110 HEAT. 



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The quantity is defined to be the Kinetic Energy or Energy of 



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Motion of the body. It measures the work which the body can do in 

 exhausting its motion. Since it is equal to work it can be measured in 

 foot-pounds, foot-poundals, kilogramme-metres, ergs, <fcc., according to 

 the units chosen. 



Potential Energy. Let us consider the special case in which a 

 body of mass m is projected straight upwards against its own weight with 

 velocity v. For simplicity let us suppose that there is no air-resistance, 

 so that the weight alone acts. As the body rises its kinetic energy 

 gradually disappears, and at the highest point reached the body is for 

 an instant at rest and without kinetic energy. But we do not suppose 

 that this energy is gone out of existence. For, as the body falls it 

 regains energy, and when it has come back to the starting point its 



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velocity is again v and its kinetic energy again . 



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We suppose that the energy did not cease to exist, but that it took 

 a new form no longer manifested in motion but in change of position 

 or change of configuration with respect to the earth. This new form we 

 term Potential Energy or Energy of Position. 



We recognise the existence of kinetic energy by our sense of 

 sight we see the body moving, but we think of potential energy in 

 terms of the muscular sense as well as in terms of the sense of sight. 

 For constraint is always needed to preserve at rest a configuration 

 involving potential energy, and we think of ourselves as upholding by 

 pull or push a body possessing such energy. 



It is convenient to measure the gain in potential energy of a body 

 when rising against its weight, by the work done in moving it from 

 its original to its new position. The gain in potential energy is then 

 equal to the loss in kinetic energy, and the sum of the two energies 5 

 potential and kinetic, remains constant. 



It might seem at first sight that this constancy is merely a result of 

 definition and does not involve any observation or experiment. But it 

 is to be remembered that the force acting is the weight of the body, 

 which is the same whatever the velocity or the direction of its motion, 

 and whenever the motion takes place. Hence the velocity and the 

 kinetic energy are the same at any given point, both in the rise and 

 fall, and the possibility of regaining in the fall all the kinetic energy lost 

 in the rise depends entirely on the nature of the force acting. Were 

 the force dependent on the velocity or its direction, or did it change 

 with time, then the kinetic energy at a given point would be no longer 

 the same in the rise and fall. Indeed, in reality, the air-resistance is 

 always opposed to the motion and the kinetic energy lost against this is 

 not regained in the fall, so that at re-arrival at the starting-point there 

 is a diminution. The loss of kinetic energy is still, of course, equal to 

 the work done against the forces, but this work can no longer be 

 regarded as measuring potential energy stored. 



This simple case will serve as an illustration of the general principle 

 that the kinetic energy of a system is only wholly regained on return 

 to the original configuration, when the forces depend solely on the con- 

 figuration and not on the motion of the parts, or on the time at which 



