Question

A spider swings in the breeze from silk thread with a period of 0.6sec.How long is the spider's strand of skill​

Answer 1

Concept:

The time period of an object or particle in motion is the amount of time required for it to complete one oscillation.

A simple pendulum is a machine in which the point mass is hung from fixed support by a light, inextensible string.

Given:

A spider swings in the breeze from a thread for a period of $0.6$ seconds.

Find:

The length of the spider's strand of silk.

Solution:

When the spider swings in the breeze, the motion of the spider is similar to that of a simple pendulum.

The time period of a simple pendulum in simple harmonic motion with length $L$ and acceleration due to gravity $g$ is:

$T=2\pi \sqrt{\frac{L}{g} }$

$T^2=\frac{4\pi ^2L}{g}$

$L=\frac{gT^2}{4\pi ^2}$

Now, we have

$T=0.06s\\g=10m/s^2$

Therefore,

$L=\frac{(10)(0.6)^2}{4\pi ^2}$

$L=0.09m$

The length of the spider's strand of silk is $0.09m$.

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