 0.500 kg 9.80 m/s 2 1.00 m = 4.90 kg m 2 /s 2 = 4.90 J.

Note that the units of gravitational potential energy turn out to be joules, the same as for work and other forms of energy. As the clock runs, the mass is lowered. We can think of the mass as gradually giving up its 4.90 J of gravitational potential energy, without directly considering the force of gravity that does the work .

Using potential energy to simplify calculations

The equation Δ PE g = mgΔh size 12{Δ"PE" rSub { size 8{g} } = ital "mgh"} {} applies for any path that has a change in height of Δh size 12{h} {} , not just when the mass is lifted straight up. (See [link] .) It is much easier to calculate mgΔh size 12{ ital "mgh"} {} (a simple multiplication) than it is to calculate the work done along a complicated path. The idea of gravitational potential energy has the double advantage that it is very broadly applicable and it makes calculations easier. From now on, we will consider that any change in vertical position Δh size 12{h} {} of a mass m size 12{m} {} is accompanied by a change in gravitational potential energy mgΔh size 12{ ital "mgh"} {} , and we will avoid the equivalent but more difficult task of calculating work done by or against the gravitational force.

There is a four-story building. A person is carrying a television up the stairs of the building. The height of third story is h from the ground. A girl is standing outside the building and is lifting a similar television with the help of a pulley.
The change in gravitational potential energy ( Δ PE g ) size 12{ \( Δ"PE" rSub { size 8{g} } \) } {} between points A and B is independent of the path. Δ PE g = mgΔh size 12{Δ"PE" rSub { size 8{g} } = ital "mgh"} {} for any path between the two points. Gravity is one of a small class of forces where the work done by or against the force depends only on the starting and ending points, not on the path between them.

The force to stop falling

A 60.0-kg person jumps onto the floor from a height of 3.00 m. If he lands stiffly (with his knee joints compressing by 0.500 cm), calculate the force on the knee joints.

Strategy

This person’s energy is brought to zero in this situation by the work done on him by the floor as he stops. The initial PE g size 12{"PE" rSub { size 8{g} } } {} is transformed into KE size 12{"KE"} {} as he falls. The work done by the floor reduces this kinetic energy to zero.

Solution

The work done on the person by the floor as he stops is given by

W = - F d ,

with a minus sign because the displacement while stopping and the force from floor are in opposite directions. The floor removes energy from the system, so it does negative work.

The kinetic energy the person has upon reaching the floor is the amount of potential energy lost by falling through height Δh size 12{h} {} :

KE = Δ PE g = mgΔh , size 12{"KE"= - Δ"PE" rSub { size 8{g} } = - ital "mgΔh"} {}

The distance d size 12{d} {} that the person’s knees bend is much smaller than the height Δh size 12{h} {} of the fall, so the additional change in gravitational potential energy during the knee bend is ignored.

The work W size 12{W} {} done by the floor on the person stops the person and brings the person’s kinetic energy to zero:

W = KE = mgΔh . size 12{W= - "KE"= ital "mgΔh"} {}

Combining this equation with the expression for W size 12{W} {} gives

Fd = mgΔh . size 12{ - ital "Fd"= ital "mgΔh"} {}

Recalling that Δh size 12{h} {} is negative because the person fell down , the force on the knee joints is given by

F = mgΔh d = 60.0 kg 9.80 m /s 2 3 . 00 m 5 . 00 × 10 3 m = 3 . 53 × 10 5 N. size 12{F= - { { ital "mgh"} over {d} } = - { { left ("60" "." 0" kg" right ) left (9 "." "80"" m/s" rSup { size 8{2} } right ) left ( - 3 "." "00"`m right )} over {5 "." "00" times "10" rSup { size 8{ - 3} } " m"} } =3 "." "53" times "10" rSup { size 8{5} } `N "." } {}

Discussion

Such a large force (500 times more than the person’s weight) over the short impact time is enough to break bones. A much better way to cushion the shock is by bending the legs or rolling on the ground, increasing the time over which the force acts. A bending motion of 0.5 m this way yields a force 100 times smaller than in the example. A kangaroo's hopping shows this method in action. The kangaroo is the only large animal to use hopping for locomotion, but the shock in hopping is cushioned by the bending of its hind legs in each jump.(See [link] .)

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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Akash Reply
it is a goid question and i want to know the answer as well
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Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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?
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China
Cied
types of nano material
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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many many of nanotubes
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what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
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Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Concepts of physics with linear momentum. OpenStax CNX. Aug 11, 2016 Download for free at http://legacy.cnx.org/content/col11960/1.9
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