A steel wire 1 mm in diameter can support a tension of 0.2 kN. Suppose you need a cable made of these wires to support a tension of 20 kN. The cable’s diameter should be of what order of magnitude?
Answers
Answer:
A steel wire of diameter 1 mm can support tension 0.2 kN. A cable to support tension 20 kN should have a diameter of what order of magnitude? A2 A1 = F2L◦/(Y ∆L) F1L◦/(Y ∆L) = F2 F1 , or A2 = F2 F1 A1 = ( 20 kN 0.2 kN) 0.8 mm2 = 80 mm2.
Answer:
One millimetre diameter steel wire can withstand 0.2 kN of stress. A cable that can handle 20 kN of tension should have a diameter of that magnitude.A2 A1 = F2L◦/(Y ∆L) F1L◦/(Y ∆L) = F2 F1 , or A2 = F2 F1 A1 = ( 20 kN 0.2 kN) 0.8 mm2 = 80 mm2.
Explanation:
How do you find the order of magnitude?
An exponential shift in a quantity or unit's value of plus or minus 1 is known as an order of magnitude. Typically, the phrase is used in connection with scientific notation using powers of 10. In order to make the scale of numbers and measurements of things more logical and understandable, order of magnitude is used.
The standard way to express an order of magnitude is as 10 to the nth power. The magnitude is indicated by the n. A number is effectively multiplied by 10 when it is raised by one order of magnitude. A number is essentially multiplied by 0.1 if it is decreased by one order of magnitude. We then declare that 800 and 450 are of the same magnitude, or 103.
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