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Homework Statement
The diagram shows a simple pendulum consisting of a mass M suspended by a thin, massless string. The magnitude of the tension is T. The mass swings back and forth between +/- theta_0. Which of the following are true statements?
A. T is the largest at the bottom (theta = 0 deg).
B. T = Mg at some angle between zero and theta_0.
C. The vertical component of tension is constant.
D. T equals Mg when theta = theta_0
E. T is greater than Mg when theta = theta_0
F. T is smallest when theta = +/- theta_0
Homework Equations
T = (mv^2)/r + mg
The Attempt at a Solution
Using the above equation, the tension should be greatest at the bottom of the swing (v reaches it's maximum) and a minimum at +/- theta_0 when v = 0. Therefore:
A. T is the largest at the bottom (theta = 0 deg).
True: This is where v reaches a maximum so the tension will be maximum.
B. T = Mg at some angle between zero and theta_0.
False: T = Mg only when (mv^2)/r = 0, which occurs at theta_0.
C. The vertical component of tension is constant.
True: The vertical component is Mg which remains constant.
D. T equals Mg when theta = theta_0
True: v = 0 so T = m0^2/r + Mg ==> T = Mg
E. T is greater than Mg when theta = theta_0
False: Can't be true if T = Mg from above statement
F. T is smallest when theta = +/- theta_0
True: There is no velocity at +/- theta_0, so this is where T must be a minimum.
I've tried the above answer set, also with C as false (I wasn't sure if maybe the vertical component related to more than just Mg), but both attempts were wrong. If my pendulum tension equation accurately describes the above scenario, I'm not sure where I went wrong in my reasoning.
Thanks,
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