Two gratings A and B have slit separations dA and dB, respectively. They are used with the same light and the same observation screen. When grating A is replaced with grating B, it is observed that the first-order maximum of A is exactly replaced by the second-order maximum of B.
a.) I already found that the ratio of db/da is 2
b.) Find the next two principal maxima of grating A and the principal maxima of B that exactly replace them when the gratings are switched. Identify these maxima by their order numbers

Answer:

a. 14,400 Watts

Explanation:

Power is current times voltage.

P = IV

Voltage is current times resistance.

V = IR

Substitute:

P = I²R

P = (12 A)² (100 Ω)

P = 14,400 W

Answer:

The  period is  [tex]T = 1.286 \ s[/tex]

Explanation:

From the question we are told that

   The mass of the spring is  [tex]m = 0.150 \ kg[/tex]

   The spring constant is  [tex]k = 3.58 \ N/m[/tex]

Generally the  period is mathematically represented as

      [tex]T = 2 \pi \sqrt{ \frac{m}{k} }[/tex]

substituting values

     [tex]T = 2 \pi \sqrt{ \frac{ 0.150}{3.58} }[/tex]

      [tex]T = 1.286 \ s[/tex]

Answer

a)0.0495 J

b)0.01681 m

c)0.7218 m/s

Explanation:

Given

Mass of the.toy M = 0.190 kg

force constant k = 350 N/m

Displacement from equilibrium x = 0.0140 m

Speed v = 0.400 m/s

a)What is the toy's total energy at any point of its motion?

The total energy at any point of it's motion can be calculated by adding together both the potential and kinetic energy of the toy, since it's posses potential energy when at rest and kinetic energy at motion

Total energy E = kinetic energy + potential energy

E = ¹/₂mv² + ¹/₂kx²

E = ¹/₂ (0.190)(0.4)² + ¹/₂ (350)(0.0140)²

E = 0.0495 J

Hence,the total energy is 0.0495 J

b) the amplitude of the motion can be calculated using below formula

Let amplitude = A

E = ¹/₂KA²

if we make Amplitude A the subject of the formula we have

A=√(2E/k)

But we have calculated our E up there, our K was given in question then if we substitute we have

A= √(2×0.0495)/350

Ans: 0.01681 m

Hence, our Amplitude is 0.01681 m

c) the the toy's maximum speed during its motion can be calculated using the expression below

Let maximum speed = vmax

E = (1/2)M * vmax^2

If we make vmax the subject of the formula we have

vmax =√(2E/m)

vmax= √(2×0.0495)/0.190

vmax=0.7218 m/s

Hence our vmax is 0.7218 m/s

Answer:

"You can create an electromagnet by wrapping an insulated wire around a metal with ferromagnetic properties and applying an electric current."

Explanation:

An electromagnet is created by coiling a ferromagnetic material with the help of an insulated wire around it and applying a  current . Insulated wire carrying current produces magnetic field around it . This field produces magnetic flux in the magnetic material and makes it magnet . When we switch of current , magnetic field ceases to exist and therefore , magnetic material ceases to be a magnet .

Explanation:

Answer:

C the particle must be somewhere.

Explanation:

This is because normalization of wave function means the maximum probability of finding a particle in a region is 1. And a Wave function describes the probability of finding a particle in region. Also Since it is a probability distribution, its integral over all space must be 1, explaining that the probability that the particle is somewhere and thus it must integrate to 1, meaning it must be it must be normalizable

Answer:

6.03x 10^-10 m

Explanation:

Given that

E= hc/ wavelength

And also

E= h²n2/8mL²

Equating the two and if we say the transition was from energy level 1 to 2 then

E2 - E1 = h²2/(8mL²) x ( 2² - 1²) = 3h²2/(8mL²)

So

L² = 3 h lambda / (8mc)

= 3 x6.626 10^-34 kg m^2/s x 400 10^-9 m /( 8 x 9.11 x10^-31 kg x3.00 10^8 m/s)

= 36.4 x 10^-20 m^2

L = 6.03 x 10^-10 m

The length of the box that absorbs the light is;

L = 6.03 × 10^(-10) m

We are given;

Longest wavelength of spectrum; λ = 400 nm = 400 × 10^(-9) m

Now, the formula for energy of quantization is;

E = h²n²/8mL²

Also, Energy of a photon is;

E = hc/λ

Thus;

hc/λ = h²n²/8mL²

h will cancel out to give;

c/λ = hn²/8mL²

Where;

h is Planck's constant = 6.626 × 10^(-34) m².kg/s

c is speed of light = 3 × 10^(8) m/s

λ is wavelength = 400 × 10^(-9) m

L is length of box

m is mass of electron = 9.11 × 10^(-31) kg

n² is difference in energy levels = (2² - 1²) = 3

Making L the subject gives;

L = √(hn²λ/8mc)

Thus;

L = √((6.626 × 10^(-34) × 3 × 400 × 10^(-9))/(8 × 9.11 × 10^(-31) × 3 × 10^(8))

L = √(3.636663007683 × 10^(-19))

L = 6.03 × 10^(-10) m

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Answer:

r = 17.05 cm

Explanation:

Given that,

Length of silicon bar is 4 cm or 0.04 m

Resistance of the bar is 280 ohms

We know that the resistivity of the silicon is 640 Ωm

We need to find the cross-sectional radius of the bar. Let it is r.

Using definition of resistance of an object. It is given by :

[tex]R=\rho\dfrac{l}{A}[/tex]

A is area of bar, A = πr²

So,

[tex]R=\rho\dfrac{l}{\pi r^2}\\\\r^2=\dfrac{\rho l}{R\pi}\\\\r^2=\dfrac{640\times 0.04}{280\pi}\\\\r=0.1705\ m\\\\r=17.05\ cm[/tex]

So, the cross-sectional radius of the bar is 17.05 cm.

Answer:

Explanation:

Displacement of train = 60 - 25 = 35 mile

= 35 x 1.6 = 56 km

duration of time = 45 - 15 = 30 minutes

= 30 x 60 = 1800 s

velocity of train = displacement / time

= 56 / 1800 = .03111 km /s

= 31.111 m / s

Answer:

The question is not complete. Let me explain Michelson interferometer and how to calculate a question like this.

Answer 4.85 * [tex]10^{-4}[/tex]m

Explanation:

The Michelson Interferometer is an instrument which produces interference fringes by splitting a light beam into two parts, it then recombines them after they have travelled different optical paths.

The formula to measure the minute displacement is Δd=m * λ[tex]_{0}[/tex]/2

where m is the number of fringes passing a given point as the movable plane mirror is moved

and λ[tex]_{0}[/tex] is the monochromatic lamp of wavelength

In the question, m = 1600. Let us assume that the wavelength is 606 nm

Solution

Δd=m * λ[tex]_{0}[/tex]/2

Δd=1600 * 606nm/2 = 1600 * 303nm = 484800nm

We convert the nm to m (nm / [tex]10^{-9}[/tex])

4.85 * [tex]10^{-4}[/tex]m

Answer:

The distance traveled by the balloon is 10.77 m

Explanation:

velocity of the ball, [tex]v_b[/tex] = 2 m/s south

velocity of the air, [tex]v_a[/tex] = 5 m/s west

To determine the distance the balloon will travel after 2 seconds, first determine the resultant velocity of the balloon.

                                       | 2m/s

                                       |

                                       |

                                      ↓

      5m/s  ←------------------

the two velocities forms a right angled triangle and the resultant will be the hypotenuses side of the triangle.

R² = 5² + 2²

R² = 29

R = √29

R = 5.385 m/s

The distance traveled by the balloon is calculated as;

d = R x t

where;

t is time of the motion = 2 seconds

d = 5.385 x 2

d = 10.77 m

Therefore, the distance traveled by the balloon is 10.77 m.

Explanation:

(a) An observer on the station has a speed of 0 km/h.  The speed of  a passenger on Train A is 100 km/h.  The relative speed is 100 km/h − 0 km/h = 100 km/h.

(b) The speed of both passengers is 100 km/h, in the same direction.  The relative speed is 100 km/h − 100 km/h = 0 km/h.

(c) The speed of both passengers is 100 km/h, in opposite directions.  The relative speed is 100 km/h − (-100 km/h) = 200 km/h.

Answer:

Explanation:

Given:

Two resistors (Parallel)

R1 = 150 ohms

R2 = 75 ohm

Current (I) = 0.18 A

Find:

Current through R1

Computation:

Common resistance

1/R = 1/R1 + 1/R2

1/R = 1/150 + 1/ 75

R = 50 ohms

V = IR

V = 0.18 x 50

V = 9v

So,

V = IR1

9 = I (150)

Current through R1 = 9 / 150

Current through R1 = 0.06 A

Answer:

2.42631E-13m

Explanation:

First we find the mass defect

Which is m= 0-2(9.10939E-33kg)

= - 1.82188E-30kg

Now find the energy

S

E= mc²=( -18.82188E-30)(2.999792E8)²

= 1.63742E-13J

Thus energy per photon will be

1.63742E-13J/2= 8.18710E-14J

So wavelength is given as

Lambda= hc/E

= (6.62608E-34)(2.997E8)/8.18710J

= 2.42631E-13m

The wavelength of radiation used to annihilate a positron and an electron is required.

The wavelength of the electromagnetic radiation used is 2.42 pm.

The mass of positron and electron are equal

m = Mass = [tex]\dfrac{0.000549}{6.022\times 10^{26}}=9.11\times 10^{-31}\ \text{kg}[/tex]

c = Speed of light = [tex]3\times 10^{8}\ \text{m/s}[/tex]

h = Planck's constant = [tex]6.626\times 10^{-34}\ \text{Js}[/tex]

Total energy in the collision is

[tex]E_T=mc^2+mc_2\\\Rightarrow E_T=2mc^2\\\Rightarrow E_T=2\times 9.11\times 10^{-31}\times (3\times 10^{8})^2\ \text{J}[/tex]

Energy released per photon is

[tex]E=\dfrac{E_T}{2}\\\Rightarrow E=\dfrac{2\times 9.11\times 10^{-31}\times (3\times 10^{8})^2}{2}\\\Rightarrow E=9.11\times 10^{-31}\times (3\times 10^{8})^2\ \text{J}[/tex]

Energy is given by

[tex]E=\dfrac{hc}{\lambda}\\\Rightarrow \lambda=\dfrac{hc}{E}\\\Rightarrow \lambda=\dfrac{6.626\times 10^{-34}\times 3\times 10^8}{9.11\times 10^{-31}\times (3\times 10^{8})^2}\\\Rightarrow \lambda=2.42\times 10^{-12}\ \text{m}=2.42\ \text{pm}[/tex]

The wavelength of the electromagnetic radiation used is 2.42 pm.

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Answer:

a. It always points perpendicular to the contact surface.

Explanation:

"Normal" means perpendicular.  Normal forces are always perpendicular to the contact surface.

Answer:

The  value is  [tex]l = 8.58 \ m[/tex]

Explanation:

From the question we are told that

  The  frequencies of two successive harmonics  is  [tex]f_ a = 220 \ Hz[/tex] , [tex]f_b = 240 \ Hz[/tex]

   The  speed of sound in the air is  [tex]v = 343 \ m/s[/tex]

Generally a harmonic frequency is mathematically represented as

        [tex]f_n = \frac{n * v }{2l}[/tex]

here l is the length of the pipe

n is the order of position of the harmonics

 Now since we do not know the order of the given harmonic frequencies but we are told that they are successive then the frequencies can be mathematically represented as

     [tex]220 = \frac{n * v}{ 2 l }[/tex]

and

     [tex]240 = \frac{ (n+1 ) v }{2l}[/tex]

So  

    [tex]240 - 220 = \frac{ (n+1 ) v }{2l} - \frac{n * v}{ 2 l }[/tex]

   [tex]20 = \frac{v}{2l}[/tex]

=>   [tex]l = 8.58 \ m[/tex]

Answer:

Explanation:

i.  CW moment = 10 N (10 cm) + 30 N (30 cm) - 60 N (40 cm) = - 1400 N-cm

ii.  ACW momenet = 60 N (40 cm) - 10 N (10 cm) + 30 N (30 cm) = 1400 N-cm

iii.  No. The lever is not balanced in the situation. Because the moment is ± 1400 N-cm.  if balance, the moment must be Zero.

iv.   the location of 10N by keeping the other loads unchanged to balance the lever is 150 cm

take moment from Δ (support)

60(40) = 10(x) + 30(30)

2400 = 10x + 900

10x = 2400 - 900

10x = 1500

x = 1500/10

x = 150 cm  

therefore, the location of 10N by keeping the other loads unchanged to balance the lever is 150 cm

Answer:

B

Explanation:

in graph B, you can see that the position increases and remains constant for a while before returning to 0

Answer:

The  temperature rise [tex]\Delta T = 0.3088 \ ^oC[/tex]

Explanation:

From the question we are told that

  The  speed is  [tex]v = 60 \ km /h = 16.67 \ m/s[/tex]

Generally according to the law of energy conservation we have that

   The  kinetic energy  =  increase in the internal energy of the car

i,e          [tex]\frac{1}{2} * m * v^2 = m * c_p * \Delta T[/tex]

Here  [tex]c_p[/tex] of  iron is  [tex]c_p = 450 \ J/kg K[/tex]

      So  

            [tex]0.5 * 16.67^2 = 450 * \Delta T[/tex]

=>         [tex]\Delta T = 0.3088 \ ^oC[/tex]

The temperature increase of each car will be 0.3088 °C.

Temperature directs to the hotness or coldness of a body. In clear terms, it is the method of finding the kinetic energy of particles within an entity. Faster the motion of particles more the temperature.

The given data in the problem is;

v is the velocity= 60 km/h=16.67 m/sec

ΔT is the temperature difference=?

[tex]\rm c_P[/tex] is the specific heat of iron=450 J/KgK

From the law of energy conservation of the energy, the kinetic energy is equal to the increase in the internal energy of the car.

[tex]\rm KE=\triangle E \\\\\ \frac{1}{2} mv^2=mc_p \triangle T \\\\ \triangle T=\frac{v^2}{2C_p} \\\\\ \triangle T=\frac{(16.67)^2}{2\times 450} \\\\ \triangle T=0.3088 ^0\C[/tex]

Hence the temperature increase of each car will be 0.3088 °C.

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Answer:

264 m

Explanation:

The complete question is

Suppose that you measure the length of a spaceship, at rest relative to you, to be 400 m. How long will you measure it to be if it flies past you at a speed of v = 0.75c

using the length contraction relationship,

[tex]l = l_{0} \sqrt{1 - \beta ^{2} }[/tex]

where [tex]\beta = \frac{v}{c}[/tex]

[tex]l[/tex] is the relativistic length

[tex]l_{0}[/tex] is the actual length = 400 m

v is the velocity of the spaceship

c is the speed of light

since v = 0.75c

v/c = 0.75

substituting, we have

[tex]l = 400 * \sqrt{1 - 0.75 ^{2} }[/tex] = 400 x 0.66 = 264 m

A paper pinwheel is spinning in the wind.

Which statement is correct about the forces responsible for the rotation?

The components of gravity and the force of wind that point through the pivot are responsible for the rotation.

Only the perpendicular component of wind is responsible for the rotation, because gravity points downward.

Only the perpendicular component of gravity is responsible for the rotation, because wind points toward the pivot.

The perpendicular components of gravity and the force of wind are responsible for the rotation.

Answer:

Only the perpendicular component of gravity is responsible for the rotation because wind points toward the pivot.

Explanation:

A pinwheel is a plaything that is made up of paper that is designed to spin when the wind comes in contact with it. The paper is held fast to its axle by a pin which enables it to spin.

Therefore, if the pinwheel is spun anti-clockwise, it brings electrical energy, converting the wind energy and only the perpendicular component of gravity is responsible for the rotation because wind points toward the pivot.

Answer:

The net force on the ball is zero.

Explanation:

The net force and the acceleration on the falling skydiver is upward. An upward net force on a downward falling object would cause that object to slow down. The skydiver thus slows down. As the speed decreases, the amount of air resistance also decreases until once more the skydiver reaches a terminal velocity.A force can cause a resting object, or it can accelerate a moving object by changing the object's speed or direction. When the forces on an object are balanced, the net force is zero and there is no change in the object's motion. When an unbalanced force acts on an object, the object accelerates.

Explanation:

Assuming constant speed:

Distance = speed × time

17.8 m = (5.3 m/s) t

t = 3.36 s

Answer:

F = 3.03 10⁷ N

Explanation:

We will eat by calculating the pressure in the tank

         P = ρ g h

the pressure totals the sum of the pressure of each liquid

       P_total = P_oil + P_water + P_Hg

       P_total = ρ_oil ​​g h_oil + ρ_water g h_water + ρ_Hg g h_Hg

       P_total = g (ρ_oil ​​h_oil + ρ_water h_water + ρ_Hg h_Hg)

       P_total = 9.8 (800 8 + 1000 6 + 13 600 5)

        P_total = 7,879 10⁵ Pa

The definition of Pressure is

       P = F / A

        F = P A

The area of ​​a tank is the area of ​​a circle

       A = π r² = π d² / 4

      F = P π d² / 4

let's calculate

      F = 7,879 10⁵ π 7²/4

      F = 3.03 10⁷ N

In this calculation the atmospheric pressure was not taken into account because they ask the hydrostatic pressure

Answer:

The force the  gymnast  must exert is 2812.6 N.

Explanation:

Given;

mass of the gymnast, m = 41 kg

her deceleration, -a = 7g = 7 x 9.8m/s² = 68.6 m/s²

Apply Newton's second law of motion;

F = ma

where;

F is the magnitude of the force exerted

m is the mass of the gymnast

a is the deceleration

Substitute in the given values of m and a into the force equation;

F = ma

F = 41 x 68.6

F = 2812.6 N

Therefore, the force the  gymnast  must exert is 2812.6 N.

Answer:

a) the size of the sport DECREASES  , b)the spot size is increased

c)  it has no effect  and d) spot size DECREASES

Explanation:

The expression for constructive interference in diffraction is

         a sin θ = m λ

the chaff of the spot is given by the minimum interference m = 1

           a sin θ = λ

let's use trigonometry to find the angle

         tan λ= y / L

         tan θ = sin θ / cos t = sin θ

         sin θ = y / L

          a y / L = lam

in the case of materials with circular dome, the problem must result in polar coordinates, with which a numerical constant is introduced

          y = 1.22 L / a lam

let's analyze each electrode action in this equation

a) Decrease lam

         y ’= 1.22 L / a lm2

          lam2 <lamo

          y '<y

therefore the size of the sport DECREASES

b) decreases the lens diameter

       a '<a

         y ’= 1.22 L / a’ lam

         y '> y

the spot size is increased

c) Decrease the focal length

The expression does not depend on the focal length, so it has no effect

d) decrease in L

         y ’= 1.22 L’ / a lam

spot size DECREASES

Answer:

The  value is  [tex]\mu_k = 0.102 0[/tex]

Explanation:

From the question we are told that

    The initial speed is  [tex]u = 10 \ m/s[/tex]

    The  distance traveled is  [tex]d = 50 \ m[/tex]

Generally we can obtain the acceleration using the kinetic equation as follows

     [tex]v^2 = u^2 + 2as[/tex]

=>   [tex]a = \frac{v^2 - u^2 }{ 2s}[/tex]

=>   [tex]a = \frac{0^2 - 10^2 }{ 2 * 50 }[/tex]

=>   [tex]a = -1 m/s^2[/tex]

The  negative sign shows that the pluck is decelerating

  The force driving the pluck is mathematically evaluated as

       [tex]F = ma[/tex]

 This force is also equivalent to the frictional force acting on the pluck

So  

      [tex]ma = m * g* \mu_k[/tex]

=>  [tex]\mu_k = \frac{a}{g}[/tex]

=>   [tex]\mu_k = \frac{1}{9.8 }[/tex]

=>   [tex]\mu_k = 0.102 0[/tex]

Answer:

B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy.

Explanation:

The complete question is

Two identical balls are thrown directly upward, ball A at speed v and boll B at speed 2v. and they feel no air resistance. Which statement about these balls is correct? A) Ball B will go twice as high as ball A because it had twice the initial speed. B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy. C) The balls will reach the same height because they have the same mass and the same acceleration. D) At its highest point, ball B will have twice as much gravitational potential energy as ball A because it started out moving twice as fast. E) At their highest point, the acceleration of each ball is instantaneously equal to zero because they stop for an instant.

According to conservation of energy, the mechanical energy of a ball thrown up is equal to the sum of the potential energy and the kinetic energy. At its highest point, all the mechanical energy will be equal to the potential energy. At the instant when it was thrown, all the mechanical energy is proportional to its kinetic energy, which will be proportional to the potential energy at the highest point. Also, potential energy is proportional to the maximum height reached.

We know that the kinetic energy is given as [tex]\frac{1}{2}mv^{2}[/tex]

where

m is the mass of the balls, which is the same for both ball,

and v is the velocity.

We can see that the kinetic energy is proportional to the square of the initial velocity with which the ball is thrown.

For the ball A thrown with velocity v, the kinetic energy is proportional to [tex]v^{2}[/tex],

and for the ball B with velocity 2v, kinetic energy is proportional to [tex]4v^{2}[/tex]

comparing the two, we'll see that the ball B will had 4 times the energy of ball A. Therefore ball B will go four times as high as ball A because it had four times the initial kinetic energy

Answer:

   I_FWHW = 3.2 μW / m²

Explanation:

In the analysis of optics and electricity a very useful magnitude is the width at half height (FWHW) and the intensity at this height, which is given by

               I_FWHW = I₀ / 2

corresponds to the width of the line for this intensity.

In this case they give the maximum intensity for which

               I_FWHW = 6.2 / 2

               I_FWHW = 3.2 μW / m²

You do not give more data in your exercise, but the most interesting calculation is to find the angle values ​​for which you have this intensity since it is this range is 50% of the energy of the system, have I write the equation for this calculation

             I = Io cos² x₁   (sin x / x)²

             x₁ = π d sin θ /λ

             x = π b sin θ /λ

where d is the separation of the slits and b the width of each slit