PAP111_Lecture08 - PAP111 Lecture8 Theorem...

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PAP 111  Mechanics and Relativity  Lecture 8 Energy and Energy Transfer The Concept of Work Done Kinetic Energy and the Work-Kinetic Energy  Theorem Conservation of Energy
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Revision on Vector Algebra The scalar product of  two vectors is  written  as  A . B It is also called the dot  product. A . B  A B  cos  θ A  and  B  are the  magnitude of the vectors  A  and  B  respectively,  while  θ  is the angle  between them.
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Scaler Product 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 For unit vectors   ,   ,   , in the positive x, y and z directions respectively, we  have The scaler products of A and B in component form are as follows: i ˆ j ˆ k ˆ 0 k j k i j i k k j j i i = = = = = = ˆ ˆ ˆ ˆ ˆ ˆ 1 ˆ ˆ ˆ ˆ ˆ ˆ 2 ˆ ˆ ˆ ˆ ˆ ˆ A A A A A A A B A B A B A B B B A A A z z y y x x z z y y x x z y x z y x = + + = + + = + + = + + = A A B A k j i B k j i A
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The Concept of Energy The concept of energy is one of the most important topics in science. Every physical process that occurs in the Universe involves energy  and energy transfers or transformations. Energy is not easily defined, but a proper definition is essential for  the concept to be useful. A fundamental notion that involves energy is the  Conservation of  Energy . This important concept extends beyond physical and  chemical systems to the realm of biological organisms, technological  systems and engineering situations. The energy approach also provides an alternative approach to the  solution of mechanical problems. It is especially useful when the  force is not constant.
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Systems and Environment System   A single object or particle.  A collection of objects or particle.  A region of space. Universe Environment System  Boundary Energy Flows from the Environment into the System Energy Flows from the System into the Environment
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Work Definition: The work,  W , done on a system by an agent exerting a constant  force on the system is the product of the magnitude  F  of the force,  the magnitude  Δ r  of the displacement of the point of application of  the force, and cos  θ ,  where  θ  is the angle between the force and  the displacement vectors: θ cos r F W = r F (8.1)
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Remarks on Work No work is done on the object if  the force does not move  through a displacement.
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