Question

A 2.3 g spider is hanging at the end of a silk thread. You can make the spider bounce up and down on the thread by tapping lightly on his feet with a pencil. You soon discover that you can give the spider the largest amplitude on his little bungee cord if you tap exactly once every 3 seconds.What is the spring constant of the silk thread?

Answer 1

Answer:$k=10.091\times 10^{-3} N/m$

Explanation:

Given

mass of spider $m=2.3 gm$

Largest amplitude can be obtained by Tapping after every 3 second

i.e. Time period of oscillation is $T= 3 s$

considering spider to execute Simple harmonic motion

time of oscillation is given by

$T=2\pi\sqrt{\frac{m}{k}}$

substituting values

$3=2\pi \sqrt{\frac{2.3\times 10^{-3}}{k}}$

$\frac{3}{2\pi }=\sqrt{\frac{2.3\times 10^{-3}}{k}}$

$0.477=\sqrt{\frac{2.3\times 10^{-3}}{k}}$

$(0.477)^2=\frac{2.3\times 10^{-3}}{k}$

$\frac{2.3\times 10^{-3}}{k}=0.228$

$k=10.091\times 10^{-3} N/m$