Question

A 3.1 g spider is dangling 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 second.What is the spring constant of the silkthread?

Answer 1

Answer:0.122 N/m

Step-by-step explanation:

Given

Maximum Amplitude can be obtained when tapped after every second

i.e. Time Period
`T=1 s`

mass of spider
`m=3.1 gm`

and we know

`T\cdot \omega =2\pi`

where
`\omega`=natural frequency of oscillation

T=time Period

`\omega` is also given by
`\omega =\sqrt{(k)/(m)}`

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

`1\cdot \sqrt{(k)/(3.1* 10^(-3))}=2\pi`

`k=(2\pi )^2* 3.1* 10^(-3)`

`k=0.122 N/m`