A simple pendulum is made from a 0.71 m long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed?
I found the period, which is 1.69. I figured the fastest speed would come at 1/2 that, which is .84 s. But it's wrong! I can't figure out what to do next!
2006-11-13 01:58:42 · 2 answers · asked by sglass359 1 in Science & Mathematics ➔ Physics
I agree with Edward but would like to say it a different way.
In fact, I agreed with you at first. But a full period is the time to return to the release point. At T/2 it's at rest at the far side of its swing. The fastest speed is at the bottom: T/4
2006-11-13 02:39:20 · answer #1 · answered by sojsail 7 · 0⤊ 0⤋
Yes it is
it should by 1/4 of a period
You know that
T=2pi(l/g) ^.5 ( or square root of l/g)
So T=2(3.14)(.71/9.81)^.5=1.69 sec (so you are correct in your computations)
But keep in mind that you have let the pendulum swing a few times to establish this period of oscillations.
The max speed will be achieved as the potential energy gets converted into kinetic energy at the at the very low point. It will occur twice during a full cycle or a full period. So the answer is T/4= .423sec.
2006-11-13 10:22:58 · answer #2 · answered by Edward 7 · 1⤊ 0⤋