Question

How would forced an stress on the wooden pillar in this figure change is the tone weight (on the top) was the same size but the wooden pillar was narrower?

Answer 1

If a wooden pillar with the same weight on top was made narrower, the compressive stress on the pillar would increase because stress is inversely proportional to cross-sectional area. The strain would also increase since it's directly related to stress when Young's modulus is constant.

Step-by-step explanation:

The question asks how the stress on a narrower wooden pillar would change if it bore the same weight as a wider pillar. According to physics, stress (σ) is calculated by the formula σ = F/A, where F is the force applied perpendicular to the surface of an object and A is the cross-sectional area of that object.

If the cross-sectional area (A) of the pillar decreases while keeping the same weight (force, F) on top of it, the compressive stress experienced by the pillar would increase because stress is inversely proportional to the cross-sectional area.

To find the compressive strain, we need to know the material's Young's modulus (E), which represents the stiffness of the material.

The compressive strain (ε) is given by ε = σ / E. Since the Young's modulus for granite remains constant, a narrower pillar with increased stress will experience increased strain, leading to more potential compression of the pillar itself given the same material properties.