Net Force on a Spinning Ball Attached to a String Question

[D.Strauss]

Hi all,

I have a conceptual question about the net force of a rotating or spinning ball attached to a string. If we have a situation such as a tether-ball game where the ball is being swung around a string at an angle to the vertical, is the net force the tension in the string, or the component of the tension that acts as the centripetal force? To me personally it seems that the net force should be the centripetal force as this is what is causing the balls acceleration, but then again the only force that can act on the ball (aside from gravity) is through the string.

Any help in clearing this up is greatly appreciated, thanks in advance for any answers.

 

[tiny-tim]

Welcome to PF!

Hi D.Strauss! Welcome to PF!

… is the net force the tension in the string, or the component of the tension that acts as the centripetal force? To me personally it seems that the net force should be the centripetal force as this is what is causing the balls acceleration, but then again the only force that can act on the ball (aside from gravity) is through the string.

This is why I personally think that nobody should ever mention centripetal force … it's confusing.

There is no separate centripetal force … there's only two forces: tension and gravity.​

By definition, centripetal force must be towards the centre, and as you say, that's horizontal.

The net force is the tension plus gravity, and in equilibrium (but not if the ball is rising or falling), that is horizontal.

So in equilibrium, the net force is centripetal, and otherwise it isn't.​

 

[D.Strauss]

Thank you for the welcome and quick reply. :)

I agree with your opinion on the topic, not only is it confusing, it's also pretty rare to find good explanations.
Thank you for clearing this up though, like you said we can only take into account tension and gravity, so the net force must be the sum of the two, which in this case is the centripetal force, right?
I think a lot of the confusion comes from the fact that the name centripetal force suggests a separate force which, as you said, it isn't.

 

[rcgldr]

only take into account tension and gravity, so the net force must be the sum of the two, which in this case is the centripetal force, right?

Only if there is no vertical component of velocity (or acceleration). The ball would have to move in a circle of constant radius along a horizontal plane.

 

[PJC01]

I can provide an explanation for the net force acting on a spinning ball attached to a string. The net force in this scenario is indeed the centripetal force, which is responsible for the ball's circular motion. This force is directed towards the center of the circle and is provided by the tension in the string.

The tension in the string is the only force acting on the ball (aside from gravity), and it is the only force that can change the ball's direction and cause it to accelerate towards the center of the circle. This is why the tension in the string is considered the centripetal force in this situation.

It is important to note that the net force is always equal to the mass of the object times its acceleration, as stated in Newton's Second Law. In this case, the acceleration is towards the center of the circle, and the mass of the ball remains constant. Therefore, the net force is equal to the centripetal force, which is provided by the tension in the string.

I hope this explanation helps to clarify the concept of net force on a spinning ball attached to a string. If you have any further questions, please do not hesitate to ask.