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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 PE g = mgh , size 12{Δ"PE" rSub { size 8{g} } = ital "mgh"} {}

where, for simplicity, we denote the change in height by h size 12{h} {} rather than the usual Δ h size 12{Δh} {} . Note that h size 12{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

mgh = 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 = mgh size 12{Δ"PE" rSub { size 8{g} } = ital "mgh"} {} applies for any path that has a change in height of h size 12{h} {} , not just when the mass is lifted straight up. (See [link] .) It is much easier to calculate mgh 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 h size 12{h} {} of a mass m size 12{m} {} is accompanied by a change in gravitational potential energy mgh 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 = mgh 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 = Fd cos θ = Fd , size 12{W= ital "Fd""cos"θ= - ital "Fd"} {}

with a minus sign because the displacement while stopping and the force from floor are in opposite directions ( cos θ = cos 180º = 1 ) size 12{ \( "cos"θ="cos""180""°=" - 1 \) } {} . 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 h size 12{h} {} :

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

The distance d size 12{d} {} that the person’s knees bend is much smaller than the height h 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 = mgh . size 12{W= - "KE"= ital "mgh"} {}

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

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

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

F = mgh 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] .)

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Questions & Answers

how many subject is in physics
Adeshina Reply
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
Tamdy Reply
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
the range of objects and phenomena studied in physics is
Bethel Reply
what is Linear motion
Hamza Reply
straight line motion is called linear motion
then what
Amera
linear motion is a motion in a line, be it in a straight line or in a non straight line. It is the rate of change of distance.
Saeedul
Hi
aliyu
your are wrong Saeedul
Richard
Linear motion is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension
Jason
is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimensions. 
Praise
what is a classical electrodynamics?
Marga
what is dynamics
Marga
dynamic is the force that stimulates change or progress within the system or process
Oze
what is the formula to calculate wavelength of the incident light
David Reply
if a spring is is stiffness of 950nm-1 what work will be done in extending the spring by 60mmp
Hassan Reply
State the forms of energy
Samzy Reply
machanical
Ridwan
Word : Mechanical wave Definition : The waves, which need a material medium for their propagation, e.g., Sound waves. \n\nOther Definition: The waves, which need a material medium for their propagation, are called mechanical waves. Mechanical waves are also called elastic waves. Sound waves, water waves are examples of mechanical waves.t Definition: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave.h
Clement Reply
correct
Akinpelu
what is mechanical wave
Akinpelu Reply
a wave which require material medium for its propagation
syed
The S.I unit for power is what?
Samuel Reply
watt
Okoli
Am I correct
Okoli
it can be in kilowatt, megawatt and so
Femi
yes
Femi
correct
Jaheim
kW
Akinpelu
OK that's right
Samuel
SI.unit of power is.watt=j/c.but kw.and Mw are bigger.umots
syed
What is physics
aish Reply
study of matter and its nature
Akinpelu
The word physics comes from a Greek word Physicos which means Nature.The Knowledge of Nature. It is branch of science which deals with the matter and energy and interaction between them.
Uniform
why in circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction
Syafiqah Reply
reasonable
Femi
because it is balanced by the inward acceleration otherwise known as centripetal acceleration
MUSTAPHA
What is a wave
Mutuma Reply
Tramsmission of energy through a media
Mateo
is the disturbance that carry materials as propagation from one medium to another
Akinpelu
mistakes thanks
Akinpelu
find the triple product of (A*B).C given that A =i + 4j, B=2i - 3j and C = i + k
Favour Reply
Difference between north seeking pole and south seeking pole
Stanley Reply
Practice Key Terms 1

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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