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Lesson 3.2 Energy

# Lesson 3.2 Energy - Energy Energy is required to do work...

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Energy Energy is required to do work. Energy is measured in the same unit as work, namely joule (J) Energy is the ability to do work. 1000 J = 1 kJ Consider a book of mass m kg on the floor. Its weight mg acts vertically down What is the force required to lift it without causing an acceleration? mg Since there is no acceleration caused by lifting, there is no net force on the book. Let F is the force required to lift it: F – mg = 0 F = mg F 1

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Potential Energy A force F = mg is required to lift the book without acceleration. Let this force F lift the book through a height h What is the work done by the force F = mg W = F·h = mgh J This is the same as saying that the energy used in doing this work is mgh . This energy in turn allows the book to do work when you stop supporting it. The book placed at a height h has a certain amount of energy stored in it. mg This energy is called the potential energy of the book. Potential energy is represented by U and is measured in joules ( J ) Potential energy of a book placed at a height h is: F h U = mgh 2
Conservative and non-conservative forces Weight of an object is a measure of the gravitational force on it . The gravitational force on the book is -mg What is the work done by the gravitational force when the book is raised through a height h? The force –mg is displaced by h m If the book is now allowed to fall, the gravitational force –mg is displaced by -h . The work done by gravitational force now is: W = -mg(-h) = mgh mg The total work done by the force of gravity for the entire trip is: h W = -mgh -h W = -mgh + mgh = 0 3

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mg A force is conservative if the total work it does on an object is zero when the object moves around in any closed path returning to its initial position. h -h Gravitational force is a conservative force. The restoring force of a spring is a conservative force. 4
When a spring is compressed by a force F , the spring applies a force –F trying to restore the length of the spring. This is called the restoring force of the spring. The work done by the restoring force is: When the applied force is removed, the restoring force stretches the spring back to its initial position doing an amount of work The total work done by the restoring force (-F) in the whole process is F 2 1 W = - kx 2 2 1 W = kx 2 2 2 total 1 1 W = - kx kx 0 2 2 + = -F x 2 1 W = - kx 2 5

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The tendency of a conservative force is to decrease the potential energy.
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