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Lecture2 - Effect depends on vertical displacement –[h =...

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Click to edit Master subtitle style 2/23/11 Lecture 2: Derivatives, Falling Bodies Ph 1a Fall 2009
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2/23/11 Picture 5
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2/23/11 Order of magnitude estimates How much money is in an armored car ? A ream of paper (500 sheets) is 5 cm thick Volume of a $20 bill is 6 cm x 15 cm x 0.01 cm = 1 cm3 Volume of compartment is (2 m)3 ~ 10 m3 = 107 cm3 If the car is carrying $20 bills (ATM servicing), a full compartment is worth $200M. How much does the money “weigh” ? Density of paper is similar to water, 1 g cm-3 So mass = 107 cm3 x 1 g cm-3 = 107 g = 104
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2/23/11 Dimensional analysis Must always check that dimensions are consistent Can often guess the solution to a problem by finding the appropriate combination of input quantities that has the same dimensions as the desired output quantity Picture 3
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2/23/11 Gravitational effect on clocks
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Unformatted text preview: Effect depends on vertical displacement – [h] = L • Note that gh/c2 is dimensionless • A good guess for the fractional change in clock rate (frequency) ? 2/23/11 The latest in timekeeping Picture 3 Picture 4 Picture 5 2/23/11 Derivatives • On blackboard. .. • Position, velocity, acceleration • Definition of derivative as limit • Derivative of tn using Pascal’s triangle • Product rule, quotient rule, chain rule • Constant acceleration: expressions for velocity and position vs time 2/23/11 Demonstrations • Comparison of two identical pendula – Dependence of period on swing amplitude • Driven pendulum – Horizontal drive at pendulum frequency, vs vertical drive at twice the frequency • Free fall – penny and feather, in vacuum and air...
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