W5.3 - Physics for Scientists & Engineers 1 Spring...

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February 5, 2008 1 Engineers 1 Engineers 1 Spring Semester 2008 Lecture 18
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February 5, 2008 2 Work Work Formal Definition: Work is defined as energy transferred to an object or transferred from an object due to the action of a force. Positive work is defined as a transfer of energy to the object, and negative work is a transfer of energy from the object. Positive work is work done on the object, while negative work is work done by the object. Please note: we have not specified what kind of energy is transferred. This work definition holds for all kinds of energy, but in particular also for kinetic energy
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February 5, 2008 3 Example: Vase Example: Vase on an Inclined Plane on an Inclined Plane Vase is sliding a distance Δ r along the inclined plane (friction free sliding, for now) Kinetic energy Introduce angle α = 90°- θ Acceleration: a = g sin ! = g cos " v 2 = v 0 2 + 2 a ! r = 2 g cos "! r # K = 1 2 mv 2 = mg ! r cos (again v 0 =0)
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February 5, 2008 4 Example: Vase Example: Vase on an Inclined Plane (2) on an Inclined Plane (2) In this case, work (= change in kinetic energy) done on the vase by gravitational force is ( α = angle between force and displacement Limiting cases: K = mg ! r cos " = ! F g ! ! r cos α = 0 (force and displacement parallel): we recover the result already derived for the case of the falling vase. α = 90° (force perpendicular to displacement): no acceleration => no change in the kinetic energy => no work done by gravitational force on vase
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5 Scalar product of two vectors and is defined as: (where is the angle between the two vectors) Symbol used for scalar multiplication is . It resembles a dot, hence the alternate name “dot product” Scalar product has the commutative property Mathematical Insert: Scalar Product (1) Mathematical Insert: Scalar Product (1) ! A A
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W5.3 - Physics for Scientists & Engineers 1 Spring...

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