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The height y can be found by subtracting Lcos(θ) from L. Therefore, the potential energy is given by:
b.)In order to sketch a potential energy function of the angle θ, make
the y-axis potential energy, U, and make the x-axis the angle θ. The
pendulum has its greatest potential energy when its farthest away from
the origin. So start with a large potential energy at -210° and slowly
decrease until there is zero potential energy at 0°. The potential
energy will again increase as displacement from the origin increases so
draw an increasing potential energy to 210°. Remember that the
potential energy of a pendulum cannot be negative, so your graph will
only appear in the first and second quadrants. The sketch should look
c.)The tangential force is equal to the sine of the angle time the mass
and gravity of the pendulum. In this case: Ftangential=sinθ(mg)
d.)At the initial state of the pendulum we have zero potential energy
and nonzero kinetic energy. Thus, by the Conservation of Energy, we
Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 3rd, 2015
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