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lecture 10 - Lecture 10 Work and Energy The scalar product...

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1 Lecture 10 Work and Energy The scalar product Kinetic energy The work-energy theorem
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2 Energy is a scalar quantity that is associated with a state (or condition) of an object. Kinetic energy is associated with an object’s state of motion. Potential energy is associated with an object’s position (or configuration).
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3 Work is the amount of energy transferred to or from an object by means of a force acting on it. If W >0 then energy is added If W < 0 then energy is removed The unit of work and energy is the joule (J). 1 J = 1 Nm = 1 kg m 2 /s 2 .
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4 It is only the force in the direction of the displacement that does work. = = r F d W work B A d r F θ
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5 Their dot (or scalar) product is AB cos θ B A B A = + + = z z y y x x B A B A B A z y x B z y x A ˆ ˆ ˆ ˆ ˆ ˆ z y x z y x B B B A A A + + = + + = Consider two vectors
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6 ( 29 ( 29 ( 29 ( 29 6 3 4 2 3 - = - + = + = y y x x B A B A B A y x B y x A ˆ 3 ˆ 2 ˆ 4 ˆ 3 - = + = Example: What is the scalar product of the two vectors A and B ? What is the magnitude of each vector? What is the angle between the two vectors? 13 25 2 2 2 2 2 2 = + = = = + = = y x y x B B A A B B B A A A x y A B θ
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7 ( 29 ( 29 ° = - = - = = = 109 333 . 0
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