# Concept Of Energy Conservation

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Long ago, a man named Yugong (foolish man) lived in a house sitting behind two giant mountains. One morning, Yugong started taking rocks away from the mountains and told his neighbors that he was going to move them because they were blocking his way. One of his neighbors, known as Zhisou
(wise man) heard the story and laughed: “Have you seen the sizes of the mountains? How could you ever have them moved?” Yugong answered, “I will just get it started. My children will continue; so will my grandchildren.
Generation after generation, we will eventually have the mountains moved.”
As the story goes, Yugong’s spirit touched Heaven so that immortals were sent down to help him finish the job, as shown in Fig. 5.1.
Then we will expand the concept to the process involving several constant forces and the process involving variable forces.
After introduce the concept of kinetic energy, we will show the transformation between energy and work. Finally we will generalize these concepts to any system going through any process that involves energy and work and elucidate the fundamental concept of energy conservation.
5.1 Work
The work that we are talking about is what a force produces during a process of moving an object. Two things must be there before we can talk about work, a force on an object and a relevant displacement of the object. “Relevant” here means that the displacement must have a nonzero component in the direction of the force, or vise versa. Consider the case of a person pulling a box with a force, fa, across a level floor, as shown in Fig. 5.3. We know intuitively that the person is doing some work in moving the box.
To get a better picture on how the person does his work, let us concentrate on the role of force fa exerted on the box. We know from Chapter 3 that the friction between the floor and the box is kinetic. The box can
Note that the forces have really contributed to the total work in the above example are the applied force (positive work) and kinetic friction (negative work) because the gravity and the normal force on the box are perpendicular to the displacement.
Before we look into more complicated cases, let us use another example to demonstrate that the weight on an object can in fact do work as well.
Consider the case of climbing a mountain again. We know that a person needs to push the ground to gain enough normal force to move his body up during the climbing phase. When he comes down the mountain, the weight of his body helps him descend. Thus his weight does negative work when he goes up the mountain but positive work when he comes down the mountain.
Later we will show that we can quantify the work done by the weight

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