Calculating the Speed of a Pendulum Bob Using Energy Equations

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To calculate the speed of a pendulum bob at the bottom of its swing, one must consider the conversion of potential energy to kinetic energy. The pendulum's length is 2.71 m, and it is released from an angle of 35.8° with the vertical, with gravitational acceleration at 9.8 m/s². The initial potential energy can be calculated using the height derived from the angle, which then converts to kinetic energy at the lowest point. Attempts to use sine and cosine functions for direct speed calculations were incorrect, as they do not yield speed but rather height or displacement. Understanding the relationship between potential and kinetic energy is crucial for solving this problem effectively.
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1.) Homework Statement
A(n) 2.71 m long pendulum is released from rest when the support string is at an angle of 35.8◦ with the vertical.
The acceleration of gravity is 9.8 m/s2 . What is the speed of the bob at the bottom of the swing?
Answer in units of m/s

2.) Relevant equations
Not sure

3.) The attempt at a solution
I tried to do 2.71sin(35.8) and I got 1.585. It's not the right answer. I also tried to do do cos(35.8) but that did not work either. Are there any other equations I have to use to find the speed of the bob?
 
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Vanessa Avila said:
1.) Homework Statement
A(n) 2.71 m long pendulum is released from rest when the support string is at an angle of 35.8◦ with the vertical.
The acceleration of gravity is 9.8 m/s2 . What is the speed of the bob at the bottom of the swing?
Answer in units of m/s

2.) Relevant equations
Not sure

3.) The attempt at a solution
I tried to do 2.71sin(35.8) and I got 1.585. It's not the right answer. I also tried to do do cos(35.8) but that did not work either. Are there any other equations I have to use to find the speed of the bob?

Where does the energy come from that results in the bob having a velocity?
 
gneill said:
Where does the energy come from that results in the bob having a velocity?

Does the energy come from the string?
 
The best way to solve is to draw a neat diagram and show all the forces acting on the object. This might seem trivial but helps in better understanding of many concepts of physics.
 
Vanessa Avila said:
I tried to do 2.71sin(35.8)
What would the result of that calculation represent? What would its units be?
 
haruspex said:
What would the result of that calculation represent? What would its units be?
since 2.71 is m I assume it would be m as well not m/s.
 
Vanessa Avila said:
since 2.71 is m I assume it would be m as well not m/s.
Right, so it is not a speed.
What do you know about potential and kinetic energy? Any equations you know of?
 

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