Question

Web Spiders and Oscillations All spiders have special organs that make them exquisitely sensitive to vibrations. Web spiders detect vibrations of their web to determine what has landed in their web, and where. In fact, spiders carefully adjust the tension of strands to "tune" their web. Suppose an insect lands and is trapped in a web. The silk of the web serves as the spring in a spring-mass system while the body of the insect is the mass. The frequency of oscillation depends on the restoring force of the web and the mass of the insect. Spiders respond more quickly to larger - and therefore more valuable - prey, which they can distinguish by the web's oscillation frequency. Suppose a 14 mg fly lands in the center of a horizontal spider's web, causing the web to sag by 4.0 mm. Assuming that the web acts like a spring, what is the spring constant of the web? Which of the following is it?a. 0.027N/mb. 27N/mc. 2.7N/md. 0.27N/mModeling the motion of the fly on the web as a mass on a spring, at what frequency will the web vibrate when the fly hits it? Which of the following is it?a. 25Hzb. 7.9Hzc. 0.79Hzd. 2.5Hz

Answer 1

Complete Question

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Answer:

Step-by-step explanation:

From the question we are told that

The mass of the fly is
`m_f = 11 mg = 11*10^(-3) g = 1.1*10^(-5) \ kg`

The extension of the web is
`e= 4.00 \ mm = 0.004 \ m`

The spring constant is mathematically evaluated as

`k = (mg)/(e)`

substituting values

`k = (1.1 *10^(-5) *9.8)/(0.004)`

`k = 0.027 \ N/m`

The frequency of vibration is

`f = (1)/(2 \pi) \sqrt{(k)/(m) }`

substituting values

`f = (1)/(2 * 3.142 ) \sqrt{(0.027)/(1.1*10^(-5)) }`

`f = 7.9 Hz`