Two parallel slits are illuminated with monochromatic light of wavelength 567 nm. An interference pattern is formed on a screen some distance from the slits, and the fourth dark band is located 1.83 cm from the central bright band on the screen. (a) What is the path length difference corresponding to the fourth dark band? (b) What is the distance on the screen between the central bright band and the first bright band on either side of the central band? (Hint: The angle to the fourth dark band and the angle to the first bright band are small enough that tan θ ≈ sin θ.)

Answer:

2 cm.

Explanation:

Data obtained from the question include the following:

Original Length (L₁ ) = 10 m

Initial temperature (T₁) = 0°C

Final temperature (T₂) = 400°C

Linear expansivity (α) = 5×10¯⁶ /°C

Increase in length (ΔL) =..?

Next, we shall determine the temperature rise (ΔT).

This can be obtained as follow:

Initial temperature (T₁) = 0°C

Final temperature (T₂) = 400°C

Temperature rise (ΔT) =..?

Temperature rise (ΔT) = T₂ – T₁

Temperature rise (ΔT) = 400 – 0

Temperature rise (ΔT) = 400°C

Thus, we can obtain the increase in length of the airplane by using the following formula as illustrated below:

Linear expansivity (α) = increase in length (ΔL) /Original Length (L₁ ) × Temperature rise (ΔT)

α = ΔL/(L₁ × ΔT)

Original Length (L₁ ) = 10 m

Linear expansivity (α) = 5×10¯⁶ /°C

Temperature rise (ΔT) = 400°C

Increase in length (ΔL) =..?

α = ΔL/(L₁ × ΔT)

5×10¯⁶ = ΔL/(10 × 400)

5×10¯⁶ = ΔL/4000

Cross multiply

ΔL = 5×10¯⁶ × 4000

ΔL = 0.02 m

Converting 0.02 m to cm, we have:

1 m = 100 cm

Therefore, 0.02 m = 0.02 × 100 = 2 cm.

Therefore, the length of the plane will increase by 2 cm.

Answer:

10.75 A

The current is in opposite direction since it causes a repulsion force between the wires

Explanation:

Force per unit length on the wires = 4.30×10^−5 N/m

distance between wires = 2.6 cm = 0.026 m

current through one wire = 0.52 A

current on the other wire = ?

Recall that the force per unit length of two wires conducting and lying parallel and close to each other is given as

[tex]F/l[/tex] = [tex]\frac{u_{0}I_{1} I_{2} }{2\pi r }[/tex]

where [tex]F/l[/tex] is the force per unit length on the wires

[tex]u_{0}[/tex] = permeability of vacuum = 4π × 10^−7 T-m/A

[tex]I_{1}[/tex] = current on the first wire = 0.520 A

[tex]I_{2}[/tex] = current on the other wire = ?

r = the distance between the two wire = 0.026 m

substituting the value into the equation, we have

4.30×10^−5 = [tex]\frac{4\pi *10^{-7}*0.520*I_{2} }{2\pi *0.026}[/tex] =  [tex]\frac{ 2*10^{-7}*0.520*I_{2} }{0.026}[/tex]

4.30×10^−5 = 4 x 10^-6 [tex]I_{2}[/tex]

[tex]I_{2}[/tex] = (4.30×10^-5)/(4 x 10^-6) = 10.75 A

The current is in opposite direction since it causes a repulsion force between the wires.

Answer

Work done is 57.9KJ

Explanation

First solve the problem according to work done due to variation in temperature

So W= intergral Cu( 1-Tu/T). at Tu and T

So Given that

C = Heat capacity of the Brick

TEPc= Cold Temperature

TEPh = Hot Temperature

W = C ( TEPh-TEP) - TEPhCln ( TEPh/TEPc)

So

W= (1)-(300-150)-300 (1) ln 2

W= -57.9KJ

Answer:

y = 12.82 m

Explanation:

We can solve this exercise using the energy work theorem

          W = ΔEm

friction force work is

          W = fr . s = fr s cos θ

the friction force opposes the movement, therefore the angle is 180º

           W = - fr s

we write Newton's second law, where we use a reference frame with one axis parallel to the plane and the other perpendicular

           N -Wy = 0

           N = mg cos θ

the friction force remains

            fr = μ N

            fr = μ mg cos θ

work gives

           W = - μ mg s cos θ

initial energy

           Em₀ = ½ m v²

the final energy is zero, because it stops

we substitute

          - μ m g s cos θ = 0 - ½ m v²

          s = ½ v² / (μ g cos θ)

let's calculate

          s = ½ 20² / (0.55 9.8 cos 20)

          s = 39.49 m

this is the distance it travels along the plane, to find the vertical distance let's use trigonometry

            sin 20 = y / s

           y = s sin 20

           y = 37.49 sin 20

           y = 12.82 m

Answer:

ΔP.E = 6.48 x 10⁸ J

Explanation:

First we need to calculate the acceleration due to gravity on the surface of moon:

g = GM/R²

where,

g = acceleration due to gravity on the surface of moon = ?

G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

M = Mass of moon = 7.36 x 10²² kg

R = Radius of Moon = 1740 km = 1.74 x 10⁶ m

Therefore,

g = (6.67 x 10⁻¹¹ N.m²/kg²)(7.36 x 10²² kg)/(1.74 x 10⁶ m)²

g = 2.82 m/s²

now the change in gravitational potential energy of rocket is calculated by:

ΔP.E = mgΔh

where,

ΔP.E = Change in Gravitational Potential Energy = ?

m = mass of rocket = 1090 kg

Δh = altitude = 211 km = 2.11 x 10⁵ m

Therefore,

ΔP.E = (1090 kg)(2.82 m/s²)(2.11 x 10⁵ m)

ΔP.E = 6.48 x 10⁸ J

Answer:

physical feature of a wave is related to the depth of the wave base is The circular orbital motion

B. The wave base is the depth, and the still water level is the horizontal level

Answer:

The width of the slit is 0.4 mm (0.00040 m).

Explanation:

From the Young's interference expression, we have;

(λ ÷ d) = (Δy ÷ D)

where λ is the wavelength of the light, D is the distance of the slit to the screen, d is the width of slit and Δy is the fringe separation.

Thus,

d = (Dλ) ÷ Δy

D = 3.30 m, Δy = 4.7 mm (0.0047 m) and λ = 563 nm (563 ×[tex]10^{-9}[/tex] m)

d = (3.30 × 563 ×[tex]10^{-9}[/tex] ) ÷ (0.0047)

  = 1.8579 × [tex]10^{-6}[/tex] ÷ 0.0047

  = 0.0003951 m

d = 0.00040 m

The width of the slit is 0.4 mm (0.00040 m).

Answer:

I believe the answer is A volleyball player sliding across the court while diving for the ball.

Explanation:

Kinetic friction is a body moving on the surface experiences a force in the opposite direction of its movement.

Hope this helps! （づ￣3￣）づ╭❤～

Explanation:

Given that,

Linear speed of both disks is 5 m/s

Mass of disk 1 is 10 kg

Radius of disk 1 is 35 cm or 0.35 m

Mass of disk 2 is 3 kg

Radius of disk 2 is 7 cm or 0.07 m

(a) The angular velocity of disk 1 is :

[tex]v=r_1\omega_1\\\\\omega_1=\dfrac{v}{r_1}\\\\\omega_1=\dfrac{5}{0.35}\\\\\omega_1=14.28\ rad/s[/tex]

(b) The angular velocity of disk 2 is :

[tex]v=r_2\omega_2\\\\\omega_2=\dfrac{v}{r_2}\\\\\omega_2=\dfrac{5}{0.07}\\\\\omega_2=71.42\ rad/s[/tex]

(c) The moment of inertia for the two disk system is given by :

[tex]I=I_1+I_2\\\\I=\dfrac{1}{2}m_1r_1^2+\dfrac{1}{2}m_2r_2^2\\\\I=\dfrac{1}{2}(m_1r_1^2+m_2r_2^2)\\\\I=\dfrac{1}{2}\times (10\times (0.35)^2+3\times (0.07)^2)\\\\I=0.619\ kg-m^2[/tex]

Hence, this is the required solution.

Answer:

a barometer is used to measure atmospheric pressure, and a manometer is used to measure gauge pressure.

Explanation:

A barometer measures air pressure at any locality with sea level as the reference.

However, a manometer is used to measure all pressures especially gauge pressures. Thus, if the aim is to measure the pressure at any point below a fluid surface, a barometer is used to determine the air pressure. The manometer may now be used to determine the gauge pressure

The algebraic sum of these two values gives the absolute pressure.

Answer:

e) west

Explanation:

According to Lorentz left hand rule, the left hand is used to represent the motion of an electron in a magnetic field. Hold out the left hand with the fingers held out parallel to the palm, and the thumb held at right angle to the other fingers. If the thumb represents the motion of the electron though the field, and the other fingers represent the direction of the field, then the palm will push in the direction of the force on the particle.

In this case, if we point the thumb to the south (towards your body), with the palm facing up, then the fingers will point west.

Explanation:

The De-Broglie wavelength is given by :

[tex]\lambda=\dfrac{h}{p}[/tex]

h is Planck's constant

p is momentum

In this case, an electron and a proton both moving at nonrelativistic speeds have the same de Broglie wavelength. Mass of electron and proton is different. It means their velocity and energy are different.

Only momentum is the factor that remains same for both particles i.e. momentum.

Answer:

 circumference of the satellite orbit  = 4.13 × 10⁷ m

Explanation:

Given that:

the time period T = 88.5 min = 88.5 × 60  = 5310 sec

The mass of the earth [tex]M_e[/tex] = 5.98 × 10²⁴ kg

if  the radius of orbit is r,

Then,

[tex]\dfrac{V^2}{r} = \dfrac{GM_e}{r^2}[/tex]

[tex]{V^2} = \dfrac{GM_e r}{r^2}[/tex]

[tex]{V^2} = \dfrac{GM_e }{r}[/tex]

[tex]{V} =\sqrt{ \dfrac{GM_e }{r}}[/tex]

Similarly :

[tex]T = \sqrt{\dfrac{ 2 \pi r} {V} }[/tex]

where; [tex]{V} =\sqrt{ \dfrac{GM_e }{r}}[/tex]

Then:

[tex]T = {\dfrac{ 2 \pi r^{3/2}} {\sqrt{ {GM_e }} }[/tex]

[tex]5310= {\dfrac{ 2 \pi r^{3/2}} {\sqrt{ {6.674\times 10^{-11} \times 5.98 \times 10^{24} }} }[/tex]

[tex]5310= {\dfrac{ 2 \pi r^{3/2}} {\sqrt{ 3.991052 \times 10^{14} }}[/tex]

[tex]5310= {\dfrac{ 2 \pi r^{3/2}} {19977617.48}[/tex]

[tex]5310 \times 19977617.48= 2 \pi r^{3/2}}[/tex]

[tex]1.06081149 \times 10^{11}= 2 \pi r^{3/2}}[/tex]

[tex]\dfrac{1.06081149 \times 10^{11}}{2 \pi}= r^{3/2}}[/tex]

[tex]r^{3/2}} = \dfrac{1.06081149 \times 10^{11}}{2 \pi}[/tex]

[tex]r^{3/2}} = 1.68833392 \times 10^{10}[/tex]

[tex]r= (1.68833392 \times 10^{10})^{2/3}}[/tex]

[tex]r= 2565.38^2[/tex]

r = 6579225 m

The  circumference of the satellites  orbit can now be determined by using the formula:

 circumference = 2π r

 circumference = 2π  × 6579225 m

 circumference = 41338489.85 m

 circumference of the satellite orbit  = 4.13 × 10⁷ m

Answer:

a lower energy than

Explanation:

sorry im a month late but is lower energy than

Answer:

The near point is  [tex]n =44.8 \ cm[/tex]

Explanation:

From the question we are told that

   The power is  [tex]P = 1.50[/tex]

   The  distance from the eye is  [tex]k = 1.8 \ cm[/tex]

    The distance of the book from the eye is [tex]z = -28 \ cm[/tex]

Generally the focal length of the glasses is  

       [tex]f = \frac{1}{P}[/tex]

=>   [tex]f = \frac{1}{1.50 }[/tex]

=>   [tex]f = 0.667 \ m[/tex]

=>   [tex]f = 66.7 \ cm[/tex]

The object distance is evaluated as

     [tex]u = z + k[/tex]

=>   [tex]u = -28 + 1.8[/tex]

=>  [tex]u = -26.2 \ cm[/tex]

The image distance is evaluated from lens formula as

       [tex]\frac{1}{v} = \frac{1}{f} + \frac{1}{u}[/tex]

=>   [tex]\frac{1}{v} = \frac{1}{66.7} + \frac{1}{-26.2}[/tex]

=>   [tex]v=- \frac{1}{0.0232}[/tex]

=>    [tex]v=- 43 \ cm[/tex]

The  near point is evaluated as

      [tex]n = -v + k[/tex]

=>    [tex]n =-(-43) + 1.8[/tex]

=>    [tex]n =44.8 \ cm[/tex]

Each electron winds up with kinetic energy of

(270 keV)

plus

(whatever KE it had when it started accelerating).

Answer:

692 J/kg/°C

Explanation:

Electric energy added = amount of heat

Power × time = mass × SHC × increase in temperature

Pt = mCΔT

(15 V × 3 A) (10 min × 60 s/min) = (0.6 kg) C (85°C − 20°C)

C = 692 J/kg/°C

Answer:

The induced emf in the coil is 7.843 V

Explanation:

Given;

number of turns of the coil, N = 1300 turn

diameter of the coil, d = 2.4 cm = 0.024 m

initial magnetic field, B₁ = 0 T

final magnetic field, B₂ = 0.12 T

change in time, dt = 9.0 ms = 9 x 10⁻³ s

Area of the coil is given by;

A = πr²

radius of the coil, r = 0.024 / 2

radius of the coil, r = 0.012 m

A = π(0.012)²

A = 4.525 x 10⁻⁴ m²

The induced emf in the coil is given by;

E = NA(dB/dt)

E =  NA [(B₂ - B₁) /dt]

E = 1300 x 4.525 x 10⁻⁴ (0.12 - 0) / (9 x 10⁻³)

E = 7.843 V

Therefore, the induced emf in the coil is 7.843 V

Answer:

Change in the frequency (in Hz) = 104.96 Hz

Explanation:

Given:

Speed of sound in air (v) = 343 m/s

Speed of car (v1) 36 m/s

Frequency(f) = 500 Hz

Find:

Change in the frequency (in Hz)

Computation:

Frequency hear by the observer(before)(f1) = [f(v+v1)] / v

Frequency hear by the observer(f1) = [500(343+36)] / 343

Frequency hear by the observer(f1) = 552.48 Hz

Frequency hear by the observer(after)(f2) = [f(v-v1)] / v

Frequency hear by the observer(f2) = [500(343-36)] / 343

Frequency hear by the observer(f2) = 447.52 Hz

Change in the frequency (in Hz) = f1 - f2

Change in the frequency (in Hz) = 552.48 Hz - 447.52 Hz

Change in the frequency (in Hz) = 104.96 Hz

Answer:

a) true

Explanation:

Answer:

she need to use 20 cm thick

Explanation:

given data

wants the attic insulated = R-30

purchased = 10 cm thick

solution

as per given we can say that

10 cm is for the R 15

but she want for R 30

so  

R 30 thickness = [tex]\frac{30}{15} \times 10[/tex]  

R 30 thickness = 20 cm

so she need to use 20 cm thick

Answer:

speed of the alpha particle is 2 x 10^7 m/s.

Explanation:

energy of alpha particle = 8.3 Mev

1 Mev = 1.602 x 10^-13 J

8.3 Mev = [tex]x[/tex]

solving, [tex]x[/tex] = 8.3 x 1.602 x 10^-13 = 1.329 x 10^-12 J

mass of a alpha particle = 6.645 x 10^−27 kg

The energy of the alpha particle is the kinetic energy KE of the alpha particle

KE = [tex]\frac{1}{2}mv^{2}[/tex]

where m is the mass of the alpha particle

v is  the velocity of the alpha particle

substituting values, we have

1.329 x 10^-12 = [tex]\frac{1}{2}*6.645*10^{-27}*v^{2}[/tex]

[tex]v^{2}[/tex] = 4 x 10^14

[tex]v = \sqrt{4*10^{14} }[/tex] = 2 x 10^7 m/s

Answer:

Option (c) : 20°C

Explanation:

[tex]t(final) = \frac{w1 \times t1 + w2 \times t2}{w1 + w2} [/tex]

T(final) = 500* 10 + 100*70/600 = 20°C

Answer:

If the magnet is moved, the galvanometer needle will deflect, showing that current is flowing through the coil which will increase total induced electromotive force

Explanation:

galvanometer is an instrument that can detect and measure small current in an electrical circuit.

If the magnet is moved, the galvanometer needle will deflect, showing that current is flowing through the coil. If it is move in a way into the coil,the needle deflect in that way and if it move in another way, it will deflect in the other way.

The total induced emf is equal to the emf induced in each loop by the changing magnetic flux, then multiplied by the number of loops and an increase in the number of loops will cause increase in the total induced emf.

Answer:

1. 0.2m

1. 66m

Explanation:

See attached file

The expressions of fluid mechanics allows to find the result for the maximum height that the water leaves through the two points are;

1) The maximum height when the water leaves the hose is: Δy = 0.20 m

2) The maximum height of the water leaves the nozzle is: Δy = 68.6m

Given parameters

To find

   1. Maximum height of water in hose

  2. Maximum height of water at the nozzle

Fluid mechanics studies the movement of fluids, liquids and gases in different systems, for this it uses two expressions:

           A₁v₁ = A₂.v₂

          P₁ + ½ ρ g v₁² + ρ g y₁ = P₂ + ½ ρ g v₂² + ρ g y₂

Where the subscripts 1 and 2 represent two points of interest, P is the pressure, ρ the density, v the velocity, g the acceleration of gravity and y the height.

1, Let's find the exit velocity of the water in the hose.

Let's use subscript 1 for the nozzle and subscript 2 for the hose.

The continuity equation of the flow value that must be constant throughout the system.

      Q = A₁ v₁

      v₁ = [tex]\frac{Q}{A_1 }[/tex]  

The area of ​​a circle is:

     A = π r²

Let's calculate the velocity in the hose.

    A₁ = π (0.94 10⁻²) ²

    A₁ = 2.78 10⁻⁴ m²

    v₁ = [tex]\frac{0.55 \ 10^{-3}}{2.78 \ 10^{-4}}[/tex]

    v₁ = 1.98 m / s

Let's use Bernoulli's equation.

When the water leaves the hose the pressure is atmospheric and when it reaches the highest point it has not changed P1 = P2

      ½ ρ v₁² + ρ g y₁ = ½ ρ v₂² + ρ g v₂

      y₂-y₁ = ½  [tex]\frac{v_i^2 - v_2^2}{g}[/tex]  

At the highest point of the trajectory the velocity must be zero.

     y₂- y₁ = [tex]\frac{v_1^2}{2g}[/tex]

Let's calculate

     y₂-y₁ =  [tex]\frac{1.98^2}{2 \ 9.8}[/tex]  

     Δy = 0.2 m

2.  Let's find the exit velocity of the water at the nozzle

          A₁ = π r²

          A₁ = π (0.22 10⁻²) ²

          A₁ = 0.152 10⁻⁴ m / s

With the continuity and flow equation.

           Q = A v

            v₁ = [tex]\frac{Q}{A}[/tex]  

             v₁ = [tex]\frac{0.55 \ 10{-3} }{0.152 \ 10^{-4} }[/tex]  

             v₁ = 36.67 m / s

Using Bernoulli's equation, where the speed of the water at the highest point is zero.

           y₂- y₁ =  [tex]\frac{v^1^2}{g}[/tex]  

Let's calculate.

           Δy =  [tex]\frac{36.67^2 }{2 \ 9.8 }[/tex]  

           Δy = 68.6m

In conclusion using the expressions of fluid mechanics we can find the results the maximum height that the water leaves through the two cases are:

      1) The maximum height when the water leaves the hose is:

          Δy = 0.20 m

      2) The maximum height of the water when it leaves the nozzle is:

          Δy = 68.6 m

Learn more here:  https://brainly.com/question/4629227

Answer:

   L = 44,096 m

Explanation:

The speed of the sound wave is constant therefore we can use the relations of uniform kinematics

             v = x / t

the speed of the wave in the bar is

            v = 15 v or

            v = 15 343

             v = 5145 m / s

The sound at the bar goes the distance

             L = v t

Sound in the air travels the same distance

             L = v_air (t + 0.12)

as the two recognize the same dissonance,

             v t = v_air (t +0.12)

             t (v- v_air) = 0.12 v_air

              t = 0.12 v_air / (v -v_air)

l

et's calculate

             t = 0.12 343 / (5145 - 343)

             t = 8.57 10-3 s

The length of the bar is

              L = 5145 8.57 10-3

              L = 44,096 m

Given that,

Temperature = 10⁸ K

We need to calculate the peak wavelength in the blackbody spectrum

Using formula of peak wavelength

[tex]peak\ wavelength = \dfrac{2.898\times10^{-3}}{T}[/tex]

Where, T= temperature

Put the value into the formula

[tex]peak\ wavelength = \dfrac{2.898\times10^{-3}}{10^{8}}[/tex]

[tex]peak\ wavelength = 2.90\times10^{-11}\ m[/tex]

[tex]peak\ wavelength = 290\ nm[/tex]

This range of wavelength is ultraviolet.

Hence, The peak wavelength in the blackbody spectrum is 290 nm and the range of wavelength is ultraviolet electromagnetic spectrum .

Answer:

2.98 kN, 69.1° below the horizontal

Explanation:

Sum of forces in the x direction:

Fₓ = 3 kN cos 30° − 2 kN cos 40°

Fₓ ≈ 1.07 kN

Sum of forces in the y direction:

Fᵧ = -3 kN sin 30° − 2 kN sin 40°

Fᵧ = -2.79 kN

Magnitude of the resultant force is:

F² = Fₓ² + Fᵧ²

F = 2.98 kN

The direction of the resultant force is:

tan θ = Fᵧ / Fₓ

θ = -69.1°

Answer:

Explanation:

When plastic balloon is rubbed with wool , charges are created on both balloon and silk in equal amount . Rubber balloon will acquire negative charge and silk will acquire positive charge .

Now when balloon is brought near a wall , there is induction of charge on the wall due to charge on the balloon . On the near surface of wall positive charge is produced and on the surface deep inside the wall negative charge is produced . The charge deep inside goes inside the earth but the positive charge near the surface of wall can not escape . It remains trapped by negative charge on the balloon .

hence there is mutual attraction between balloon and surface of wall is just like attraction between opposite charges . But once the ballon due to mutual attraction comes in contact with the wall , the charge on balloon and on wall neutralises each other and hence after some time the balloon falls off from the wall on the ground . It does not remain attracted to wall for ever . It happens due to neutralisation of charges on balloon and wall .

Answer:

The distance is  [tex]d = 0.00029065 \ m[/tex]

Explanation:

From the question we are told that

    The  first wavelength is  [tex]\lambda _1 = 588.9950 nm = 588.9950 *10^{-9} \ m[/tex]

     The  second wavelength is  [tex]\lambda _2 = 589.5924 nm = 589.5924 *10^{-9} \ m[/tex]

     The  difference in the  fringe pattern is  n =  1.0  

Generally the equation defining the effect of the movement of  the mirror M 2 in a Michelson interferometer is mathematically represented as

          [tex]2 * d = [\frac{\lambda _1 * \lambda_2 }{\lambda_2 - \lambda _1 } ] * n[/tex]

Here d is the mirror M 2  must be moved

substituting values

         [tex]2 * d = [\frac{(588.9950*10^{-9} ) * (589.5924 *10^{-9}) }{(589.5924 *10^{-9}) - (588.9950*10^{-9} ) } ] * 1.0[/tex]

        [tex]d = 0.00029065 \ m[/tex]