Finding the Velocity of the Bob on a Pendulum

In summary, the problem involves a 2.0 m pendulum being released from rest at an angle of 25 degrees with the vertical. The goal is to find the speed of the bob at the bottom of the string. Using the equations KE=1/2mv^2 and PE=mgh, and assuming all PE is converted to KE at the bottom, the correct equation is gh=1/2v^2. After correcting for a mistake in the height calculation, the final velocity is determined to be 1.92 m/s.
  • #1
LukeStarChief
2
0

Homework Statement


A 2.0 m pendulum is released from rest when the support string is at an angle of 25 degrees with the vertical. What is the speed of the bob at the bottom of the string?


Homework Equations


KE=1/2mv^2
PE=mgh


The Attempt at a Solution


I thought that height would just be 2cos25. Since at the bottom of the pendulum, all PE is converted to KE, PE would equal KE. That makes sense. So my equation was gh=1/2v^2 (Mass cancels). My velocity came out to be .59 m/s and I'm unsure if this is correct or not. Some other sites for this problem talked about height being 2-2cos25. If that is true, why would that be height as opposed to just 2cos25?
 
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  • #2
attachment.php?attachmentid=41262&stc=1&d=1322276156.jpg
 

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  • #3
gneill said:
attachment.php?attachmentid=41262&stc=1&d=1322276156.jpg

I've Calculated the velocity as 1.92m/s now. The diagram helped, thank you!
 

What is a pendulum?

A pendulum is a weight suspended from a fixed point that is able to swing back and forth due to the force of gravity.

How do you find the velocity of the bob on a pendulum?

The velocity of the bob on a pendulum can be found by using the formula v = √(gL(1-cosθ)), where g is the acceleration due to gravity, L is the length of the pendulum, and θ is the angle of the swing.

What is the relationship between the length of the pendulum and its velocity?

The length of the pendulum has a direct relationship with its velocity. As the length of the pendulum increases, the velocity also increases. This means that a longer pendulum will have a higher velocity than a shorter pendulum.

What factors can affect the velocity of the bob on a pendulum?

The velocity of the bob on a pendulum can be affected by factors such as the length of the pendulum, the angle of the swing, and the force of gravity. Other factors that can impact the velocity include air resistance, friction, and the weight of the bob.

How is the velocity of the bob on a pendulum used in real-world applications?

The velocity of the bob on a pendulum is used in many real-world applications, such as in the design of clocks and pendulum-based instruments. It is also used in physics experiments to study the properties of motion and gravity. Additionally, the concept of pendulum velocity is applied in fields such as engineering, astronomy, and seismology.

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