Finding frequency if you know mass and length of rope.

AI Thread Summary
To find the frequency of a girl swinging from a rope, the period can be calculated using the simple pendulum formula T = 2π√(L/g), where L is the length of the rope and g is the acceleration due to gravity. For a rope length of 2.8 m, the calculated period is approximately 3.35 seconds. The frequency is then determined by taking the reciprocal of the period, resulting in the correct answer. The discussion highlights the transition from using a physical pendulum equation to the simpler pendulum formula for accurate results. This method effectively demonstrates the relationship between mass, length of the rope, and swinging frequency.
astru025
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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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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.
 
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!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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