Question about falling objects

[TheGenericGeek]

G'day Guys and Gals,

I'm working on trying to come up with a best-fit excel sheet for work.
Basically I'm trying to find out where dirt/rocks will peak if dropped down a pipe at any given angle.

As attached, my crude diagram - I'm trying to calculate the blue line.
The height of the container will vary, the angle of the pipe will vary, the length of the pipe will vary, and I'm trying to get a rough idea of what trajectory the dirt/rocks will follow, and turn this into an excel sheet (Just need assistance with the equations to calculate it all)
Currently the only assumption made is that the dirt/rocks will fall straight from wherever the pipe enters the container, straight down - Obviously this is not the case.

Any help you could offer is great appreciated.

Cheers,
TheGenericGeek

 

[Andrew Mason]

Welcome to PF generic!

This is a relatively simple problem to solve if you know the speed of the material exiting the end of the pipe, $v_0$. The direction that the material is moving is given by the angle of the pipe relative to the horizontal, $\theta$. It is then a matter of applying principles of projectile motion.

The time of fall is the solution to the quadratic equation:

$\frac{1}{2}gt^2 + (v_0\sin\theta) t - h = 0$ where h is the vertical fall distance from the end of the pipe.

The horizontal distance moved in that time is the horizontal velocity exiting the pipe: $v_0\cos\theta$ multiplied by the time of fall, t:

$\Delta x = (v_0\cos\theta) t$

$v_0$ can be determined if you know the height that the material falls from an initial rest position to the end of the pipe AND the coefficient of kinetic friction between the material and the pipe, as well as the angle of the pipe. Otherwise, you have to measure it.

AM