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* 10^(-3) N/m`

Step-by-step 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{(m)/(k)}`

substituting values

`3=2\pi \sqrt{(2.3* 10^(-3))/(k)}`

`(3)/(2\pi )=\sqrt{(2.3* 10^(-3))/(k)}`

`0.477=\sqrt{(2.3* 10^(-3))/(k)}`

`(0.477)^2=(2.3* 10^(-3))/(k)`

`(2.3* 10^(-3))/(k)=0.228`

`k=10.091* 10^(-3) N/m`