Finding frequency if you know mass and length of rope.

In summary, a girl with a mass of 40 kg swinging from a 2.8 m rope can calculate her frequency by using the equation T=2∏ (√I / mgh ) for a physical pendulum, or T= 2 x pie x square root of L / g for a simple pendulum. Plugging in the values of 2.8 for length and 9.8 for acceleration due to gravity, the calculated period is 3.35 seconds, resulting in a frequency of 1/3.35.
  • #1
astru025
163
0

Homework Statement



A girl with a mass of 40 kg is swinging from a rope with a length of 2.8 m. What is the frequency of her swinging?

Homework Equations



I could find the period of the situation and then from there could calculate the frequency. For the period I'm not sure what equation I should use. I tried using the equation T=2∏ (√I / mgh ). This did not work for me though. Any help would be nice!

The Attempt at a Solution


Attempt shown above.
 
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  • #2
astru025 said:
I tried using the equation T=2∏ (√I / mgh ). This did not work for me though.
That's the formula for a physical pendulum, which should work just fine. Show what you did.

Of course, since you are ignoring the mass of the rope (I presume), you can also treat this as a simple pendulum.
 
  • #3
Okay I used the equation for a simple pendulum: T= 2 x pie x square root of L / g. Square root of 2.8 / 9.8 x 2pie gave me 3.35 for a period. Then I plugged in 1/3.35 for the frequency and came up with the right answer. Thanks so much!
 

What is frequency?

Frequency is the number of times a repeating event occurs in a given time period. In this case, it refers to the number of times a rope vibrates in a specific time period.

How do mass and length affect the frequency of a rope?

The mass and length of a rope affect the frequency by changing the tension and stiffness of the rope. A heavier and longer rope will have a lower frequency, whereas a lighter and shorter rope will have a higher frequency.

How do you calculate frequency if you know the mass and length of a rope?

The formula for frequency is f=1/T, where T is the time period of one complete vibration. The time period can be calculated by dividing the length of the rope by the speed at which the wave travels through the rope. The speed is determined by the tension and mass per unit length of the rope.

What units are used to measure frequency?

Frequency is measured in Hertz (Hz), which represents the number of vibrations per second. It can also be measured in cycles per second (cps) or revolutions per minute (rpm).

How does frequency affect the behavior of a rope?

The frequency of a rope determines its resonant frequency, which is the frequency at which the rope naturally vibrates. When an external force is applied at this frequency, resonance occurs and the amplitude of the vibrations increases. This can lead to destructive vibrations if the frequency is too high.

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