Calculating Force Needed to Push 40in PVC Pipe Over

[BrownApple67]

I was walking through my garage and bumped into a pvc pipe. The pipe fell over and I was wonder how I could calculate the force needed to push the pipe over. The pipe is 40 in. tall and has a 4 in. radius. The force would be applied perpendicular to the pipe and at the very top of it. any help would be great!

 

[torquil]

As it topples, its centre of gravity is raised. You have to calculate by how much it is raised as the pipe is at different angles. The maximum value will determine how much potential energy V it needs to "get over the hump" in the potential energy of the pipe as a function of its angle.

If your mass is much larger than the pipe (no offence intended!), you can assume that the pipe is immediately given the same speed as you had when you bumped into it. Thus you can calculate its kinetic energy K immediately after the collision. If K > V, it will topple. To find K is a bit difficult, since it involves determining the moments of inertia and angular velocities.

This assumes that the collision is simple (vertical pipe, straight on, not pipe rotation, etc...)

If you mass is not large compared to the pipe, you need to do a proper collision analysis, taking into account the change in your own momentum as you hit the pipe.