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Q. 32

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 416

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Short Answer

A 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 silk thread?

The spring constant of the silk thread is

See the step by step solution

Step by Step Solution

Step1: Concept and principle.

Forced Oscillations and Resonance:

If an external driving force with angular frequency acts on an oscillating system with natural angular frequency the system oscillates with angular frequency

The amplitude of the system is largest when

or

Step2: Given data.

  • The mass of the spider is
  • The spider has the largest amplitude on its cord if it is tapped once every second.
  • We are asked to determine the spring constant of the silk thread.

Step3: Solution of the silk thread.

The spider's amplitude is greatest when the person's driving angular frequency matches the natural angular frequency of the spider's system and the silk thread from the equation.

where is the frequency at which the person taps the spider which is equal to since the spider is tapped once each second, is the spring constant of the silk thread, and is the mass of the spider. Solve for

Subtitle numerical value.

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