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S10P1CLec13D

# S10P1CLec13D - Physics 1C Lecture 13D"Fluctuat nec mergitur...

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Physics 1C Lecture 13D "Fluctuat nec mergitur. = She is swayed by the waves but does not sink." --Motto of the city of Paris

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Pendulum Example A 300g mass on a 30cm long string oscillates as a pendulum. It has a speed of 0.25m/s as it passes through the lowest point. What maximum angle does the pendulum reach? (Assume the angle remains small enough for the motion to be SHM.) Answer First, you must de±ne a coordinate system. The lowest possible point can be y=0, let’s de±ne up as +y.
Pendulum Answer Choose the initial instant of time to be when the mass is moving through its lowest point: Choose the Fnal instant of time to be when the mass reaches its highest point: Next, let’s turn to conservation of energy. E i = KE i + PE i = KE max + 0 E i = 1 2 mv max 2 E f = KE f + PE f = 0 + PE max E f = mgh max

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Pendulum Answer The height it rises from the lowest to highest point. What does this height represent? Energy is conserved, so: E i = E f 1 2 mv max 2 = mgh max h max = v max 2 2 g = 0.25 m ( ) 2 2 9.8 N ( ) = 3.19mm v max = 2 E f m L=0.3m L-h The angle we want to solve will have a hypotenuse of 0.3m and
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S10P1CLec13D - Physics 1C Lecture 13D"Fluctuat nec mergitur...

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