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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 periodical.
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 have:
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