Question

why is stress the force divided by the cross sectional area and not force divided by the total area ?

meaning if I have a metal rod with a mass on top why is the stress just the weight of the mass divided by the cross sectional area? will the stress be less if its a really really long metal rod because it gets divided by the length or something?

Answer 1

Think about it, F/A,the force is a vector quantity, and aplies in the direction of force,if some lady weighing 100lb is wearing a pointy stileto shoe and then steps on your feet, the pain will be great, however if they wore wide shoes the pain on your feet might not be as unbearable as case 1

Answer 2

as u know,the definition "force per unit area"(F/A) suggests that stress is pressure.further, effective pressure acts on surface(or cross section area same to that surface) where load is kept not to whole surface area.hence as force acts direct to the surface where it is kept this very surface is effective surface and stress is given as force acting per unit cross sectional area(same as the area of surface where load is kept) on that body.

Answer 3

the force will increase as the length of the rod increases as it has mass. Otherwise we could build a ten mile needle which wpouldn't bend.