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W E + W C + W N C = Δ K

Generally, we drop the summation sign with the understanding that we mean “summation”. We simply say that both work and kinetic energy refers to the system – not to a particle :

W E + W C + W N C = Δ K

However, work by conservative force is equal to negative of change in potential energy of the system.

W C = - Δ U

Substituting in the equation above,

W E Δ U + W N C = Δ K

W E + W N C = Δ K + Δ U = Δ E mech

Work by non-conservative force

One of the familiar non-conservative force is friction. Work by friction is not path independent. One important consequence is that it does not transfer kinetic energy as potential energy as is the case of conservative force. Further, it only transfers kinetic energy of the particle into heat energy, but not in the opposite direction. What it means that friction is incapable to transfer heat energy into kinetic energy.

Nonetheless, friction converts kinetic energy of the particle into heat energy. A very sophisticated and precise set up measures this energy equal to the work done by the friction. We have seen that gravitational potential energy remains in the system. What about heat energy? Where does it go? If we consider a “Earth-incline-block” system, in which the block is released from the top, then we can visualize that heat so produced is distributed between “block” and “incline” (consider that there is no radiation loss). Next thing that we need to answer is “what does this heat energy do to the system?” We can infer that heat so produced raises the thermal energy of the system.

W N C = - Δ E thermal

Note that work by friction is negative. Hence, we should put a negative sign to a positive change in thermal energy in order to equate it to work by friction.

Putting this in the equation of “Work-kinetic energy” expression, we have :

W E = Δ K + Δ U + Δ E thermal = Δ E mech + Δ E thermal

Law of conservation of energy

We now turn to something which we have not studied so far, but we shall employ those concepts to complete the picture of conservation of energy in the most general case.

Without going into detail, we shall refer to a consideration of thermodynamics. Work on the system, besides bringing change in the kinetic energy, also brings about change in the “internal” energy of the system. Similarly, combination of internal and external forces can bring about change in other forms of energy as well. Hence, we can rewrite “Work-kinetic energy” expression as :

W E = Δ E mech + Δ E thermal + Δ E others

This equation brings us close to the formulation of “conservation of energy” in general. We need to interpret this equation in the suitable context of system type. We can easily see here that we have developed this equation for a system, which allows energy transfers through work by external force. Hence, context here is that of special “closed” system, which allows transfer of energy only through work by external force. What if we choose a system boundary such that there is no external force. In that case, closed system becomes isolated system and

W E = 0

Putting this in “work – kinetic energy” expression, we have :

Questions & Answers

List the application of projectile
Luther Reply
How can we take advantage of our knowledge about motion?
Kenneth Reply
pls explain what is dimension of 1in length and -1 in time ,what's is there difference between them
Mercy Reply
what are scalars
Abdhool Reply
show that 1w= 10^7ergs^-1
Lawrence Reply
what's lamin's theorems and it's mathematics representative
Yusuf Reply
if the wavelength is double,what is the frequency of the wave
Ekanem Reply
What are the system of units
Jonah Reply
A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
58asagravitasnal firce
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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