<< Chapter < Page Chapter >> Page >

Definition of potential energy

Having decided the universal zero reference, we are now in position to define potential energy, using the expression obtained for the change in potential energy :

Δ U = U 2 U 1 = W C

If we set initial position at infinity, then U 1 = 0 . Let us denote potential energy of a system to be “U” for a given configuration. Then,

U 0 = W C

U = W C = 0 F C r

Hence, we can now define potential energy as given here :

Potential energy
The potential energy of a system of particles is equal to “negative” of the work by the conservative force as a particle is brought from infinity to its position in the presence of other particles of the system.

We should understand that the work by conservative force is independent of path and hence no reference is made about path in the definition. This work has a unique value. Hence, it gives a unique value of potential to the system of particles.

Distribution of potential energy

There is a peculiar aspect of the definition of potential energy, presented above. It defines potential energy of the system of particles in terms of work on a “single” particle. This peculiarity can be explained as it defines work in the presence of other particles and as such accounts for the forces operating on the particle due to their presence.

This definition, however, is not clear about how potential energy is distributed among the particles in the system. The value of potential energy does not throw any light on this aspect. As a matter of fact, it is not possible to segregate potential energy for the individual constituents of the system. Potential energy, therefore, belongs to all of them – not to any one of them.

Potential energy and external force

The potential energy is defined in terms of work by conservative force and zero reference potential at infinity. It is equal to the “negative” of work by conservative force :

U = W C = 0 F C r

Can we think to express this definition of potential energy in terms of external force? In earlier module, we have analyzed the motion of a body, which is raised by hand slowly to a certain vertical height. The significant point of this illustration was the manner in which body was raised. It was, if we can recall, raised slowly without imparting kinetic energy to the body being raised. It was described so with a purpose. The idea was to ensure that work by the external force (in this case, external force is equal to the normal force applied by the hand) is equal to the work by gravity.

Since speed of the body is zero at the end points, “work-kinetic energy” theorem reduces to :

W = K f K i = 0

W = 0

This means that work by “net” force is zero. It follows, then, that works by gravity (conservative force) and external force are equal in magnitude, but opposite in sign.

W = W C + W F = 0

W F = W C

Under this condition, the work by external force is equal to negative of work by conservative force :

W F = F C r

where “ F C ” is conservative force. It means that if we work on the particle slowly without imparting it kinetic energy, then work by the external force is equal to negative of the work by conservative force. In other words, work by external force without a change in kinetic energy of the particle is equal to change in potential energy only. Equipped with this knowledge, we can define potential energy in terms of external force as :

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics for k-12' conversation and receive update notifications?

Ask