Your mom wants you to hang a flower pot from a round steel wire. The radius of the wire is .05 inches. The pot weighs 20 lbs. Using the equation of stress:

The stress \(\sigma\) in a material is calculated using the equation:

\[
\sigma = \frac{F}{A}
\]

where:
- \(\sigma\) is the stress (force per unit area),
- \(F\) is the force (or weight in this case) applied,
- \(A\) is the cross-sectional area of the wire.

### Step 1: Determine the Cross-Sectional Area of the Wire

Since the wire is round, we can calculate its cross-sectional area \(A\) using the formula for the area of a circle:

\[
A = \pi r^2
\]

where:
- \(r\) is the radius of the wire,
- \(\pi \approx 3.14159\).

Given:
- Radius \(r = 0.05\) inches.

So,

\[
A = \pi (0.05)^2 = \pi \times 0.0025 \approx 0.00785 \text{ square inches}
\]

### Step 2: Calculate the Force \(F\)

Since the pot weighs 20 pounds, and weight is a force due to gravity, we can use \(F = 20\) lbs directly in the stress equation.

### Step 3: Calculate the Stress

Using the stress formula:

\[
\sigma = \frac{F}{A} = \frac{20}{0.00785} \approx 2547.17 \text{ psi (pounds per square inch)}
\]

### Answer

The stress on the steel wire is approximately **2547.17 psi**.

Would you like to go into more detail or have any questions?

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Here are some related questions you might consider:

1. How would the stress change if the radius of the wire were doubled?
2. What would be the maximum weight the wire could hold if the tensile strength of steel is known?
3. How does temperature affect the stress in a steel wire?
4. What is the difference between stress and strain in materials?
5. How would using a material other than steel impact the wire’s ability to support the pot?

**Tip:** In material science, stress is often considered alongside strain to understand how materials deform under load.

Learn how to calculate the stress on a round steel wire with a radius of 0.05 inches supporting a 20 lb flower pot. This detailed solution explores key concepts in material science, including stress calculations and cross-sectional area determinations. Ideal for high school students.

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