A pendulum consists of a bob of mass A hanging from a string of non-zero mass m. Its maximum displacement is p/4 [whatever that p means, I do not know. the question writers do a poor job of writing questions]. What is true of the tension in the string?
- 1) It is greatest at the top.
- 2) It is greatest at the bottom.
- 3) It is uniform throughout.
- 4) It does not vary when the pendulum is put in motion.
- 5) It is greatest when the pendulum is it its maximum amplitude.
The Attempt at a Solution
I attempted this by putting down 2, but the authors believe it is 1.
Here's how I thought of it.
Sum of centripetal forces = m * centripetal acceleration
T - mg [at bottom, maybe I need a sine or cosine term to account for angle] = m (v^2 / r)
T = m ( v^2 /r ) + mg.
Thus, the T would be greatest at the bottom as the speed of a pendulum bob is maximum at the bottom [maximum kinetic energy], according to my logic. How does this work, why are the writers right, and why is my approach wrong?
Thanks in advance for the assistance!