Simple Pendulum - Maximum Speed

AI Thread Summary
The discussion revolves around calculating the maximum speed of a simple pendulum with a mass of 0.25 kg and a length of 1.0 m, displaced at an angle of 5.0°. The user correctly calculated the maximum angular acceleration as 0.855 rad/s² and the maximum restoring force as 0.214 N but struggled with finding the maximum speed. They attempted to use the relationship between force and energy but received feedback that they were incorrectly equating force to energy. The conversation emphasizes the need to determine the potential energy based on the vertical height from the lowest point to the displaced position.
mparsons06
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1. Homework Statement :

A simple pendulum has a mass of 0.25 kg and a length of 1.0 m. It is displaced through an angle of 5.0° and then released.

1. What is the maximum speed?

2. What is the maximum angular acceleration?
Answer: 0.855 rad/s2

3. What is the maximum restoring force?
Answer: 0.214 N2. The attempt at a solution:

I got numbers 2 and 3 right, but I can't figure out number 1.

Here's my attempt:

m*g*L*sin \theta = 1/2 *m*v2
(0.250)*(9.81)*(1.0)*(sin 5) = 1/2 * (0.250)*v2
0.124 = (0.125)v2
v2 = 1.712 = 1.31 m/s

It is incorrect. Can someone please help me as to where I went wrong?
 
Last edited:
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You are equating a force to energy.

First draw a free body diagram and find the potential energy when it is displaced at 5°.
 
I drew the diagram, but I'm not sure how to find the potential energy?
 
mparsons06 said:
I drew the diagram, but I'm not sure how to find the potential energy?

From the lowest point to where it is displaced, what is the vertical height?
 
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