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10_P11InstructorSolution

# 10_P11InstructorSolution - 10.11 Model In the absence of...

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10.11. Model: In the absence of frictional and air-drag effects, the sum of the kinetic and gravitational potential energy does not change as the pendulum swings from one side to the other. Visualize: The figure shows the pendulum’s before-and-after pictorial representation for the two situations described in parts (a) and (b). Solve: (a) The quantity g K U + is the same at the lowest point of the trajectory as it was at the highest point. Thus, 1 g1 0 g0 means K U K U + = + 2 2 2 2 1 1 0 0 1 1 0 0 2 2 1 0 1 0 1 1 2 2 2 2 2 (0 m) (0 m/s) 2 2 mv mgy mv mgy v gy v gy v g gy v gy + = + + = + + = + = From the pictorial representation, we find that 0 cos30 . y L L = ° Thus, 2 1 2 (1 cos30 ) 2(9.8 m/s )(0.75 m)(1 cos30 ) 1.403 m/s v gL = ° = ° = The speed at the lowest point is 1.40 m/s. (b) Since the quantity g K U + does not change,

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10_P11InstructorSolution - 10.11 Model In the absence of...

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