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Arada [10]
3 years ago
12

A particle of charge q moving through a magnetic field B experiences the force where v is the velocity of the particle. Show tha

t: (i) The force does no work in moving the particle along its path from t = 0 to t=T. (i1) The speed v(t) Iv(O)ll of the particle is constant in time e particle 1s constant in time
Physics
1 answer:
MrRa [10]3 years ago
3 0

Answer:

       dx/Dt x B . x  =0

Explanation:

Let's calculate the work and the magnetic force, the expression for magnetic force is

        F = qv x B

Bold indicate vector quantities, the expression for the job is

         W = F. X

Let's replace in this equation

       W = q v x B . X

The definition of speed is

      v =  dX / dt

With what work is left

     W = q dX / dt x B . X

As we can see the vector product gives us a vector perpendicular to dX and its scalar product by X of zero

Second part

   The speed a vector and although the magnitude is constant the change of direction implies a change in the speed.

   Let's calculate the magnitudes of speed (speed)

       F = qv B sin θ

       F = ma

       q v B sin θ = ma

       a = qvB / m senT

     

This acceleration is perpendicular to the magnetic field and the velocity, so it does not change if magnitude but its direction, it is directed to the center of the circle.

   | v | = q vB/m sin θ

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kari74 [83]
We need to be careful here.
The calculation of the gravitational force between two objects
refers to the distance between their centers. 
The minimum possible distance between the Earth's and moon's
centers is the sum of their radii (radiuses).

Earth's radius . . . . .  6,360 km  =  6.36 x 10⁶ meters
Moon's radius . . . . .  1,738 km  =  1.738 x 10⁶ meters
Sum of their radii  =                      8.098 x 10⁶ meters

Also:
Earth's mass . . . . .  5.972 x 10²⁴ kg
Moon's mass . . . . .  7.348 x 10²²  kg
<span>
and now we're ready to go !

       Gravitational force = 

                   G  M₁ M₂ / R²

= (6.67 x 10⁻¹¹ N-m²/kg²)(</span><span>5.972 x 10²⁴ kg)(7.348 x 10²²  kg)/</span>(8.098 x 10⁶ m)²

= (6.67 · 5.972 · 7.348 / 8.098²) · (10²³)      Newtons

=    (I get ...)        4.463 x 10²³ Newtons

That's almost exactly   10²³ pounds 

                           =  50,153,000,000,000,000,000 tons.     

Those are big numbers. 
All I can say is:  I wouldn't exactly call that "resting" on the surface".
7 0
3 years ago
10.
myrzilka [38]

Answer:

<em>The new period of oscillation is D) 3.0 T</em>

Explanation:

<u>Simple Pendulum</u>

A simple pendulum is a mechanical arrangement that describes periodic motion. The simple pendulum is made of a small bob of mass 'm' suspended by a thin inextensible string.

The period of a simple pendulum is given by

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

Where L is its length and g is the local acceleration of gravity.

If the length of the pendulum was increased to 9 times (L'=9L), the new period of oscillation will be:

T'=2\pi \sqrt{\frac{L'}{g}}

T'=2\pi \sqrt{\frac{9L}{g}}

Taking out the square root of 9 (3):

T'=3*2\pi \sqrt{\frac{L}{g}}

Substituting the original T:

T'=3*T

The new period of oscillation is D) 3.0 T

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