Calculating Acceleration of 20 kg Pendulum at Lowest Point

AI Thread Summary
To calculate the vertical acceleration of a 20 kg pendulum at its lowest point, one must first determine the pendulum's length using its period of 1.5 seconds. The angle of 13 degrees helps find the height the pendulum has risen, which is essential for applying conservation of energy principles. This approach transitions potential energy into kinetic energy, allowing the calculation of velocity. The centripetal acceleration formula, a_c = v^2/r, is then used to find the acceleration at the lowest point. The discussion concludes with the realization that the correct method involves these steps to arrive at the solution.
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Homework Statement



Let's go back to the original pendulum of mass 20 kg with a period of 1.5 sec, displaced an angle of 13 degrees from the vertical. What would its acceleration be in the vertical (y) direction as it reachs the lowest point on its swing?

[PLAIN]https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-15-SHM/simp_pendulum/3.gif


Homework Equations


\omega = \sqrt{g/l}
a_{c} = \frac{v^{2}}{r}

The Attempt at a Solution


I think I'm missing something in this problem. It sounds like it should be easy but I just can't get it. I first thought that since its going through centripetal acceleration at its lowest point, the y component of the acceleration would equal the total acceleration. So I solved for w and used w2*r = acen. The answer I got was 9.81 (gravity), but that's not the right answer.

Could someone help step me through this? And happy Thanksgiving!
 
Last edited by a moderator:
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Never mind, just figured it out.

If anyone is curious how:

1. From the period you can find the length of the pendulum
2. from the angle you can find how high up the pendulum has gone
3. conservation of energy (all potential -> all kinetic)
4. use v2/r = acen
 

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