Mechanics | Suspended ball | Loop The Loop?

[dharavsolanki]

A ball of mass m is suspended by a thread of length l. With
what minimum velocity has the point of suspension to be shifted
in the horizontal direction for the ball to move along the circle about
that point? What will be the tension of the thread at the moment it
will be passing the horizontal position?

Was trying my hand at this Physics Puzzle! Got no idea how to start and where to start. Don't feel like this question has got anything to do with "Home work help".

 

[dharavsolanki]

OK. I see no discussion going on round here. Maybe i can give some inputs which others can build up on.

I initially thought in terms of a pseudo force, but it doesn't take much time to realize that there is no acceleration involved.

The support end is constantly moving, so the string moves along with and so does the ball with the string. Now, because of this, the string has to be tense, and plus at an incination. Maybe because of this, there's an unbalanced component of the tension that cause this motion?

I may have not solved the problem with this thought but maybe ou guys could actually build up on this!

 

[WiFO215]

Hi dharavsolanki,
Okay. Let's see what they've given us to work with.
1// For minimum velocity to complete a vertical circle, the tension in the thread can die out to zero, and the centripetal accn. can be provided for by the weight force.

2//We have a thread. When you push a thread inwards, it doesn't push you back, it just buckles.

3// You have already realized there is no pseudo force involved. Imparting velocity to the ball would be equivalent to imparting velocity to the ball.
Imagine there are two observers. One of them sitting on the ball and the other sitting in the frame where the hinge point is stationary.

When the ball is imparted velocity in the lab frame, the ball will see the hinge point moving backwards.

What do you think you can do from here?

 

[dharavsolanki]

i feel it's a simple problem where in we have to calculate the minimum velocity to be imparted to a simple pendulum bob so that it completes a circle. Nice.

OK. another question. does this minimum velocity depend on what has been moved? i mean, whether it is the point of suspension or the bob itself? in other words, does the frame mean something?

 

[WiFO215]

i feel it's a simple problem where in we have to calculate the minimum velocity to be imparted to a simple pendulum bob so that it completes a circle. Nice.

Very good.

OK. another question. does this minimum velocity depend on what has been moved? i mean, whether it is the point of suspension or the bob itself? in other words, does the frame mean something?

Imagine sitting on the bob. The pseudo force you mark on the hinge point will provide the centripetal force for the bob. In this frame, the hinge will rotate around you.