The Physics of Knocking Things Over

[Peppino]

I've encountered a problem that I do not believe I am able to answer using my very basic knowledge of classical and calculus-based physics, dealing with knocking objects over.

Say we had a cylinder of length L and radius R and mass M. And suppose we shot a bullet of mass m at the very top of the cylinder, and suppose the bullet immediately bounces off the cylinder.

In terms of the above quantities, can we find the minimum speed necessary to knock over the cylinder? Is there anything else that needs to be determined?

I have found that the cylinder must be lifted greater than 45 degrees off the ground or else gravity will restore it, but I am unsure what the rotational inertia would be of this sort, among other things.

Any help would be greatly appreciated!

 

[pnorm91]

correct me if I am wrong, but isn't there a correlation between the length of the cylinder and the angle at which it will begin to fall? also, I am assuming you're speaking of a cylinder of uniform volume, and not thicker at the top, middle, or bottom? additionally, it would seem to me that you would need to know precisly where on the cylinder the force was being applied. It would tip much easier if it were at the top edge versus the bottom edge. just a few things to consider.

 

[Peppino]

Possibly, but on the various objects I have tested (a marker, a textbook, a can of Dr Pepper, a sliced cucumber) the 45 degree rule seems to uphold. If only I had a large range of various sized cylinders could this be tested.

And the bullet is direct towards the very top of the cylinder, and everything is uniform.

 

[Nugatory]

Possibly, but on the various objects I have tested (a marker, a textbook, a can of Dr Pepper, a sliced cucumber) the 45 degree rule seems to uphold. If only I had a large range of various sized cylinders could this be tested.

Ever tried cutting down a tall (twenty meters or so) tree? It doesn't take anywhere near 45 degrees for it to be going over.

Find the center of gravity of the cylinder... When you tilt the cylinder enough that a vertical line through the center of gravity intersects the ground outside of the base of the cylinder, it's no longer stable and will tip over. The longer and thinner cylinder, the smaller the angle at which this happens.

 

[pmacias]

I would first suggest that you consider the conservation of energy and momentum in this scenario. When the bullet hits the cylinder, it will transfer some of its kinetic energy to the cylinder. This will cause the cylinder to move and potentially knock over. The minimum speed necessary to knock over the cylinder would depend on the mass and geometry of the cylinder, as well as the speed and mass of the bullet.

To find the minimum speed, you could calculate the energy and momentum of the bullet before and after it hits the cylinder and use conservation laws to solve for the minimum speed. You would also need to consider the coefficient of restitution, which describes how much energy is lost during the collision between the bullet and the cylinder.

Additionally, as you mentioned, the rotational inertia of the cylinder would also play a role in determining whether it will be knocked over. This would depend on the shape and mass distribution of the cylinder.

In summary, to fully understand the physics of knocking things over, you would need to consider various factors such as energy and momentum conservation, the coefficient of restitution, and the rotational inertia of the object. I would also recommend seeking guidance from a physics expert or conducting experiments to further investigate this problem.