A 1.9 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 at a frequency of 1.2 hz. what is the spring constant of the silk thread?

Question

Physics

Raymond Paul

3 March, 02:23

A 1.9 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 at a frequency of 1.2 hz. what is the spring constant of the silk thread?

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Answers (1)

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Kaiya Snow · Answer 1

M = 1.9 g = 1.9 x 10⁻³ kg, the mass of the spider

f = 1.2 Hz, the fundamental frequency

The circular frequency is

ω = 2πf = 2.4π cycles/s

For oscillatory motion,

ω² = k/m

where k = the spring constant.

Therefore

k/m = (2.4π) ²

k = (1.9 x 10⁻³ kg) * (2.4π 1/s) ² = 0.108 N/m

Answer: 0.108 N/m