Question

Each of the rods depicted below were machined from same stock metal. They were originally machined to be the same length, but their cross-sectional areas were different. If axial force is applied to each rod such that they all change length by the same amount, which rod experienced the largest force

Answer 1

The force required to extend a rod increases as the cross sectional area

increases.

The rod that experiences the largest force is rod B

Reason:

The elongation of a rod by the application of a force is given by the

following formula;

$\Delta L = \dfrac{F \cdot L}{A \cdot E}$

From the above equation, we have that the elongation is inversely

proportional to the cross sectional area, such that the extension of a rod by

a given force reduces as the cross sectional area of the rod increases.

Therefore, the force required to extend the length of a rod by a specific

amount increases as the cross sectional area of the rod increases,

indicating that the rod with the largest cross sectional area require the

most force and therefore, experiences the largest force.

The rod that experiences the largest force is the rod with the largest cross

sectional area, which is rod B

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