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Montano1993 [528]
2 years ago
8

Estimate frequency of vibration of your arm. Let the length of the arm be 0.57 m. Consider the arm as a simple pendulum and assu

me its center of mass is about 2/3 its length from the shoulder. Express your answer with the appropriate units. Estimate the natural period of vibration of your arm.
Physics
1 answer:
skad [1K]2 years ago
3 0

Answer:

0.80865 Hz

1.23662 seconds

Explanation:

g = Acceleration due to gravity = 9.81 m/s²

l = Length of arm = 0.57 m

Length of simple pendulum is given by

L=\dfrac{2}{3}l\\\Rightarrow L=\dfrac{2}{3}\times 0.57\\\Rightarrow L=0.38\ m

The frequency is given by

f=\dfrac{1}{2\pi}\sqrt{\dfrac{g}{L}}\\\Rightarrow f=\dfrac{1}{2\pi}\sqrt{\dfrac{9.81}{0.38}}\\\Rightarrow f=0.80865\ Hz

The frequency is 0.80865 Hz

The time period is given by

T=\dfrac{1}{f}\\\Rightarrow T=\dfrac{1}{0.80865}\\\Rightarrow T=1.23662\ s

The time period is 1.23662 seconds

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If 270 watts of power is used in 42 seconds, how much work was done<br>​
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Answer: W = 11340J

Explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

So this is the Formula: Power = Work / Time.

<u>Step 1:</u><em><u> Find the Formula</u></em>

P = W / T

<em><u> </u></em>

<u>Step 2: </u><u><em>Make W the subject of the equation.</em></u>

W = PT

<u>Step 3:</u><u> </u><u><em>Given.</em></u>

P = 270 Watts, T = 42 seconds

<u>Step 4:</u><u><em> Substitute these values into equation 2 .</em></u>

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~I hope I helped you! :)~

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A girl coasts down a hill on a sled, reaching level ground at the bottom with a speed of 7.4 m/s. The coefficient of kinetic fri
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Answer: 62.22 meters

Explanation:

Two solve this, we need to know first how the Sled interact with the snow. While the Sled runs over the snow, the snow opposes to it movement, this is call friction. Frictions creates is a force that goes against any movement and is caused by the interaction between surfaces.

Friction can be calculated using the following equation:

Friction's Force (Ff) = m*N

Where m is the Frictions coficient and N is call Normal, which is a force created by the contact between any weight and a surface. Because the sled is and the surface are totally horizontal, the Normal is equal to the Sled's Weight.

So for this case, we can calculate the Friction's Force:

Ff = 0.045 * 735 N

Ff = 33,07 N

This force will cause a negative acceleration the Sled causing it to slow down and finally stop. To know this accelaration we can use the following equation:

Force (F) = Mass (m) * Accelaration (a)

Looking for the accelaration:

Acceleration (a) = F / M

As a side note:

Mass (M) = F / a                                        (1)

Where we know that F is equal to our Friction Force (Ff) and the Mass for the girl and the Sled can be obtained using the previous equation (1) like this

Girl and sled Mass (M) = 735 N / (9.81 m/s)

M = 74,92 Kg

This is posible, because the Girl and The Sled are aplying a Force on the ground equal to 735 N. The accelartion for their mass is the gravity

Now, with the mass we can found the Accelaration caused by friction:

Acceleration (a) = Ff / M

Accelaration (a) = 33,07 N / 74,92 Kg

a = 0,44 m/s^{2}

To know how far the Sled travel we can use the following equation:

V_{f} ^{2} = V_{0} ^{2} + 2ax

Where Vf is the Final Velocity, which is when the sled finally stops (Vf = 0), Vo is the Initial Speed of the Sled equal to 7.4 m/s and a is equal to the negative accelaration that causes the friction.

(0)^{2} = (7.4 m/s)^{2} + 2(-0,44)x

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x = \frac{0 - (7.4 m/s)^{2} }{-0.88}

x = \frac{0 - (7.4 m/s)^{2} }{-0.88}

x = \frac{0 - (7.4 m/s)^{2} }{-0.88}

x = 62.22 meters

The girls will run over the snow 62.22 meter until finally stopping

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