Question

A 20,000 lb load is placed on top of an 10" x 10" rectangular prism. Starting with the formula relating stress (f) to load (P) and cross-sectional Area (A), calculate the stress in the prism,

Answer 1

The stress in a 10" x 10" rectangular prism with a 20,000 lb load is calculated by dividing the load by the cross-sectional area, resulting in a stress of 200 lbf/in².

Step-by-step explanation:

To calculate the stress in the prism, we start by using the formula for stress:

stress (f) = load (P) / cross-sectional Area (A)

Given a load (P) of 20,000 lb placed on top of a 10" x 10" rectangular prism, we first convert the area to square inches (since 1 inch = 2.54 cm):

1. Area (A) = 10 in x 10 in = 100 in².
2. Then we convert the load from pounds to pounds-force (lbf), noting that in the Imperial system, lb is a unit of mass. For this calculation, we assume that lb and lbf are equivalent in the context given (as is common in engineering practice in the Imperial system), so P = 20,000 lbf.
3. Now, we apply the formula to find the stress:
4. Stress (f) = 20,000 lbf / 100 in² = 200 lbf/in².

The stress in the prism is therefore 200 lbf/in².