Sci-fi physics: horizontal gravity

Problem

If gravity were horizontal instead of vertical, what would happen to a block resting on an inclined plane? Reconsider the decompositions and constraint reactions.

Solution

The whole standard analysis of the inclined plane rests on an implicit assumption: the weight $\vv P = m\vv g$ is vertical. We decompose it into a component along the plane $mg\sin\theta$ (which tends to make the block slide down) and a component perpendicular to it $mg\cos\theta$ (which presses the block against the surface and determines the normal force $N = mg\cos\theta$). The constraint works precisely because part of the weight pushes the block into the plane.

If gravity now became horizontal, parallel to the ground, this decomposition would break down completely:

• The weight is no longer directed “downward” along the vertical, but sideways. The direction “down the slope” no longer coincides with that of the force.
• The component that pressed the block onto the surface changes: depending on how the plane is oriented relative to the new direction of $\vv g$, the normal force can be reduced or even vanish, and the constraint no longer holds the block as before.
• The block would not slide down along the line of steepest descent, but would be accelerated horizontally, in the direction of the new gravity, sliding sideways and possibly detaching from the plane.

In short: “sliding down the inclined plane” only makes sense with vertical gravity. With horizontal gravity the block does not slide down but sideways, and the whole treatment of components and constraint reactions must be redone from scratch relative to the new direction of the weight.

$\ev{\text{Horizontal weight} \Rightarrow \text{the block does not slide down the slope but slides sideways}}$

Linked items

Topics: Dinamica Concepts: Forza peso · Forza normale Skills: Analisi di casi limite e fantafisica · Scomposizione sul piano inclinato Objects: Piano inclinato