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Section09

# Section09 - Physics 204A Class Notes Section 9 Potential...

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Physics 204A Class Notes 9-1 Section 9 – Potential Energy & Energy Conservation Why do objects do what they do? One explanation is they do what they do because of the forces that act on them. Another answer is they do what they do because of the Law of Conservation of Linear Momentum. Another powerful idea is the Law of Conservation of Energy, which we will develop in this section. Section Outline 1. Conservative and Non-conservative Forces 2. Work and Potential Energy 3. Two Types of Potential Energy 4. The Law of Conservation of Energy 5. Energy in Collisions 1. Conservative and Non-conservative Forces Imagine giving a toy car a push causing it to roll up an incline. The Work-Energy Theorem explains the stopping of the car because the initial kinetic energy is removed by the negative work done by gravity on the car. When the car comes to rest, it begins to roll back down the hill because gravity now begins doing positive work to increase the kinetic energy. The work done on the way up is equal and opposite to the work done on the way down, so the kinetic energy at the bottom is equal to the kinetic it had when it started. The gravitational force has the ability to return any kinetic energy that it does work against. Now imagine giving a stapler a push along a desk. Again, the Work-Energy Theorem explains the stopping of the stapler, because the initial kinetic energy is removed by the negative work done by friction. However, unlike the case with gravity, the frictional force is unable to do positive work to return the kinetic energy of the stapler. Why does gravity return the kinetic energy, but friction doesn’t? Before we can understand why, we need a name to describe this property of a force. A force that always returns the kinetic energy is said to be a “conservative force” while a force that does not return the kinetic energy is called a “non- conservative force. Naming the effect is great, but why is gravity a conservative force and friction a non-conservative force? The physicists answer is, “The work done by gravity around a closed loop is zero, while the work done by friction around a loop is not zero.” Wasn’t that helpful? Let’s see what we can do about building some understanding of this idea. Example 9.1: A 100g car is taken from the base to the top of a 10.0cm high ramp. Find the total work done by gravity as the car is taken up the ramp, vertically down the side, and back horizontally to its starting point. Given: m = 0.100kg and h = 0.100m Find: W = ? s y x θ path 1 path 3 h l path 2

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Physics 204A Class Notes 9-2 The first thing to do is find the work done along each distinct path. Using the definition of work, along path 1, W " r F d r s # \$ W 1 = r F g d r s # . Using the mass/weight rule and the fact that the angle between r F g and d r s is !
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