A 55-cm steel rod has a diameter of 30 cm. The compressive strength of steel is 500 × 10⁶ N/m². What is the compression force that would break the rod? A)3.5 × 10⁷ N B)2.4 × 10⁷ N C)1.4 × 10⁸ N D)4.7 × 10⁸ N E)8.9 × 10⁸ N

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Quizplus · Accepted Answer

The compressive strength of steel is the maximum force that can be applied to a steel rod before it breaks. The compressive strength is given by the formula:$$\sigma = \frac{F}{A}$$where:* $\sigma$ is the compressive strength (N/m²)* $F$ is the force (N)* $A$ is the cross-sectional area (m²)The cross-sectional area of a rod is given by the formula:$$A = \frac{\pi d^2}{4}$$where:* $d$ is the diameter (m)In this problem, we are given the following information:* $\sigma = 500 imes 10^6$ N/m²* $d = 30$ cm = 0.3 m* $A = \frac{\pi (0.3 ext{ m})^2}{4} = 0.0707 ext{ m}^2$We can now use the formula for compressive strength to calculate the force that would break the rod:$$F = \sigma A = (500 imes 10^6 ext{ N/m}^2)(0.0707 ext{ m}^2) = 3.5 imes 10^7 ext{ N}$$Therefore, the correct answer is A) 3.5 × 10⁷ N.

A 55-Cm Steel Rod Has a Diameter of 30 Cm