What is the Speed and Total Mechanical Energy of a Simple Pendulum?

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Homework Help Overview

The discussion revolves around a simple pendulum problem involving its speed and total mechanical energy. The original poster presents a scenario where a pendulum of length 0.84 m and mass 0.68 kg is displaced by an angle of 7.8° and released from rest, with an emphasis on calculating angular frequency, total mechanical energy, and speed at the lowest point of the swing.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the types of energy present at different points in the pendulum's motion, particularly focusing on potential energy at the highest point and the implications for total mechanical energy at the lowest point. There is also a suggestion that the original poster may be overcomplicating the problem with too many equations.

Discussion Status

Participants are actively engaging with the original poster's calculations, offering guidance on energy conservation principles and questioning the necessity of certain equations. There is an acknowledgment of the original poster's confusion regarding the calculations, and some participants are providing clarifications without reaching a consensus on the correct values.

Contextual Notes

The original poster expresses uncertainty about the correctness of their calculations for speed and total mechanical energy, indicating a need for further exploration of the principles involved.

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[SOLVED] Pendulum Speed and total ME

Homework Statement



The length of a simple pendulum is 0.84 m and the mass of the particle (the "bob") at the end of the cable is 0.68 kg. The pendulum is pulled away from its equilibrium position by an angle of 7.8 ° and released from rest. Assume that friction can be neglected and that the resulting oscillatory motion is simple harmonic motion. (a) What is the angular frequency of the motion? (b) Using the position of the bob at its lowest point as the reference level, determine the total mechanical energy of the pendulum as it swings back and forth. (c) What is the bob's speed as it passes through the lowest point of the swing?

Homework Equations



E = .5mv^2+.5Iw^2+mgh+.5kx^2
w = sqrt(g/L)
L-Lcos@ = max height of pendulum bob
I of pendulum = (1/3)ML^2

The Attempt at a Solution



so w = 3.416 rad/s
The total energy:
.5(.68)(v^2) + .5(1/3 ML^2)(w^2) + mgh + .5kx^2
kx^2 is potential energy, which is 0 at the bottom of the swing
.34v^2 + (1/6)(.68*.84^2)(3.416^2) + .68*-9.8*.00777
.34v^2 + .88137
v^2 = 2.5922
v = 1.61 m/s

Plugging this in gives a total ME of 1.7627 J

The v and total E are wrong, but I'm not sure how to remedy this. Ideas, please? Thanks!
 
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Whao, slow down there, your using way too many equations! When the plumb bob is at it's highest point, what type of energy does it have?
 
It has potential energy, mgh. But the question asks for total mechanical energy at the bob's LOWEST point.
 
thatgirlyouknow said:
It has potential energy, mgh. But the question asks for total mechanical energy at the bob's LOWEST point.
Yes, but if you know that at it's highest point it only has potential energy and you know the energy is conserved, then what is the value of the total energy at the lowest point?
 
So I totally overanalyzed that one... oh well.

Thanks for the help!
 
thatgirlyouknow said:
So I totally overanalyzed that one... oh well.

Thanks for the help!
No worries :approve:
 

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