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liraira [26]
3 years ago
9

We can model a small merry-go-round as a uniform circular disk with mass 88 kg and diameter 1.8 m. How many 22 kg children need

to ride the merry-go-round, standing right at the outer edge, to double the moment of inertia of the system?
Physics
1 answer:
Softa [21]3 years ago
7 0

Answer:

n = 2 children

Explanation:

Given

M = 88 Kg

D = 1.8 m ⇒  R = D/2 = 1.8 m/2 = 0.9 m

m = 22 Kg

n = ?

We apply the formula

Icm = M*R²/2

⇒ Icm = (88 Kg)*(0.9 m)²/2 = 35.64 Kg*m²

If

I = 2*Icm = 2*35.64 Kg*m² = 71.28 Kg*m²

we apply Steiner's Theorem as follows

I = Icm + n*m*R²

⇒  n = (I - Icm) / (m*R²)

⇒  n = (71.28 Kg*m² - 35.64 Kg*m²) / (22 Kg*(0.9 m)²)

⇒  n = 2 children

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2 years ago
The refractive index n of transparent acrylic plastic (full name Poly(methyl methacrylate)) depends on the color (wavelength) of
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Answer:

The angle between the blue beam and the red beam in the acrylic block is  

 \theta _d  =0.19 ^o

Explanation:

From the question we are told that

     The  refractive index of the transparent acrylic plastic for blue light is  n_F  =  1.497

     The  wavelength of the blue light is F  =  486.1 nm  =  486.1 *10^{-9} \ m

    The  refractive index of the transparent acrylic plastic for red light is  n_C  =  1.488

       The  wavelength of the red light is C =  656.3 nm  = 656.3 *10^{-9} \  m

    The incidence angle is  i  =  45^o

Generally from Snell's law the angle of refraction of the blue light  in the acrylic block  is mathematically represented as

       r_F =  sin ^{-1}[\frac{sin(i) *  n_a }{n_F} ]

Where  n_a is the refractive index of air which have a value ofn_a =  1

So

     r_F =  sin ^{-1}[\frac{sin(45) *  1 }{ 1.497} ]

      r_F  =  28.18^o

Generally from Snell's law the angle of refraction of the red light in the acrylic block is mathematically represented as

       r_C =  sin ^{-1}[\frac{sin(i) *  n_a }{n_C} ]

Where  n_a is the refractive index of air which have a value ofn_a =  1

So

     r_C =  sin ^{-1}[\frac{sin(45) *  1 }{ 1.488} ]

      r_F  =  28.37^o

The angle between the blue beam and the red beam in the acrylic block

     \theta _d  =  r_C  - r_F

substituting values

       \theta _d  = 28.37 -  28.18

       \theta _d  =0.19 ^o

 

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3 years ago
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