Optimizing Pendulum Release Height for Maximum Tension and Circular Motion

In summary, the conversation discusses the necessary conditions for a pendulum bob to swing properly and how to calculate the required centripetal force. It also mentions the forces acting on the bob at the top of the swing and how to ensure the string remains taut. Some calculations are suggested, but it is ultimately left unresolved.
  • #1
reganw
19
0
pendulum.jpg

The pendulum bob in the above figure must circle the rod interrupting its swing, and the string must remain taut at the top of the swing. How far up must the bob be raised before releasing it to accomplish these goals?

I don't know where to begin with this because I don't quite understand what I'm supposed to find.. I've tried finding Ep and Ek using 1/2mv2=mgh but i don't seem to have enough info.

Thank you in advance for any suggestions.
 
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  • #2
Well from ½ mv2 = mgh, what would v2 be equal to?

Since the distance of the rod to the bottom of the swing is 10 cm, what is the centripetal force required? (in term of 'm')

At the top of the swing what are the forces acting and in what directions are they acting? (The resultant of these two will be the same as the centripetal force required)
 
  • #3
rock.freak667 said:
Well from ½ mv2 = mgh, what would v2 be equal to?

Since the distance of the rod to the bottom of the swing is 10 cm, what is the centripetal force required? (in term of 'm')

At the top of the swing what are the forces acting and in what directions are they acting? (The resultant of these two will be the same as the centripetal force required)


the velocity is equal to 1.4m/s and the force acting upon the bob is gravity... but don't i need to know the mass of the bob in order to figure out the force of gravity? still not sure where to go with it..
 
  • #4
reganw said:
the velocity is equal to 1.4m/s and the force acting upon the bob is gravity... but don't i need to know the mass of the bob in order to figure out the force of gravity? still not sure where to go with it..

At the top you will have both tension and gravity acting the same direction.

So T + mg = mv2/r or T = mv2/r - mg.

For the string to be taut T≥ 0.

Also in v2 = 2gh, 'h' is not necessarily 10 cm since that would mean you've already found 'h' when you're in fact trying to find 'h'.
 
  • #5
I'm really not understanding this at all, thanks though! I guess i'll just leave it.
 

FAQ: Optimizing Pendulum Release Height for Maximum Tension and Circular Motion

What is a pendulum bob?

A pendulum bob is a mass attached to the end of a string or rod, which is free to swing back and forth.

Why must the pendulum bob circle the rod?

The circular motion of the pendulum bob is necessary because it allows the pendulum to maintain a constant period of oscillation, regardless of the amplitude or initial angle of release.

What is the purpose of the rod in a pendulum?

The rod serves as the axis of rotation for the pendulum bob, providing a fixed point for the bob to swing around.

How does the length of the rod affect the motion of the pendulum bob?

The length of the rod directly affects the period of the pendulum, with longer rods resulting in longer periods of oscillation.

What factors can affect the motion of a pendulum bob?

The motion of a pendulum bob can be affected by factors such as the length of the rod, the amplitude of the swing, and external forces such as air resistance or friction.

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