Thread: Circular motion

Hi!
There's something I don't understand with circular motion.
Suppose we suspend a ball in rope. Now, we lift the ball up to a certain height, and drop it from this position. Let's look at the ball from an inertial frame of reference. Then there will be a normal force provided by the rope acting on the ball, and a also a gravitational force acting on the ball. As we all know, the resultant force of these two forces will be the resultatnt force acting on the ball, which is equal to the centripetal force.

But now consider the case when the ball is in the position where the the rope is horizontal. The force of gravity will still act on the ball in the vertical direction, the centripetal force will, as always, act towards the center of the motion, in this case in the horizontal direction. But then, if the centripetal force is the resultatnt force of the string force and the force of gravity, the string force must have a vertical component. However, the string is horizontal so how can this be?

Is the explanation that the string isn't actually horizontal, but slightly bent?

Thanks in advance!

You got it. It can never quite get to a horizontal position.

Originally Posted by thyristor

Hi!
There's something I don't understand with circular motion.
Suppose we suspend a ball in rope. Now, we lift the ball up to a certain height, and drop it from this position. Let's look at the ball from an inertial frame of reference. Then there will be a normal force provided by the rope acting on the ball, and a also a gravitational force acting on the ball. As we all know, the resultant force of these two forces will be the resultatnt force acting on the ball, which is equal to the centripetal force.

But now consider the case when the ball is in the position where the the rope is horizontal. The force of gravity will still act on the ball in the vertical direction, the centripetal force will, as always, act towards the center of the motion, in this case in the horizontal direction. But then, if the centripetal force is the resultatnt force of the string force and the force of gravity, the string force must have a vertical component. However, the string is horizontal so how can this be?

Is the explanation that the string isn't actually horizontal, but slightly bent?

Thanks in advance!

Harold is correct, and therefore so are you.

The easiest way to look at this is just draw a free body diagram and consider all of the forces.

You can conclude from the same line of reasoning that if you tie a rope to a wall and suspend a weight from the cent of the rope, it is impossible to pull on the rope with sufficient force to ever make it perfectly horizontal. All ropes must sag at least a little bit.

Okay, thanks to both of you!