How to Calculate Percent Decrease in the Length of a Three-Legged Wooden Bar Stool
What is the percent decrease in the length of the legs when a man sits on a wooden bar stool?
When a 65 kg man sits on a three-legged wooden bar stool made of solid Douglas fir, each leg decreases in length by approximately 0.0203%. How can we calculate this percent decrease?
Calculation of Percent Decrease:
First, we need to determine the initial length of each leg of the stool before the man sits on it. Then, we can calculate the change in length caused by the weight of the man and express it as a percentage decrease.
Step-by-Step Calculation:
1. Find the initial volume of one leg of the stool using the formula for the volume of a cylinder: Volume = π * (radius)^2 * height
2. Determine the initial length of each leg based on the volume and dimensions of the stool.
3. Calculate the force exerted by the man on each leg, which is equal to the weight of the man multiplied by acceleration due to gravity.
4. Use the concepts of stress and strain to find the strain caused by the man's weight on each leg.
5. Calculate the change in length (ΔL) caused by the strain and express it as a percentage decrease.
6. The percentage decrease in the length of each leg represents the percent decrease in overall stability and support of the wooden bar stool when a person sits on it.