Horizontal Distance Material Travels After Sliding Off a Ramp

"How far will the material(rock, gravel, dirt) go in the horizontal direction after falling off the end of the ramp? "

It will travel all the way to the ground.

The speed that it leaves the ramp will determine when it hits the ground.

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This might be part of what you are looking for....

http://www.dummies.com/how-to/content/acceleration-along-ramps-including-friction.html

http://www.engineeringtoolbox.com/friction-coefficients-d_778.html

http://www.physicsclassroom.com/Class/newtlaws/u2l2b.cfm#norm

Thanks. I'll have to check out the links. Here's a picture just for a bit more detail. I guess I will have to find the speed at which the material leaves the ramp, use the angle of the ramp to figure out the direction of the force, find the horizontal component, figure out how long it will take the material to hit the ground in the vertical direction, and that time will tell me how far it traveled in the horizontal direction.

The problem responds to a bit of classical mechanics though one must allow for the spread of the dumped material as the pile begins to grow. Particle mechanics determines the "angle of repose" of the dumped material.

One could also build a scale model and take measurements, then apply these measurements to the full size problem bearing in mind that acceleration due to gravity and resistance due to passage through a viscous fluid such as air do not scale.

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That's basically correct. If there were no friction it would leave the end of the ramp at √2*g*h) parallel to the ramp. The effect of friction depends on the type of material, particle size etc. I would try to do some tests before going full scale.

Your physics are rusty? how about the steel ramp ? that will slow down the speed something slides off.

If the ramp is fixed then I guess you need to set it at the minimum sloe so that whatever is on it will slide down it regardless of how far it will shoot off the end.

I had a load of hardcore delivered in a tip-up truck to my house and the driver complained bitterly that he had to shovel the last half ton off by hand because the truck wouldn't tip up enough for it to fall off - and that was after slamming on the brakes to dislodge the load.after backing up fast.

Whereas the first half of the load fell off the level bed as soon as he raised the tailgate.

The angle-of-repose (already mentioned by others) has an effect on the load before and after it enters the ramp.

So it might be a good idea to provide a means of adjusting the slope to suit the material being conveyed.

How about a bed liner....?

http://www.rrrsupply.com/

http://www.warnerplastics.com/

Your problem is NOT trivial since result depends of many factors.

Geometry: L=length of the slide between stuff falls on and edge where it falls free

B= height of edge over plane where the "stuff" falls

Bh= distance on the horizontal (what you want to know)

µ = friction coefficient between "stuff" and slide

α= angle between horizontal plane and slide plane

g= gravity acceleration

Assumptions: friction is constant, this is in general not true but it is a first step you may empirically adapt

The "stuff" layer slides without internal sliding which could be OK if you angle is > the limit angle which you should also define empiric lly since for instance humidity content does influence it a lot.

Sliding acceleration a=g*(sinα-µ*cosα)

t1= time the "stuff" element slides along the slide t1=(2*L/a)^0.5

At slide end velocity with an angle "α" will be Vo=(2*L*g*(sinα-µ*cosα))^0.5

The horizontal velocity which stays constant during fall (assuming air resistance is neglectable) Vh=Vo*cosα.

The vertical falling velocity will be Vv= Vo*sinα+g*t At t= t2 the distance "B" will be reached → t2= Vo*sinα/g*((1+8*B*g/(Vo*sinα)^2)^0.5-1).

The distance on the horizontal will be Bh=Vh*t2.

As you see it is function of L;B;α and µ. You can use an EXCEL sheet to make the different computations with different values for the parameters.

For every friction value you will notice that there is an angle for which the distance is maximal.

I hope that now you have all what you need.

Feel free to ask if explanations are required.