Math Problem Statement

A bar is subjected to a tensile load of 200 N. The cross section of the bar is 20 mm x 5

mm. Find the tensile stress of bar.

Solution

The tensile stress (σ\sigma) on a bar subjected to a tensile load is calculated using the formula:

σ=FA\sigma = \frac{F}{A}

Where:

  • FF is the tensile force applied to the bar.
  • AA is the cross-sectional area of the bar.

Given:

  • Tensile force, F=200NF = 200 \, \text{N}
  • Cross-sectional dimensions of the bar: 20mm×5mm20 \, \text{mm} \times 5 \, \text{mm}

First, calculate the cross-sectional area (AA):

A=20mm×5mm=100mm2=100×106m2=0.0001m2A = 20 \, \text{mm} \times 5 \, \text{mm} = 100 \, \text{mm}^2 = 100 \times 10^{-6} \, \text{m}^2 = 0.0001 \, \text{m}^2

Now, calculate the tensile stress:

σ=200N0.0001m2=2,000,000N/m2=2MPa\sigma = \frac{200 \, \text{N}}{0.0001 \, \text{m}^2} = 2,000,000 \, \text{N/m}^2 = 2 \, \text{MPa}

Tensile stress:

σ=2MPa\sigma = 2 \, \text{MPa}

Would you like further details or clarifications on this problem?

Here are 5 related questions:

  1. What is the unit of tensile stress?
  2. How would the stress change if the cross-sectional area doubled?
  3. What happens to the tensile stress if the force is reduced by half?
  4. How can tensile stress be reduced in a real-world scenario?
  5. What are typical applications where tensile stress is crucial to consider?

Tip: Always ensure that force and area are in consistent units when calculating stress!

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Math Problem Analysis

Mathematical Concepts

Physics
Mechanics
Stress and Strain

Formulas

Tensile stress formula: σ = F / A

Theorems

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Suitable Grade Level

Grades 9-12