Conceptual centripetal problem of a spinning ball attached to a string

[kevin17ym]

Homework Statement

If you swing a ball in a vertical circle using a thin string, at the bottom of the circle the tension in the string must be greater than the ball's weight. True or false?

Homework Equations

F = mvv/r
F = mg

The Attempt at a Solution

The correct answer, it says, it's true. But why isn't it false? Why can't the tension and the ball's weight have an equal magnitude of force?
Is it because the "thin" string is also pushing down on the ball so the net weight is ball's weight + thin string weight?

 

[darkxponent]

What is the speed of ball at the bottom?

 

[kevin17ym]

The exact value is not given but you can assume that the ball is in continuous rotation.

 

[WannabeNewton]

What are the forces acting on the ball at the bottom? What sign should the acceleration of the ball be in order for it its trajectory to remain uniformly circular? Remember that something needs to accelerate the ball radially at each instant in an appropriate direction in order for its direction at each instant to change so as to maintain a circular trajectory.

 

[kevin17ym]

Forces acting on the ball: Tension and Gravitational force, in opposite direction.
Sign: If we call the gravitational force negative, then the acceleration is positive. If the gravitational force is positive, then the acceleration is negative.
So why does the magnitude of tension be greater than the weight? Why can't it be the same amount of force?

 

[haruspex]

Forces acting on the ball: Tension and Gravitational force, in opposite direction.
Sign: If we call the gravitational force negative, then the acceleration is positive. If the gravitational force is positive, then the acceleration is negative.
So why does the magnitude of tension be greater than the weight? Why can't it be the same amount of force?

If they were the same, what would the vertical acceleration be? Is the vertical velocity changing at this point?

 

[darkxponent]

Forces acting on the ball: Tension and Gravitational force, in opposite direction.
Sign: If we call the gravitational force negative, then the acceleration is positive. If the gravitational force is positive, then the acceleration is negative.
So why does the magnitude of tension be greater than the weight? Why can't it be the same amount of force?

Did you draw thw FBD of the ball. Once you draw the FBD, you will get the answer.

 

[shadowfalcon]

I think this is right...

True. At the bottom of the circle the net force must point upwards or otherwise center of circle. In order for this to happen, the gravitational force must be therefore less than the tension force exerted upwards.

 

[haruspex]

True. At the bottom of the circle the net force must point upwards or otherwise center of circle. In order for this to happen, the gravitational force must be therefore less than the tension force exerted upwards.

Yes.

 

[kevin17ym]

Oh I see. Thx