# lecture18 - Work Review of scalar product of vectors Work...

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Physics 1D03 - Lecture 19 Review of scalar product of vectors Work by a constant force Work by a varying force Example: a spring Work ! Serway & Jewett 7.1 – 7.3

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Physics 1D03 - Lecture 19 Work and Energy Work and Energy a m F = Energy approach : Net work = increase in kinetic energy - acceleration at any instant is caused by forces - equivalent to Newton’s dynamics - scalars, not vectors - compares energies “before and after” Newton’s approach:
Physics 1D03 - Lecture 19 ) ABcos( ) A to parallel of (component x ) A of (magnitude θ = = B B A B A The scalar product or dot product of two vectors gives a scalar result: vector • vector = scalar Math Review

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Physics 1D03 - Lecture 19 ScaIar product and cartesian components: k B j B i B B k A j A i A A z y x z y x ˆ ˆ ˆ ˆ ˆ ˆ + + = + + = z z y y x x B A B A B A B A + + = Then, (note the right-hand-side is a single scalar ) To prove this, expand using the laws of arithmetic (distributive, commutative), and notice that B A since, i, j, k are mutually perpendicular since they are unit vectors 1 ˆ ˆ ˆ ˆ ˆ ˆ 0 ˆ ˆ ˆ ˆ ˆ ˆ = = = = = = k k j j i i k i k j j i and
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lecture18 - Work Review of scalar product of vectors Work...

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