Question

(14%) Problem 7: Suppose a tightrope walker creates a tension of 3.94 x 103 N making an angle of 5° below the horizontal from each supporting pole Calculate how much this tension stretches the steel wire if it was originally 16 m long and 0.43 cm in diameter. Assume steel has a Young's modulus of 2.10 x 101 N/m2. Give your answer in cm. Grade Summary AL = 0.31 Deductions 3% Potential 97% sin( cotan cos Submissions tan 7 НОМE JT Attempts remaining: 6 (3% per attempt) detailed view acos( sinh( EAA asin 4 5 6 atan 2 acotan) 3% tanh cosh) ODegrees cotanh( END Radians VO ВАСKSPАСЕ DEL CLEAR I give up! Feedback Submit Hint Hints: 0%_deduction per hint. Hints remaining: 2 Feedback: 1% deduction per feedback

Answer 1

we know that : Youngs modulus Y is the elastic modulus when deformation is caused by either tensile or compressive stress, and is defined Dividing this equation by tensile strain, we obtain the expression for Youngs modulus : tensile stress tensile strain Where: • Y is the young's modulus . • F1 is the forces that act perpendicular to the surface. • A is the area of the surface of the wire. • T is the tension in the wire • Lo is the original length of the wire. • AL is the elongation in the wire ( the change in the length of thewire)

at first Strategy For solving the problem : from Free body diagram we calculate the force Fl , the area A F1 = T cos 0 = 3.94 x 103 cos 5 = 3525 N

A = πr^{​​​​​2} = π*0.00215² = 1.4522012*10^-5 m^{​​​​​​2}​​​

14SY41) AL = x* x Lo

ΔL = (3525 * 16) / (2.1*10¹¹ * 1.452 * 10^-5 )

ΔL = 0.01849m

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