# Calculating weight needed for a fixed pole

Imagine a game of swing ball, where the rope is 1m long, and the ball weighs 1kg. How do you calculate the weight that the pole has to be so it does not get pulled over, assuming it is not burried in the ground?

• Is the pole attached to any kind of stand? If so, what are the dimensions of the stand? – David White Nov 29 '18 at 16:39
• Do you want to get the mass of the pole for which it doesn't loose contact from ground if that is the case then find the expression for normal force between the pole and the ground and finger a condition such that N≥0 – Aditya Garg Nov 29 '18 at 16:46
• You will also need to know the maximum speed of the ball, and the width of the stand's base. – BowlOfRed Nov 29 '18 at 18:01
• Yes. Say the max speed is 10m/s. I just want to know what weight the pole has to be not to be pulled over by the force of the ball rotating around.... – Dr James Sprinks Dec 3 '18 at 12:38

In order to maintain stability, the center of mass (COM) of an object must not go over the pivot from which it is rotating: So you need to account for weight and geometry. Assuming that you have a cylindrical pole, you will have a figure similar to the image above (quite thinner, obviously), and if we also assume that the weight of the rope and ball does not change the COM, then you know the position of it.

Now you can measure the angle needed for the COM to be just over your pivot. Now you need to calculate how much energy do you need to make this rotation and compare it with the kinetic energy that the ball has.

The weight of the pole will affect how much energy you need to lift the COM over the pivot.

Reading the question again, I may have misunderstood it. Are you going to fix the pole to the ground? Like with bolts and so? Then the weight of the pole is not as important as the feature that you use to fix it to the ground.

• It is not fixed. I want to know how to work out what weight the pole has to be to stay upright as a ball is spinning.... – Dr James Sprinks Dec 3 '18 at 12:36
• Sorry rotating. – Dr James Sprinks Dec 3 '18 at 12:36