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melomori [17]
3 years ago
6

If an object moves in uniform circular motion in a circle of radius R = 1.0 meter, and the object takes 4.0 seconds to complete

ten revolutions, calculate the magnitude of the velocity around the circle. (Note: Remember, 10 revolutions is a counting number and not a measurement.) v=_____ m/s 1.6 m/s 2.5 m/s 5 m/s 16 m/s
Physics
2 answers:
boyakko [2]3 years ago
7 0

Answer: 2.5 m/s

Explanation: The velocity in in uniform circular motion is given by:

v=w^2*r where w is angular frequency

w=2*Pi/T  where T is the period

Finally we can calculate v= (2*Pi)^2/T^2*R   where R=1 m

ch4aika [34]3 years ago
3 0

Answer:

16m/s

Explanation:

The velocity v is given by the following relationship;

v=\omega R.......... (1)

where \omega is the angular velocity and R is the radius of the circular path. Angular velocity is defined as the  number of revolutions made by a body in circular motion per unit time or the angle turned through per unit time. It is measured in radians per second.

Also, the following relationship holds for \omega;

\omega=\theta /t...............(2)

where \theta is the angle turned through and t is the time taken.

Given; t = 4s, number of revolutions n = 10.

The angle turned can be obtained from the number of revolutions  by recalling the following;

1 revolution=2\pi rad\\hence\\10revolutions=10*2\pi rad=20\pi rad

Hence; \theta=20\pi rad

Substituting \theta and t into equation (2), the obtain the angular velocity as follows;

\omega=20\pi/4\\\omega=5\pi rads^{-1

Finally we substitute into equation (1) to obtain the linear velocity v as required.

v=5\pi*1=5\pi m/s

Taking \pi =22/7;

v = 15.7m/s which is approximately 16m/s

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Two large, parallel, nonconducting sheets of positive charge face each other. What is at points (a) to the left of the sheets, (
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Answer:

a)The electric Field will be zero at the point between the sheets

b)E_1=\dfrac{\sigma}{\epsilon_0}

c)E_2=\dfrac{\sigma}{\epsilon_0}

Explanation:

Let \sigma be the surface charge density of the of the non conducting parallel sheet.Let consider a Gaussian surface in the form of of cylinder such that its cross-sectional is A . Then there will be flux only due to cross sectional area as the curved sectional is perpendicular to the the electric field  so the Electric Flux due to it is zero.

Now using Gauss law we have, E be the electric Field at the distance r from the sheet then

E\times 2A=\dfrac{\sigma A}{\epsilon_0}\\E=\dfrac{\sigma}{2\epsilon_0}

The Field will be away from the sheet and perpendicular to it.

a) The Electric Field between them

E_1=\dfrac{\sigma}{2\epsilon_0}-\dfrac{\sigma}{2\epsilon_0}\\=0

b)The Electric Field to the right of the sheets

E_1=\dfrac{\sigma}{2\epsilon_0}+\dfrac{\sigma}{2\epsilon_0}\\=\dfrac{\sigma}{\epsilon_0}

c)The Electric Field to the left of the sheets

E_2=\dfrac{\sigma}{2\epsilon_0}+\dfrac{\sigma}{2\epsilon_0}\\=\dfrac{\sigma}{\epsilon_0}

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Read 2 more answers
Given vectors D (3.00 m, 315 degrees wrt x-axis) and E (4.50 m, 53.0 degrees wrt x-axis), find the resultant R= D + E. (a) Write
Eva8 [605]

Answer:

  • R = ( 4.831 m , 1.469 m )
  • Magnitude of R = 5.049 m
  • Direction of R relative to the x axis= 16°54'33'

Explanation:

Knowing the magnitude and directions relative to the x axis, we can find the Cartesian representation of the vectors using the formula

\vec{A}= | \vec{A} | \ ( \ cos(\theta) \ , \ sin (\theta) \ )

where | \vec{A} | its the magnitude and θ.

So, for our vectors, we will have:

\vec{D}= 3.00 m \ ( \ cos(315) \ , \ sin (315) \ )

\vec{D}=  ( 2.121 m , -2.121 m )

and

\vec{E}= 4.50 m \ ( \ cos(53.0) \ , \ sin (53.0) \ )

\vec{E}= ( 2.71 m , 3.59 m )

Now, we can take the sum of the vectors

\vec{R} = \vec{D} + \vec{E}

\vec{R} = ( 2.121 \ m , -2.121 \ m ) + ( 2.71 \ m , 3.59 \ m )

\vec{R} = ( 2.121 \ m  + 2.71 \ m , -2.121 \ m + 3.59 \ m )

\vec{R} = ( 4.831 \ m , 1.469 \ m )

This is R in Cartesian representation, now, to find the magnitude we can use the Pythagorean theorem

|\vec{R}| = \sqrt{R_x^2 + R_y^2}

|\vec{R}| = \sqrt{(4.831 m)^2 + (1.469 m)^2}

|\vec{R}| = \sqrt{23.338 m^2 + 2.158 m^2}

|\vec{R}| = \sqrt{25.496 m^2}

|\vec{R}| = 5.049 m

To find the direction, we can use

\theta = arctan(\frac{R_y}{R_x})

\theta = arctan(\frac{1.469 \ m}{4.831 \ m})

\theta = arctan(0.304)

\theta = 16\°54'33''

As we are in the first quadrant, this is relative to the x axis.

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3 years ago
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