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Evgesh-ka [11]
3 years ago
6

A flat sheet is in the shape of a rectangle with sides of lengths 0.400 m and 0.600 m. The sheet is immersed in a uniform electr

ic field of magnitude 95.0 N/C that is directed at 20∘ from the plane of the sheet.
Required:
Find the magnitude of the electric flux through the sheet.
Physics
1 answer:
Katen [24]3 years ago
5 0

Answer:

ФE = 9.403W

Explanation:

In order to calculate the magnitude of the electric flux trough the sheet, you use the following formula:

\Phi_E=\vec{A}\cdot \vec{E}=AEcos\theta       (1)

A: area of the rectangular sheet = (0.400m)(0.600m) = 0.24m^2

E: magnitude of the electric field = 95.0N/C

θ: angle between the direction of the electric field and the normal to the surface of the sheet

You replace the values of the parameters in the equation (1):

\Phi_E=(0.24m^2)(95.0N/m)cos(20\°)=9.304W

The magnitude of the electric flux is trough the sheet is 9.403W

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<u>The fraction of the total kinetic energy that is rotational for a uniform sphere is</u><u> 1/3.</u>

<h3>What is kinetic energy?</h3>
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Option (a) f = \frac{0.5}{1.5} = \frac{1}{3}

Option (b) uniform sphere

            f = \frac{2}{7}

C) uniform hollow sphere

           f = \frac{2}{5}

D) uniform hollow cylinder with inner radius R/2 and outer radius R

           f = \frac{5}{13}

that fraction of total energy as rotational energy is given as

     f = \frac{\frac{1}{2}Iw^{2}  }{\frac{1}{2}mv^{2} + \frac{1}{2} Iw^{2}   }

   f =  \frac{m k^{2}(\frac{v^{2} }{R^{2} })  }{mv^{2} + m k^{2}(\frac{v^{2} }{R^{2} }  )}

    f =  \frac{\frac{k^{2} }{R^{2} } }{1 + \frac{k^{2} }{R^{2} } }

A) uniform Solid cylinder for cylinder we know that

         \frac{k\\ ^{2} }{R^{2} }  = 0.5

          f = \frac{0.5}{1.5}  = \frac{1}{3}

B) uniform Sphere for sphere we know that

        \frac{k^{2} }{R^{2} } = \frac{2}{5} \\

    f = \frac{0.4}{1.4} = \frac{2}{7}

C) uniform hollow sphere for hollow sphere we know that

            \frac{k^{2} }{R^{2} } = \frac{2}{3}

         f = \frac{\frac{2}{3} }{\frac{5}{3} } = \frac{2}{5}

D) uniform hollow cylinder with inner radius R/2 and outer radius R for annular cylinder

             \frac{k^{2} }{R^{2} } = \frac{5}{8}

            f = \frac{\frac{5}{18} }{\frac{13}{8} } = \frac{5}{13}

Learn more about kinetic energy

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<u />

<u>The complete question is -</u>

It is well known that for a hollow, cylindrical shell rolling without slipping on a horizontal surface, half of the total kinetic energy is translational and half is rotational. What fraction of the total kinetic energy is rotational for the following objects rolling without slipping on a horizontal surface?Part AA uniform solid cylinder.Part BA uniform sphere.Part CA thin-walled hollow sphere.Part DA hollow, cylinder with outer radius R and inner radius R/2.

       

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