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An engineer is deciding whether to replace a bar made of an aluminum alloy with

steel of tensile strength 500 MPa. A bar of the aluminum alloy 2 cm across (square cross
section) can withstand pulling up to about 120000 N. What is the tensile strength of the
aluminum alloy, and how would a steel bar of equal tensile strength compare?
O a. about 600 MPa; an equivalent steel bar would be thicker
O b. about 300 MPa; an equivalent steel bar would be thinner
O c. about 60 MPa; an equivalent steel bar would be much thinner

An engineer is deciding whether to replace a bar made of an aluminum alloy with steel-example-1
User Quilby
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1 Answer

3 votes

Answer: About 60 MPa; an equivalent steel bar would be much thicker.

Step-by-step explanation:

The tensile strength (TS) of a material is the maximum stress it can withstand before failing under tension. It is usually measured in units of megapascals (MPa). The TS of a material depends on its composition and microstructure, as well as the testing conditions.

Given that a bar made of the aluminum alloy with a cross-section of 2 cm^2 can withstand pulling up to about 120000 N, we can calculate its tensile strength as follows:

TS = force / cross-sectional area = 120000 N / (2 cm)^2 = 30000 kPa = 30 MPa.

Therefore, the tensile strength of the aluminum alloy is about 30 MPa.

To compare with an equivalent steel bar of tensile strength 500 MPa, we need to calculate the cross-sectional area of the steel bar that can withstand the same force.

120000 N is the maximum force that the aluminum bar can withstand, so we want to find the cross-sectional area of the steel bar that can withstand 120000 N with a TS of 500 MPa:

TS = force / cross-sectional area

cross-sectional area = force / TS = 120000 N / 500 MPa = 0.24 cm^2.

Therefore, the steel bar needs to have a cross-sectional area of 0.24 cm^2 to withstand the same force as the aluminum bar. Since the steel bar has a higher tensile strength, it can be thinner than the aluminum bar.

The area of the aluminum bar is 2 cm^2, so the steel bar would be much thinner:

0.24 cm^2 / 2 cm^2 = 0.12.

Therefore, the equivalent steel bar would be much thinner than the aluminum bar. The correct answer is (C) about 60 MPa; an equivalent steel bar would be much thicker is incorrect.

User N Dorigatti
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