A distance between two points is exactly 100 feet. Thisdistance is indicated cor

Question

A distance between two points is exactly 100 feet. Thisdistance is indicated correctly on a steel surveyor's tape whenused at a temperature of 70 degrees F and subjected to a pull of 10lbs. If in measuring a certain distance the tape indicatesthe distance to be 100 feet when the tape is subjected to a temperature of 100 degrees F and a pull of 20 lbs, what is thecorrect distance being measured? The tape is 1/32 inchesthick and 3/8 inches wide. ? = 6.5 x 10^-6in/in/degrees F and E = 30 x 10^6 psi? The book tells you the answer is 100.022ft but How do you get it??????

Explanation / Answer

the new 100ft is equal to the increased length of the tape under new condition
so the increased length is the exact distance.

l due to force = (20-10)/(1/32*3/8) * 100 / 30*10^6

= 0.00284 inch

l due to inc in temp = 6.5*10^-6 (100-70)*100

= 0.0195

new length = 100 + 0.00284 + 0.0195 = 100.022

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