Question 1195308: A 100-ft steel tape weighing 2.2 lbs is of standard length under a tension of 12 lbs, supported for full length. This tape was used in laying out a line (found to be 1000.00 ft) on smooth level ground under a steady pull of 15 lbs. Assuming E = 29X 10° psi and that 3.53 cubic inches of steel weighs 1,0 lbs, determine the ff:
a) cross-sectional area of the tape
b) correction for increase in tension per tape length
c) correction for increase in tension whole length measured
d) Corrected length for the effect of increased tension.
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! **a) Cross-sectional Area of the Tape**
* **Find the volume of the tape:**
* Volume = Weight of tape / Density of steel
* Volume = 2.2 lbs / (1 lb / 3.53 in³) = 7.766 in³
* **Find the cross-sectional area:**
* Area = Volume / Length
* Area = 7.766 in³ / 100 ft * (12 in/ft) = 0.0647 in²
**b) Correction for Increase in Tension per Tape Length**
* **Formula:**
* Correction per unit length = (P - P₀) / (A * E)
* where:
* P = Applied tension during measurement (15 lbs)
* P₀ = Standard tension (12 lbs)
* A = Cross-sectional area of the tape (0.0647 in²)
* E = Modulus of elasticity of steel (29 x 10⁶ psi)
* **Calculate:**
* Correction per unit length = (15 lbs - 12 lbs) / (0.0647 in² * 29 x 10⁶ psi)
* Correction per unit length = 3 lbs / 1871300 psi
* Correction per unit length = 1.604 x 10⁻⁶ in/in
**c) Correction for Increase in Tension - Whole Length**
* **Total Correction:** Correction per unit length * Measured length
* Total Correction = 1.604 x 10⁻⁶ in/in * 1000 ft * (12 in/ft)
* Total Correction = 0.0192 in
**d) Corrected Length for the Effect of Increased Tension**
* **Corrected Length:** Measured length - Correction for tension
* Corrected Length = 1000.00 ft - (0.0192 in / 12 in/ft)
* Corrected Length = 1000.00 ft - 0.0016 ft
* Corrected Length = 999.9984 ft
**Therefore:**
* a) Cross-sectional area of the tape: 0.0647 in²
* b) Correction for increase in tension per tape length: 1.604 x 10⁻⁶ in/in
* c) Correction for increase in tension - whole length: 0.0192 in
* d) Corrected length for the effect of increased tension: 999.9984 ft
**Note:**
* This calculation assumes that the tape is perfectly elastic within the range of applied tensions.
* Other factors, such as temperature and sag, can also affect the accuracy of the measurement and may need to be considered for more precise results.
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