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P161Sp08Chapter_10

P161Sp08Chapter_10 - Chapter 10 Energy Introduction to...

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Chapter 10 Energy
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Introduction to Energy n The concept of energy is one of the most important topics in science n Every physical process that occurs in the Universe involves energy and energy transfers or transformations n Energy is not easily defined
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Energy Approach to Problems n The energy approach to describing motion is particularly useful when the force is not constant and there is no friction n An approach will involve Conservation of Energy n This could be extended to biological organisms, technological systems and engineering situations
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Object Falling Due to Gravity Alone, i.e. no air drag Recall the kinematic equation v f 2 = v i 2 + 2 a y ( y f - y i ) Multiply both sides by 1/2m and put a y = - g (for projectile motion) 1 2 m v f 2 = 1 2 m v i 2 - mg ( y f - y i ) Rearrange terms 1 2 m v f 2 + mgy f = 1 2 m v i 2 + mgy i
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Energy of Falling Object 1 2 m v f 2 + mgy f = 1 2 m v i 2 + mgy i Define kinetic energy as K = 1 2 m v 2 and gravitational potential energy as U (or GPE) = mgy The top equation says K f + GPE f = K i + GPE i This is a form of energy conservation
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Units of Energy n K = 1/2 mv 2 n Energy associated with motion n dimensions kgm 2 /s 2 n For KE 1 kgm 2 /s 2 = 1 Joule n GPE = mgy n GPE is a form of potential energy U associated with position n dimensions kg m/s 2 m = kg m 2 /s 2 n For GPE 1 kgm 2 /s 2 = 1 Joule
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Potential Energy n Potential energy is the energy associated with the configuration of a system of objects that exert forces on each other n This can be used only with conservative forces. More on conservative forces later. n When conservative forces act within an isolated system, the kinetic energy gained (or lost) by the system as its members change their relative positions is balanced by an equal loss (or gain) in potential energy. n This is Conservation of Mechanical Energy
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Types of Potential Energy n There are many forms of potential energy, including: n Gravitational n Electromagnetic n Chemical n Nuclear n One form of energy in a system can be converted into another
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Potential Energy n The energy storage mechanism is called potential energy-in general denoted by U. n A potential energy can only be associated with specific types of forces n Potential energy is always associated with a system of two or more interacting objects
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Total Mechanical Energy n The sum of kinetic and potential energies is the mechanical energy (E) of the system. n E = K + U i n If there is no friction the total energy is conserved, i.e. constant.
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Gravitational Potential Energy n Gravitational Potential Energy is associated with an object at a given distance above Earth’s surface
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Gravitational System Example n This system consists of Earth and a book n Initially the book is at rest (K = 0) at y = y b (U = mgy b ) n When the book falls and is at y a the kinetic energy is: n K a + mgy a = 0 +mgy b n K a =mg(y b - y a ) >0 n GPE is converted into K
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GPE n Note that in the last slide the kinetic energy that was converted from potential energy depends only on the relative displacement [ K a =mg(y b - y a )].
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