Bodies on Slopes – Toppling

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A body will topple when the vertical through the centre of gravity lies just outside the base. A particle on a slope is typically more susceptible to toppling because the vertical is closer to the point where it would lie just outside the base.

The triangular prism above is on a slope which makes an angle %theta with the horizontal. If a horizontal force is applied to the left at the top of the triangle, assuming the plane is rough enough so that the prism will topple before it slips, it will begin to topple when the vertical through the centre of gravity C passes through A.

The distance from the top of the triangle to the centre of the base isand the distance from C to the centre of the base is one third of this:

Angle CAB is then

The prism has to move through the extra angleand obviously as increases up to the toppling angle, this extra angle will decrease, making the prism easier to topple.

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