Question

the aluminum and steel bars from an engine mounting system shown below are of equal lenght and the cross sectional area of the aluminum is twice that of steel

Answer 1

Given the aluminum and steel bars have equal length and the aluminum's cross-sectional area is twice that of steel, the aluminum bar has a larger cross-sectional area than the steel bar.

Explanation:

The cross-sectional area
`(\( A \))` of a material is calculated as the product of its length
`(\( l \))` and its cross-sectional area
`(\( A_{\text{cross-sectional}} \))`. Here, it's given that the lengths of both aluminum and steel bars are equal
`(\( l_{\text{aluminum}} = l_{\text{steel}} \)).`

Given that the cross-sectional area of aluminum
`(\( A_{\text{aluminum}} \))` is twice that of steel
`(\( A_{\text{steel}} \))` and assuming
`\( A_{\text{aluminum}} = 2 * A_{\text{steel}} \)`, the aluminum bar's cross-sectional area is larger. This relationship holds true because the cross-sectional area of the aluminum is twice that of steel. Therefore, when comparing bars with equal length, the aluminum bar's cross-sectional area will be larger than the steel bar's.

Understanding these proportional relationships in materials' properties, such as cross-sectional area, helps engineers and designers make informed decisions about material selection based on their desired mechanical properties and strength for specific applications. In this scenario, the aluminum bar's larger cross-sectional area indicates its potential for different load-bearing capabilities compared to the steel bar, highlighting the significance of material properties in engineering designs.