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FinnZ [79.3K]
3 years ago
10

Which expression can be used to calculate centripetal acceleration?

Physics
1 answer:
meriva3 years ago
8 0
We can use multiple expressions to calculate centripetal acceleration, depending on the physical problem:

Centripetal acceleration with tangental velocity:

a=v²/r, where v is tangental velocity and r is the radius of the circular trajectory.

Centripetal acceleration with angular velocity:

a=ω²r, where ω is the angular velocity and r is the radius if the circular trajectory. 

We can calcualte it from the centripetal force Fcp:

Fcp=m*a, so a=Fcp/m, where m is mass and a is the centripetal acceleration.

And also from the equation:

a=√(a₁²+a₂²), where a is total acceleration, a₁ is centripetal acceleration and a₂ is the tangental acceleration, so to get a₁, or centripetal acceleration:

a₁=√(a²-a₂²)

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a

 \theta  =  0.0022 rad

b

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From the question we are told that  

   The  wavelength of the light is \lambda  = 550 \ nm  =  550 *10^{-9} \ m

    The  distance of the slit separation is  d = 0.500 \ mm = 5.0 *10^{-4} \ m

 

Generally the condition for two slit interference  is  

     dsin \theta =  m \lambda

Where m is the order which is given from the question as  m = 2

=>    \theta  =  sin ^{-1} [\frac{m \lambda}{d} ]

 substituting values  

      \theta  =  0.0022 rad

Now on the second question  

   The distance of separation of the slit is  

       d =  0.300 \ mm  =  3.0 *10^{-4} \ m

The  intensity at the  the angular position in part "a" is mathematically evaluated as

      I  =  I_o  [\frac{sin \beta}{\beta} ]^2

Where  \beta is mathematically evaluated as

       \beta  =  \frac{\pi *  d  *  sin(\theta )}{\lambda }

  substituting values

     \beta  =  \frac{3.142  *  3*10^{-4}  *  sin(0.0022 )}{550 *10^{-9} }

    \beta  = 0.06581

So the intensity is  

    I  =  I_o  [\frac{sin (0.06581)}{0.06581} ]^2

   I  =  0.000304 I_o

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