A. A simple pendulum of length L =0.800 m has a mass M=0.250 kg. What is the ten

Question

A. A simple pendulum of length L =0.800 m has a mass M=0.250 kg. What is the tension in the string when it is at an angle y=12.58°? Show all of your work.

B. what is the component of the weight of M that is directed along the arc of the motion of M? Show all of your work.

C. What is the period T of the motion of the pendulum? ASSUME THAT THE PERIOD IS INDEPENDENT OF Y. Show all of your work.

D. What would the period T of the pendulum be if L was unchanged but M=0.500 kg? ASSUME THAT THE PERIOD IS INDEPENDENT OF Y. Show all of your work.

E. Determind the period T of the pendulum if everything else stays the same, but y=45.08°. DO NOT ASSUME THAT THE PERIOD IS INDEPENDENT OF Y. Show all of your work.

Explanation / Answer

We know that,

T = mg cos(theta)

T = 0.25 x 9.8 x cos12.58 = 2.39 N

Hence, T = 2.39 N

b)The horizontal component is directed along the arc of the motion.

c)T =2 pi sqrt (L/g)

T = 2x 3.14 x sqrt (0.8/9.8) = 1.79 s

Hence, T = 1.79 s

d)Period will remains same, as we see in the formula that it is independent of m. T = 1.79 s

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