Question

Part One: A simple pendulum of length l = 0.800 has a mass = 0.250kg. What is the tension in the string when it is at angle theta = 12.5°? Show your force diagram and work to support your answer

Part Two: What is the period T of the motion of the pendulum in Part Two? Assume the period is independent of angle theta.

Part Three: What is the period T of the motion of the pendulum in Part One? Assume the period is independent of angle theta.

Part Four: What would be the period T of the pendulum if l was unchanged but =0.500kg ?

Part Four: Determine the period T of the pendulum if everything else stays the same, but angle theta = 45°. Do not assume that the period is independent of angle theta.

Answer 1

Part One : Tension in the string will be given as -

T = m g cos = (0.25 kg) (9.8 m/s²) cos 12.5⁰

T = (2.45 N) (0.9762)

T = 2.39 N

Part Three : The period T of the motion of pendulum in Part One which will be given as -

using a formula, we have

T = 2L / g

where, L = length of pendulum = 0.8 m

T = 2 (3.14) (0.8 m) / (9.8 m/s²)

T = (6.28) (0.2857 sec)

T = 1.79 sec

Part Four : If L was unchanged but m = 0.5 kg, then the period T of pendulum which will be given as -

using a formula, we have

T = 2L / g

where, L = length of pendulum = 0.8 m

T = 2 (3.14) (0.8 m) / (9.8 m/s²)

T = (6.28) (0.2857 sec)

T = 1.79 sec