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omeli [17]
3 years ago
15

Consider a vortex filament of strength Γ in the shape of a closed circular loop of radius R. Consider also a straight line throu

gh the center of the loop, perpendicular to the plane of the loop. Let A be the distance along the line, measured from the plane of the loop. Obtain an expression for the velocity at distance A on the line, as induced by the vortex filament.
Physics
1 answer:
Sedbober [7]3 years ago
6 0

Answer:

\vec{V} = \frac{\Gamma}{2R}\vec{A}

Explanation:

We define our values according to the text,

R= Radius

\vec{V} =Velocity

\Gamma =Strenght of the vortex filament

From this and in a vectorial way we express an elemental lenght of this filmaent as \vec{dl}. So,

\vec{dl}x\vec{r} = R*dl*\vec{A}

Where \vec{A} imply a vector acting perpendicular to both vectors.

Applying Biot-Savart law, we have,

\vec{V} =\frac{\Gamma}{4\pi}\int\frac{\vec{dl}x\vec{r}}{r^3}

Substituting the preoviusly equation obtained,

\vec{V} = \frac{\Gamma}{4\pi}\int\frac{R*dl*\vec{A}}{R^3}

\vec{V} = \frac{\Gamma}{4\pi R^2}\int^{2\pi R}_0 dl*\vec{A}

\vec{V} = \frac{\Gamma(2\pi R \vec{A})}{4\pi R^2}

So we can express the velocity induced is,

\vec{V} = \frac{\Gamma}{2R}\vec{A}

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olchik [2.2K]

Answer:

Definitely Spinning permanent magnets within an array of fixed permanent magnets

Explanation:

Any relative motion between magnets (be they permanent or electromagnetic) and a coil of wire will induce an electric current in the coil.

What will not induce an electric current is the relative motion between the two coils of wire (because there is no change in magnetic field), or the relative motion between two magnets (there are no coils of wire to induce the current into).

<em>Therefore, spinning permanent magnets within an array of fixed permanent magnets does not induce an electric current.</em>

5 0
3 years ago
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A 100 kg box is suspended from two ropes. The "left rope makes an angle of 20" degrees with the vertical, and the right rope mak
GarryVolchara [31]

Explanation:

It is given that,

Mass of the box, m = 100 kg          

Left rope makes an angle of 20 degrees with the vertical, and the right rope makes an angle of 40 degrees.  

From the attached figure, the x and y component of forces is given by :

T_{1x} =-T_1 cos (20)

T_{2x} = T_2 cos (40)

mg_x = 0

T_{1y} = T_1 sin (20)

T_{2y} = T_2 sin (40)

mg_y= -mg

Let R_x and R_y is the resultant in x and y direction.

R_x=-T_1 cos (20)+T_2 cos (40)+0

R_y=T_1 sin(20)+T_2 sin(40)-mg

As the system is balanced the net force acting on it is 0. So,

-T_1 cos (20)+T_2 cos (40)+0=0.............(1)

T_1 sin(20)+T_2 sin(40)-100\times 9.8=0..................(2)

On solving equation (1) and (2) we get:  

T_1=866.86\ N (tension on the left rope)

T_2=1063.36\ N (tension on the right rope)

So, the tension on the right rope is 1063.36 N. Hence, this is the required solution.                            

7 0
3 years ago
What are 7 examples of potential energy
yaroslaw [1]

Answer:

<em>Hewo Otaku Kun Here! (UwU)</em>

Explanation:

1. A rock sitting at the edge of a cliff has potential energy. If the rock falls, the potential energy will be converted to kinetic energy.

2. Tree branches high up in a tree have potential energy because they can fall to the ground.

3. A stick of dynamite has chemical potential energy that would be released when the activation energy from the fuse comes into contact with the chemicals.

4. The food we eat has chemical potential energy because as our body digests it, it provides us with energy for basic metabolism.

5. A stretched spring in a pinball machine has elastic potential energy and can move the steel ball when released.

6. When a crane swings a wrecking ball up to a certain height, it gains more potential energy and has the ability to crash through buildings.

7. A set of double "A" batteries in a remote control car possess chemical potential energy which can supply electricity to run the car.

<em>happy to help!</em>

<em>from: Otaku Kun ^^</em>

8 0
3 years ago
Which of the following describes the moon’s motion around Earth?
Mamont248 [21]

Answer:

i think B?

Explanation:

6 0
3 years ago
In chemical reactions, energy is absorbed or released in the form of:
disa [49]

Answer:

Heat

Explanation:

Because chemical energy is stored, it is a form of potential energy. When a chemical reaction takes place, the stored chemical energy is released. Heat is often produced as a by-product of a chemical reaction – this is called an exothermic reaction.

Hope this helped.

3 0
3 years ago
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