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kogti [31]
3 years ago
5

calcular la longitud de un péndulo que oscila a 10 Hz en santa fe de bogota, sabiendo que en esta ciudad la aceleracion de la gr

avedad es de 978 cm/s2.
Physics
1 answer:
cricket20 [7]3 years ago
5 0

Answer:

L=2.48*10^{-3} m

Explanation:

The period equation for a pendulum is given by:

T=2\pi \sqrt{\frac{L}{g}}

and we know that T = 1/f, where f is the frequency, so we will have:

\frac{1}{f}=2\pi \sqrt{\frac{L}{g}}

Now, we just need to solve this equation for L.

\frac{1}{2\pi f}=\sqrt{\frac{L}{g}}

L=\frac{g}{(2\pi f)^{2}}

  • g is the gravity in Bogota (g=9.78 m/s^{2})
  • f is 10 Hz
  • L is the lenght of the pendulum

L=\frac{9.78}{(2\pi*10)^{2}}

L=2.48*10^{-3} m

I hope it helps you!

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To solve this problem we will use the linear motion description kinematic equations. We will proceed to analyze the general case by which the analysis is taken for the second car and the tenth. So we have to:

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x= Displacement

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Since there is no initial velocity, the same equation can be transformed in terms of length and time as:

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For the second cart

2L \frac{1}{2} at_2^2

When the tenth car is aligned the length will be 9 times the initial therefore:

9L = \frac{1}{2} at_3^2

When the tenth car has passed the length will be 10 times the initial therefore:

10L = \frac{1}{2}at_4^2

The difference in time taken from the second car to pass it is 5 seconds, therefore:

t_2-t_1 = 5s

From the first equation replacing it in the second one we will have that the relationship of the two times is equivalent to:

\frac{1}{2} = (\frac{t_1}{t_2})^2

t_1 = \frac{t_2}{\sqrt{2}}

From the relationship when the car has passed and the time difference we will have to:

(t_2-\frac{t_2}{\sqrt{2}}) = 5

t_2 (\sqrt{2}-1) = 3\sqrt{2}

t_2= (\frac{5\sqrt{2}}{\sqrt{2}-1})^2

Replacing the value found in the equation given for the second car equation we have to:

\frac{L}{a} = \frac{1}{4} (\frac{5\sqrt{2}}{\sqrt{2}-1})^2

Finally we will have the time when the cars are aligned is

18 \frac{1}{4} (\frac{5\sqrt{2}}{\sqrt{2}-1})^2 = t_3^2

t_3 = 36.213s

The time when you have passed it would be:

20\frac{1}{4} (\frac{5\sqrt{2}}{\sqrt{2}-1})^2 = t_4^2

t_4 = 38.172

The difference between the two times would be:

t_4-t_3 = 38.172-36.213 \approx 2s

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The primary purpose in creating national parks is to protect the land from development and pollution.

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The main purpose for creating national parks is to reserve some space for nature. This area is protected from pollution and development.

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