What Is the Ideal Placement of a Rod on a Pendulum String for Complete Rotation?

[JonDaMon8]

Alright this is the problem, i hope i describe it so you can all understand it

You start out holding the bob at and angle of 90 degrees (horizontal), with the string tight. Then release the bob, when the angle hits 0 degrees a fixed rod is placed somewhere between the top of the string and the bob. This cuts the length of the pendulum so that the pendulum now spins around the fixed rod

At what spot on the string should the fixed rod be placed that will allow the bob to spin all the way around the fixed rod at least once

By doing guess and check i concluded that it would be at exactly half way down the string to allow it to spin around the fixed rod

But i can't figure out how you would figure it out

i kno you use mg sin theta to find the PE i believe but i can't figure out what to do from there


If you don't get my description i can prolly make a video to show what i mean

 

[Tide]

Try energy conservation!

 

[JonDaMon8]

How? When the string reaches the bottom, the potenial energy is at 100%, and then starts to turn into KE in an equal ratio. But i don't see how i can apply it into the problem

 

[JonDaMon8]

Alright i got an idea, since the length of the pendulum has been cut in half, (because of the fixed rod) half of the enegery from the original fall is used to get the bob back to horizontal with the x-axis, and the rest of the energy to get it around the bob past the y-axis and around to a complete rotation

If you set the fixed rod up at further down from the midpoint of the string, there is some energy left over

and if you set the fixed rod about the midpoint of the string, there isn't enough energy to get it to go around it would stop at around a positive angle from the -x axis...

does this make any sense or sound correct to u guys?

 

[Doc Al]

By doing guess and check i concluded that it would be at exactly half way down the string to allow it to spin around the fixed rod

This is incorrect.

As Tide suggested, you will need to use conservation of energy. But be sure that the bob has enough energy at the top of its motion so that the string remains taut. (To find out how much energy is needed to keep the string taut, consider centripetal acceleration.)

 

[JonDaMon8]

This is incorrect.

As Tide suggested, you will need to use conservation of energy. But be sure that the bob has enough energy at the top of its motion so that the string remains taut. (To find out how much energy is needed to keep the string taut, consider centripetal acceleration.)

Alright, so theoretically, if the fixed rod is at halfway between the top of the string and bottom, when the string gets to horizonal with the fixed rod, 50% of the KE is transferred, right? That means there's 50% KE left, but that 50% is not enough to keep the string taut just enough to get it to the very top and then it would fall, correct?

 

[Doc Al]

Alright, so theoretically, if the fixed rod is at halfway between the top of the string and bottom, when the string gets to horizonal with the fixed rod, 50% of the KE is transferred, right? That means there's 50% KE left, but that 50% is not enough to keep the string taut just enough to get it to the very top and then it would fall, correct?

When the bob reaches half its original height, it will have half the KE it had at the bottom. And that is not enough to keep the string taut throughout the rest of the motion. When the string goes slack the bob will follow a parabolic path, so it won't even make it to the original height. (It's not being shot straight up: the string changes the bob's trajectory. So it will never make it to the original height if the rod is placed at the halfway point.)