Question

All spiders are very sensitive to vibrations. An orb spider sits at the center of its web and monitors radial threads for vibrations created when an insect lands. Assume that these threads are made of silk with a linear density of 1.0 x 10-5 kg/m under a tension of 0.40 N. If an insect lands in the web 30 cm from the spider, how long will it take for the spider to find out

Answer 1

Answer:

The time taken by spider to catch insect 1.5 ms

Explanation:

Given:

Linear mass density $\mu = 1 \times 10^{-5}$ $\frac{kg}{m}$

Tension on the string $T = 0.40$ N

Distance between web and insect lands $x = 30 \times 10^{-2}$ m

From the formula of velocity in string,

   $v = \sqrt{\frac{T}{\mu} }$

First find the velocity and then find time,

   $v = \sqrt{\frac{0.40}{1 \times 10^{-5} } }$

   $v = 200$ $\frac{m}{s}$

The time taken is given by,

   $v = \frac{x}{t}$

   $t = \frac{x}{v}$

   $t = \frac{30 \times 10^{-2} }{200}$

   $t = 1.5 \times 10^{-3}$ sec

   $t = 1.5$ ms

Therefore, the time taken by spider to catch insect 1.5 ms