37. .. BIO Spiderweb An orb weaver spider with a mass of 0.26 g hangs vertically by one of its threads. The thread has a Young's modulus of 4.7 × 10º N/m² and a radius of 9.8 × 10¯6 m. (a) What is the fractional increase in the thread's length caused by the spider? (b) Suppose a 76-kg person hangs vertically from a nylon rope. What radius must the rope have if its fractional increase in length is to be the same as that of the spider's thread?
37. .. BIO Spiderweb An orb weaver spider with a mass of 0.26 g hangs vertically by one of its threads. The thread has a Young's modulus of 4.7 × 10º N/m² and a radius of 9.8 × 10¯6 m. (a) What is the fractional increase in the thread's length caused by the spider? (b) Suppose a 76-kg person hangs vertically from a nylon rope. What radius must the rope have if its fractional increase in length is to be the same as that of the spider's thread?
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VIEWStep 2: Find the expression for the fractional change in the length of the string:
VIEWStep 3: (a) Calculate the fractional change in the length of string when insect hangs on it:
VIEWStep 4: (b) Calculate the radius of the string when the person hangs vertically on a string:
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