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Energy

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The total energy of an isolated system does not change. Energy is not easy to define. We will focus on two main types of energy – kinetic and potential. We will lump them together and call them both mechanical energy. Is energy a substance?

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The kinetic energy of an object is half its mass multiplied by the square of its speed. We use the letter K for kinetic energy whence: K = (1/2)mv 2. The unit of kinetic (and all types) energy is kg m 2 /s 2. This unit is called the joule and is abbreviated J. What happens to the kinetic energy of an object if its speed is doubled? Tripled?

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Collisions where kinetic energy is conserved are known as elastic collisions. Macroscopic collisions are not perfectly elastic though many atomic and subatomic collisions are. Collisions in which kinetic energy is lost are known as inelastic collisions. How can we tell collisions of billiard balls are not perfectly elastic?

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The product of a force and the distance through which it acts is known as work. We abbreviate work with the letter W whence: W = Fd. The unit of work is the Nm. A newton is a kgm/s 2. Thus, a Nm is a kgm 2 /s 2 … which is a joule!

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If you hold a suitcase above your head for thirty minutes, you do no work on the suitcase. When a force on an object is perpendicular to the velocity of the object, the force does no work on the object. The normal force exerted by the ice does no work on the sliding hockey puck. Does the Earth’s gravity do work on a satellite in circular orbit? Elliptical orbit?

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The gravitational potential energy of an object is the work done by the gravitational force when the object falls from height h to height zero. We use the letter U for potential energy whence: U = mgh. We can choose any height to have the zero value. What matters is change in potential energy. When a freely falling ball gains 20 J of kinetic energy, how does its potential energy change?

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When frictional forces can be ignored and the other non-gravitational forces do no work, the total mechanical energy of a system is conserved. Mechanical energy is the sum of kinetic and potential energies. We use E m for mechanical energy whence: E m = K + U When a mass falls freely, its K increases by the same amount its U decreases. For a swinging pendulum, how do K and U change?

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If we know the mass, speed, and height of a roller coaster at some moment and can ignore friction, we can find its speed at any other time. As the roller coaster goes down (up) hills, it gains (loses) K while it loses (gains) U. If we can ignore friction, the total mechanical energy remains constant. If a roller coaster starts from rest at the top of a hill of height h, what is the upper limit on how high a hill it can subsequently climb?

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When energy is stored in a stretched or compressed spring, it is called elastic potential energy U e. A bungee jumper starts off with gravitational potential energy U g. While falling freely, U g becomes K. As the bungee cord starts to stretch, U g becomes U e too. Ultimately, all mechanical energy is stored as U e. Why does the bungee jumper not regain her initial height?

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The rate at which one form of energy is converted into another is called power. We use E for energy conversion and P for power whence: P = E/ t. Since energy is typically converted due to work being done we often write: P = W/t. The unit of power is the J/s also called the Watt, abbreviated W.

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