22 April, 2015

Rolling bottle filled with granular materials on a ramp

Question:
If we put a bottle filled with Jelly beans or sands on a ramp, will it roll down the ramp? Why?

(a)  (b) 

Figure 1. (a) Question and (b) The answer for the given conditions.




Figure 2. A sketch for discussion

Let have a look why this happens.

Basic Principle:

The toques given by the gravity and the force at the contact point determine if the bottle will roll down.

Assumption:

Mass center located on the line vertical to the free surface (liquid or granular materials)

Let us consider two types of materials (liquids and granular materials)

1. For liquid (water): the bottle will always rolls down the slope (ramp), independent of what level of water you fill. Because water will always keep a flat free surface its mass center will always locate at the lower side of the slope/ramp.

2. Granular materials (sand, jelly bean): the critical difference to liquid is granular materials will have the angle of repose (which means the surface is not flat). This affects the location of mass center. The location of the mass center varies along the red dashed line with various filling levels. When it is on the higher side of the contact point it will stay there. When it moves to the lower side of the contact point with the increase of filling level it will roll down the ramp.


Hope this will stimulate your interest in granular materials!

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