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avanturin [10]
3 years ago
9

Using a 679 nm wavelength laser, you form the diffraction pattern of a 1.1 mm wide slit on a screen. You measure on the screen t

hat the 14 th dark fringe is 8.01 cm away from the center of the central maximum. How far is the screen located from the slit?
Physics
1 answer:
sveta [45]3 years ago
7 0

To solve the problem, apply the concepts related to constructive and destructive interference. For this purpose, we will start by defining the distance from the dark fringe from the central maximum in terms of the slit separation, the number of fringe the wavelength and the distance of the screen to the slit. Mathematically this is,

y_n = \frac{(2n-1)\lambda D}{2d}

D = \frac{2dy_n}{(2n-1)\lambda}

Here,

d = Slit separation

n = Number of fringe

y_n = Distance of the dark fringe from the central maximum

D = Distance of the screen to the slit

\lambda = Wavelength

Our values are given as,

\lambda = 679nm = 679*10^{-9}m

d = 1.1mm = 1.1*10^{-3}m

y_{14} = 8.01cm = 8.01*10^{-2} m

n = 14

Replacing,

D = \frac{2(1.1*10^{-3})(8.01*10^{-2})}{(2(14)-1)(679*10^{-9})}

D = 9.61m

Therefore the screen is located from the slit to 9.61m

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Answer:

a) Ktotal = 71.85 J

b) Ktotal = 71.85 J

Explanation:

a) The total kinetic energy is that of the total mass of the bicycle plus the rotational kinetic energy of the two wheels. The linear speed of the circumference of the wheels matches the forward speed of the bicycle, so their angular speed is  

ω = v/r

The moment of inertia of one solid disk bicycle wheel is  

I = 0.5*m₂*r²

And the rotational kinetic energy of one wheel is

Kr = 0.5*I*ω² = 0.5*(0.5*m₂*r²)*(v/r)² = 0.25*m₂*v²

The total kinetic energy is then that of the frame and wheels plus the rotational kinetic energy.

Ktotal = 0.5*(m₁ + 2*m₂)*v² + 2*(0.25*m₂*v²)

⇒  Ktotal = 0.5*v²*(m₁ + 3*m₂)

where

m₁ = 6.75 Kg

m₂ = 0.820 kg

v = 3.95 m/s

then

⇒  Ktotal = 0.5*(3.95 m/s)²*(6.75 Kg + 3*0.820 kg)

⇒  Ktotal = 71.85 J

b) We can apply the same equation obtained before

⇒  Ktotal = 0.5*v²*(m₁ + 3*m₂)

where

m₁ = 675 Kg

m₂ = 82.0 kg

v = 0.395 m/s

then

⇒  Ktotal = 0.5*(0.395 m/s)²*(675 Kg + 3*82 kg)

⇒  Ktotal = 71.85 J

3 0
3 years ago
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