Energy

Energy - 1 Chapter 7: Chapter 7: Energy of a System...

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Unformatted text preview: 1 Chapter 7: Chapter 7: Energy of a System Introduction to Energy The concept of energy is one of the most important topics in science and engineering Every physical process that occurs in the Universe involves energy and energy transfers or transformations The energy approach to describing motion is particularly useful when Newtons Laws are difficult or impossible to use An approach will involve changing from a particle model to a system model This can be extended to biological organisms, technological systems and engineering situations 2 Systems A system is a small portion of the Universe We will ignore the details of the rest of the Universe A critical skill is to identify the system A valid system may be a single object or particle be a collection of objects or particles be a region of space vary in size and shape A force applied to an object in empty space System is the object Its surface is the system boundary The force is an influence on the system that acts across the system boundary A force does no work on the object if the force does not move through a displacement The work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application W = F r cos Work done by a constant force , 90 , = = = = W r F W r F W a a = . Work is a scalar quantity The unit of work is a joule (J) 1 joule = 1 Newton X 1 meter J = N m The work, W , done on a system by an agent exerting a constant force on the system = Force in the direction of the displacement X displacement 3 Work Is An Energy Transfer This is important for a system approach to solving a problem If the work is done on a system and it is positive, energy is transferred to the system If the work done on the system is negative, energy is transferred from the system If a system interacts with its environment, this interaction can be described as a transfer of energy across the system boundary This will result in a change in the amount of energy stored in the system Scalar Product of Two Vectors The scalar product of two vectors is written as A . B It is also called the dot product A . B = A B cos is the angle between A and B The scalar product is commutative A . B = B . A The scalar product obeys the distributive law of multiplication A . (B + C) = A . B + A . C k j k i j i 1 k k j j i i = = = = = = z z y y x x z y x z y x B A B A B A B A k B j B i B B k A j A i A A + + = + + = + + = 2 2 2 2 . A A A A A A z y x = + + = a a 4 Work Done by a Varying Force Assume that during a very small displacement, x , F is constant For that displacement, W ~ F x For all of the intervals, f i x x x W F x Therefore, The work done is equal to the area under the curve lim...
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Energy - 1 Chapter 7: Chapter 7: Energy of a System...

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