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2 years ago

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A laser with wavelength d/8 is shining light on a double slit with slit separation 0.500 mm. This results in an interference pat

tern on a screen a distance L away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits. What is the wavelength λ of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if d = 0.500 mm?

1 answer:

ipn [44]2 years ago

7 0

Answer:

0.000109375 m

Explanation:

d = Distance between grating = 0.5 mm

m = Order

$\lambda_1=\dfrac{d}{8}$

Minima relation

$m-\dfrac{1}{2}$

For fourth order minima

$dsin\theta=(4-\dfrac{1}{2})\lambda_1$

For second maxima

$dsin\theta=2\lambda_2$

From the two equations we get

$(4-\dfrac{1}{2})\lambda_1=2\lambda_2\\\Rightarrow \lambda_2=\dfrac{(4-\dfrac{1}{2})\lambda_1}{2}\\\Rightarrow \lambda_2=\dfrac{(4-\dfrac{1}{2})\dfrac{0.5\times 10^{-3}}{8}}{2}\\\Rightarrow \lambda_2=0.000109375\ m$

The wavelength is 0.000109375 m

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What mass needs to be attached to a spring with a force constant of 7N/m in order to make a simple harmonic oscillator oscillate

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Answer:

Mass will be 4.437 kg

Explanation:

We have given force constant k = 7 N/m

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So angular frequency $\omega =\frac{2\pi }{T}=\frac{2\times 3.14}{5}=1.256rad/sec$

We know that angular frequency is given by

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2 years ago

Two sinusoidal waves are identical except for their phase. When these two waves travel along the same string, for which phase di

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Answer:

zero or 2π is maximum

Explanation:

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x₂ = A sin (kx- wt + φ₂)

When the wave travels in the same direction

Xt = x₁ + x₂

Xt = A [sin (kx-wt + φ₁) + sin (kx-wt + φ₂)]

We are going to develop trigonometric functions, let's call

a = kx + wt

Xt = A [sin (a + φ₁) + sin (a + φ₂)

We develop breasts of double angles

sin (a + φ₁) = sin a cos φ₁ + sin φ₁ cos a

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Let's make the sum

sin (a + φ₁) + sin (a + φ₂) = sin a (cos φ₁ + cos φ₂) + cos a (sin φ₁ + sinφ₂)

to have a maximum of the sine function, the cosine of fi must be maximum

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the possible values of each phase are

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φ2 = 0, π, 2π,

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2 years ago

A metal has a strength of 414 MPa at its elastic limit and the strain at that point is 0.002. Assume the test specimen is 12.8-m

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To solve this problem, we will start by defining each of the variables given and proceed to find the modulus of elasticity of the object. We will calculate the deformation per unit of elastic volume and finally we will calculate the net energy of the system. Let's start defining the variables

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$S_{el} = 414Mpa$

Yield Strain of the Specimen

$\epsilon_{el} = 0.002$

Diameter of the test-specimen

$d_0 = 12.8mm$

Gage length of the Specimen

$L_0 = 50mm$

Modulus of elasticity

$E = \frac{S_{el}}{\epsilon_{el}}$

$E = \frac{414Mpa}{0.002}$

$E = 207Gpa$

Strain energy per unit volume at the elastic limit is

$U'_{el} = \frac{1}{2} S_{el} \cdot \epsilon_{el}$

$U'_{el} = \frac{1}{2} (414)(0.002)$

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Considering that the net strain energy of the sample is

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Therefore the net strain energy of the sample is $2.663N\codt m$

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1 year ago

Assume the motions and currents mentioned are along the x axis and fields are in the y direction. (a) does an electric field exe

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<span> (a) does an electric field exert a force on a stationary charged object?
Yes. The force exerted by an electric field of intensity E on an object with charge q is
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</span><span>(b) does a magnetic field do so?
No. In fact, the magnetic force exerted by a magnetic field of intensity B on an object with charge q and speed v is
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where $\theta$ is the angle between the direction of v and B.
As we can see, the value of the force F depends on the value of the speed v: if the object is stationary, then v=0, and so the force is zero as well.

<span>(c) does an electric field exert a force on a moving charged object?
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</span><span>(d) does a magnetic field do so?
</span>Yes. As we said in point b, the magnetic force is
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And now the object is moving with a certain speed v, so the magnetic force F this time is different from zero.

<span>(e) does an electric field exert a force on a straight current-carrying wire?
Yes. A current in a wire consists of many charges traveling through the wire, and since the electric field always exerts a force on a charge, then the electric field exerts a force on the charges traveling through the wire.

</span><span>(f) does a magnetic field do so?
Yes. The current in the wire consists of charges that are moving with a certain speed v, and we said that a magnetic field always exerts a force on a moving charge, so the magnetic field is exerting a magnetic force on the charges that are traveling through the wire.

</span><span>(g) does an electric field exert a force on a beam of moving electrons?
Yes. Electrons have an electric charge, and we said that the force exerted by an electric field is
</span> $F=qE$
<span>So, an electric field always exerts a force on an electric charge, therefore on an electron beam as well.

</span><span>(h) does a magnetic field do so?
Yes, because the electrons in the beam are moving with a certain speed v, so the magnetic force
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6 0

2 years ago

A square loop of wire with initial side length 10 cm is placed in a magnetic field of strength 1 T. The field is parallel to the

Fofino [41]

Answer:

2 x 10⁻³ volts

Explanation:

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θ = Angle of the magnetic field with the area vector = 0

E = emf induced in the loop

Induced emf is given as

E = B $\frac{dA}{dt}$

E = (1) (20 x 10⁻⁴ )

E = 2 x 10⁻³ volts

E = 2 mV

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2 years ago