Q:

What is the stress on the cube?

In a problem, it is given that a mass of 10.2 Kg is resting on a cube made out of a particular material. Assuming that the x-axis is vertically upwards, what is the stress on the cube. (We can say that the cube is lying on a surface, and the positive x-axis is pointing upwards.)
I am confused about two things:

What is the sign convention for denoting the stress. Would the stress be negative or positive (I think negative, as it is pointing in the negative x direction).
Do we also consider the stress due to normal reaction from the surface.

A:

Stress is force per unit area. There is a force from below (the surface pushing up) and above (the weight pushing down). These have to be equal and opposite so the cube doesn't accelerate anywhere. You take just one times this force to compute the stress. The sign is a matter of convention - according to this lecture the sign of compressive stress is negative. This does not depend on the coordinate system.

