How would the interference pattern change for this experiment if a. the grating was moved twice as far from the screen and b. the line density of the grating were doubled?

Answer:

Post indicator valve

Explanation:

Post Indicator Valves are commonly used to control the water flow of sprinkler systems used in public and private buildings, warehouses, and factories for fire suppression. PIVs control water flow from the public system into the building's fire suppression system.

Answer:

Energy is the strength and vitality required for sustained physical or mental activity.

Matter occupies space and possesses rest mass, especially as distinct from energy.

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Answer:

cross-sectional

Explanation:

The full definition of this is ''a research design in which several different age-groups of participants are studied at one particular point in time.''

Answer:

4.5x 10^ -9m

Explanation:

See attached file

Answer:

The radius is  [tex]r_{min} = 0.00226 \ m[/tex]

Explanation:

   From the question we are told that

      The  elastic limit(stress) is [tex]\sigma = 5.0*10^{8} \ N /m^2[/tex]

      The length is  [tex]L = 4.0 \ m[/tex]

      The weight of the commercial sign is    [tex]F_s = 8000 \ N[/tex]

       The maximum extension of the wire is  [tex]\Delta L = 5.0 \ cm = 0.05 \ m[/tex]

Generally the elastic limit of an alloy (stress) is is mathematically represented as

            [tex]\sigma = \frac{ F_s }{ A }[/tex]

Where A is the cross-sectional area of the wire which is mathematically represented as

         [tex]A = \pi r^2[/tex]

here [tex]r = r_{min}[/tex] which is the minimum radius of the wire that support the commercial sign

So

          [tex]\sigma = \frac{ F_s }{ \pi r_{min}^2 }[/tex]

=>       [tex]r_{min} = \sqrt{\frac{F_s}{\sigma * \pi} }[/tex]

substituting values

             [tex]r_{min} = \sqrt{\frac{8000}{ 5.0* 10^8 * 3.142} }[/tex]

           [tex]r_{min} = 0.00226 \ m[/tex]

Answer:

0.7707

Explanation:

From Snell's law,

n(1) * sin θ1 = n(2) * sinθ2

Where n(1) = refractive index of air = 1.0003

θ1 = angle of incidence

n(2) = refractive index of second substance

θ2 = angle of refraction

The angle of reflection through the unknown substance is the same as the angle of incidence of air. Thus this means that θ1 = 29°

=> 1.0003 * sin29 = n(2) * sin39

n(2) = (1.0003 * sin29) / sin39

n(2) = 0.7707

Explanation:

The index of refraction n of the substance is 0.7707

Here we know that

n(1) * sin θ1 = n(2) * sinθ2

here

n(1) = refractive index of air = 1.0003

θ1 = angle of incidence

n(2) = refractive index of second substance

θ2 = angle of refraction

The angle of reflection should be via the unknown substance that represent the same as the angle of incidence of air.

So,

θ1 = 29°

1.0003 * sin29 = n(2) * sin39

n(2) = (1.0003 * sin29) / sin39

n(2) = 0.7707

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Explanation:

Distance = speed × time

d = (340 m/s) (9.6 s)

d = 3264 m

Answer:

Explanation:

Before calculating the work function, we must know the formula for calculating the kinetic energy of an electron. The kinetic energy of an electron is the taken as the difference between incident photon energy and work function of a metal.

Mathematically, KE =  hf - Ф where;

h is the Planck constant

f is the frequency = c/λ

c is the speed of light

λ is the wavelength

Ф is the work function

The formula will become KE =  hc/λ - Ф. Making the work function the subject of the formula we have;

Ф = hc/λ - KE

Ф = hc/λ - 1/2mv²

Given parameters

c = 3*10⁸m/s

λ = 97*10⁻⁹m

velocity of the electron v = 3.48*10⁵m/s

h = 6.62607015 × 10⁻³⁴

m is the mass of the electron = 9.10938356 × 10⁻³¹kg

Substituting the given parameters into the formula Ф = hc/λ - 1/2mv²

Ф =  6.63 × 10⁻³⁴*3*10⁸/97*10⁻⁹ -  1/2*9.11*10⁻³¹(3.48*10⁵)²

Ф = 0.205*10⁻¹⁷ - 4.555*10⁻³¹*12.1104*10¹⁰

Ф = 0.205*10⁻¹⁷ - 55.163*10⁻²¹

Ф = 0.205*10⁻¹⁷ - 0.0055.163*10⁻¹⁷

Ф = 0.1995*10⁻¹⁷Joules

Since 1eV = 1.60218*10⁻¹⁹J

x = 0.1995*10⁻¹⁷Joules

cross multiply

x = 0.1995*10⁻¹⁷/1.60218*10⁻¹⁹

x = 0.1245*10²

x = 12.45eV

Hence the work function of the metal in eV is 12.45eV

Answer:

6ms^-1

Explanation:

Given that the frequency difference is

( 563- 544) = 19

So alsoThe wavelength of each wave is = v/f = 344 /544

and there are 19 of this waves

So it is assumed that each motorcycle has moved 0.5 of this distance

in one second thus the speed of the motorcycles will be

=> 19/2 x 344/544 = 6.0 m/s

Answer:

386.13 N

Explanation:

The kinetic energy of the baseball is converted into workdone in moving the glove backward( work energy theorem).

Therefore, KE of the ball

[tex]\frac{1}{2} mv^2 =\frac{1}{2}(0.145)35^2\\ = 88.81 \text{J}[/tex]

Now, workdone in moving the glove

W= Fd

where F = Force applied, d = displacement of the glove= 0.23 cm.

88.81 = F×0.23

F= 88.81/0.23 = 386.13 N

Answer:

145060km

Explanation: Given that

speed = dx/dt = 2t^2 +1

integrate

x = 2/3t^3 + t + c (c is constant, x is in km, t is in second)

given that at t=0, x = 1000

so 1000 = 2/3 X (0)^3 + 0 + c

or c = 1000

So x = 2/3t^3 + t + 1000

for t = 1 min = 60s

x = 2/3 X 60^3 + 60 + 1000

x = 2/3×216000+ 1060

x = 144000+1060

= 145060km

At one minute, it will be 145060km far from the earth

Answer:

Explanation:

Using the lens formula

1//f = 1/u+1/v

f is the focal length of the lens

u is the object distance

v is the image distance

For convex lens

The focal length of a convex lens is positive and the image distance can either be negative or positive.

Given f = 20cm and u = 10cm

1/v = 1/f - 1/u

1/v = 1/20-1/10

1/v = (1-2)/20

1/V = -1/20

v = -20/1

v = -20 cm

Since the image distance is negative, this shows that the nature of the image formed by the convex lens is a virtual image

For concave lens

The focal length of a concave lens is negative and the image distance is negative.

Given f = -20cm and u = 10cm

1/v = 1/f - 1/u

1/v = -1/20-1/10

1/v = (-1-2)/20

1/V = -3/20

v = -20/3

v = -6.67 cm

Since the image distance is negative, this shows that the nature of the image formed by the concave lens is a virtual image

Answer:

This means that mercury has a higher or faster expansion rate than glass

Explanation:

This is because When a container expands, the reservoir in the glass expands at the same rate as the glass. Thus, if there is something in a glass and both expand at the same rate, they have no change - but if the contents expand faster, they will fill the container to a higher level, and if the contents expand slower, they will fill the container to a lower level (relative to the new size of the container).

Answer:

1. A

2. C

3. D

Explanation:

Answer:

The maximum force that can be lifted by this system is  51,478.4 kg

Explanation:

Given;

maximum gauge pressure of the hydraulic system, Hp = 15 atm = 1.52 x 10⁶ N/m²

diameter of the piston, d = 65 cm = 0.65 m

The maximum gauge pressure of the piston is given as;

[tex]Hp = \frac{F}{A}[/tex]

Where;

F is the maximum force of the piston

A is the area of the piston

[tex]A = \pi (\frac{0.65}{2} )^2\\\\A = 0.3319 \ m^2[/tex]

F = Hp x A

F = 1.52 x 10⁶N/m² x 0.3319m²

F = 504488 N

Force is given as;

F = mg

m = F/g

m = 504488/9.8

m = 51,478.4 kg

Therefore, the maximum force that can be lifted by this system is  51,478.4 kg

Answer:

Answers a) and b) should be marked as correct.

Explanation:

Recall that the resonance in an LRC circuit occurs when the current through the circuit is at its maximum, and such takes place when the impedance  (Z) of the circuit reaches its maximum. This means that the impedance (see formula below) is at its minimum value:

[tex]Z=\sqrt{R^2+(\omega\,L-\frac{1}{\omega\,C})^2 }[/tex]

as per the impedance expression above, such happens when the term in parenthesis inside the root which contains the inductive reactance ([tex]\omega\,L[/tex]) and the capacitive reactance ([tex]1/\omega\,C[/tex]) have the same value.

Therefore, answers:

a) "The impedance of the circuit has its minimum value."

and

b) "The inductive reactance and the capacitive reactance are exactly equal to each other."

are correct answers.

(a) The impedance of the circuit has its minimum value.

(b) The inductive reactance and the capacitive reactance are exactly equal to each other

LRC series circuit consists of inductor, resistor and capacitor is series.

The impedance of the circuit is calculated as follows;

[tex]Z = \sqrt{R^2 + (X_C -X_L)^2}[/tex]

where;

The impedance of the circuit is minimum when the capacitive reactance is equal to the inductive reactance.

[tex]X_C = X_L \\\\Z = \sqrt{R^2 \ + (0)^2} \\\\Z = R[/tex]

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Answer:

A. largest: (4000 kg, 5 m/s; 1000 kg, 20 m/s)

medium: (2000 kg, 5 m/s; 500 kg, 20 m/s; 1000 kg, 10 m/s)

smallest: (500 kg, 10 m/s)

B. largest: (4000 kg, 5 m/s; 1000 kg, 20 m/s)

medium: (2000 kg, 5 m/s; 500 kg, 20 m/s; 1000 kg, 10 m/s)

smallest: (500 kg, 10 m/s)

C. You can't say anything about the forces required until we know about the time frames required for each one to stop. So If they all stopped in the same time interval, then the rankings are the same.

Answer:

) pulls the ladder in the direction opposite

Explanation:

This is in line with lenz law that states that the magnetic field induced in a conductor act to oppose the magnetic field that produced it

Answer:

5.29×10^-7

Explanation:

shear stress τ = F/ A

shear deformation δ = (VL)/ (AG)

= (τL)/ G

V=shear force

L=height of disk=6.50×10^-2

A=cross sectional area

G= shear modulus= (1.60x10^9N/m^2)

A=πd^2/4

Then substitute the values we have

4×(375N)(0.00750m)

________________ = δ

(π*0.00650^2)(1.60x10^9N/m^2)

= 5.29×10^-7

Answer:

when a magnetic field near the floors points down and is increasing then the electric field curl (a) clockwise.

Explanation:

The magnetic field this is the area that is around a magnet  which there is presence of magnetic force. The Moving electric charges can create magnetic fields.  we say In physics, that the magnetic field is a field that passes through space and which makes a magnetic force move electric charges.

The Non-coulomb electric field curls ; ( B ) counterclockwise

Non-coulomb electric field also known as induced EMF is the Negative time rate of change of a magnetic flux in a closed loop through the loop. Non-coulomb electric field is expressed as ; Fnc = qEnc

Given that the magnetic field points downwards and the value of the electric field ( ε ) is increasing ( i.e.  ε > 0  ) The direction of the non-coulomb electric field will curl in a counter-clockwise direction.

Hence we can conclude that The Non-coulomb electric field curls in a counterclockwise direction.

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Answer:

60 km/hour.

Explanation:

We'll begin by calculating the total distance traveled by the car. This is illustrated below:

Total distance traveled = sum of distance between PQRST

Total distance = 10 + 5 + 10 + 5

Total distance = 30 km

Next, we shall convert 30 mins to hour. This can obtained as follow:

Recall:

60 mins = 1 hour

Therefore,

30 mins = 30/60 = 0.5 hour.

Finally, we shall determine the average speed of the car as follow:

Distance = 30 km

Time = 0.5 hour

Speed =?

Speed = distance /time

Speed = 30/0.5

Speed = 60 km/hour

Therefore, the speed of the car is 60 km/hour.

Answer:

Here,

v (final velocity) = 0

u (initial velocity) = u

a = ?

s = 1m

t = 0.4s

using the first equation of motion,

0 = u + 0.4a

= -0.4a = u

using the second equation of motion:

1 = 0.4u + 0.08a

from the bold equation

1 = 0.4(-0.4a) + 0.08a

1 = -0.16a + 0.08a

1 = -0.08a

a = -1/0.08

a = -100/8

a = -12.5 m/s/s

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Complete Question

Two stationary positive point charges, charge 1 of magnitude 3.25 nC and charge 2 of magnitude 2.00 nC , are separated by a distance of 58.0 cm . An electron is released from rest at the point midway between the two charges, and it moves along the line connecting the two charges.

Required:

What is the speed of the electron when it is 10.0 cm from the +3.25-nC charge?

Answer:

The velocity is [tex]v = 80.82 \ m/s[/tex]

Explanation:

From  the question we are told that

   The magnitude of charge one is  [tex]q_1 = 3.25 nC = 3.25 *10^{-9} \ C[/tex]

   The  magnitude of charge two  [tex]q_2 = 2.00 \ nC = 2.00 *10^{-9} \ C[/tex]

   The distance of separation is   [tex]d = 58.0 \ cm = 0.58 \ m[/tex]

Generally the electric potential of the electron at the midway point is mathematically represented as

         [tex]V = \frac{ q_1 }{\frac{d}{2} } + \frac{ q_2}{\frac{d}{2} }[/tex]

substituting values

         [tex]V = \frac{ 3.25 *10^{-9} }{\frac{ 0.58}{2} } + \frac{ 2 *10^{-9} }{\frac{ 0.58}{2} }[/tex]

          [tex]V = 1.8103 *10^{-8} \ V[/tex]

Now when the electron is 10 cm   =  0.10 m  from charge 1 , it is  (0.58 - 0.10 =  0.48 m ) m from charge two

Now the electric potential  at that point is mathematically represented as

       [tex]V_1 = \frac{q_1}{ 0.10} + \frac{q_2}{ 0.48}[/tex]

 substituting values

      [tex]V_1 = \frac{3.25 *10^{-9}}{ 0.10} + \frac{2.0*10^{-9}}{ 0.48}[/tex]

      [tex]V_1 = 3.67*10^{-8} \ V[/tex]

Now the law of energy conservation ,

   The  kinetic energy of the electron  =  potential energy of the electron

i.e     [tex]\frac{1}{2} * m * v^2 = [V_1 - V]* q[/tex]

where q is the magnitude of the charge on the electron with value

      [tex]q = 1.60 *10^{-19} \ C[/tex]

While m is the mass of the electron with value  [tex]m = 9.11*10^{-31} \ kg[/tex]

        [tex]\frac{1}{2} * 9.11 *10^{-19} * v^2 = [ (3.67 - 1.8103) *10^{-8}]* 1.60 *10^{-19}[/tex]

         [tex]v = \sqrt{6532.4}[/tex]

        [tex]v = 80.82 \ m/s[/tex]

Answer:

Speed of the electron is 2.46 x 10^8 m/s

Explanation:

momentum of the electron before relativistic effect = [tex]M_{0} V[/tex]

where [tex]M_{0}[/tex] is the rest mass of the electron

V is the velocity of the electron.

under relativistic effect, the mass increases.

under relativistic effect, the new mass M will be

M = [tex]M_{0}/ \sqrt{1 - \beta ^{2} }[/tex]

where

[tex]\beta = V/c[/tex]

c  is the speed of light = 3 x 10^8 m/s

V is the speed with which the electron travels.

The new momentum will therefore be

==> [tex]M_{0}V/ \sqrt{1 - \beta ^{2} }[/tex]

It is stated that the relativistic momentum is 1.75 times the non-relativistic momentum. Equating, we have

1.75[tex]M_{0} V[/tex] = [tex]M_{0}V/ \sqrt{1 - \beta ^{2} }[/tex]

the equation reduces to

1.75 = [tex]1/ \sqrt{1 - \beta ^{2} }[/tex]

square both sides of the equation, we have

3.0625 = 1/[tex](1 - \beta ^{2} )[/tex]

3.0625 - 3.0625[tex]\beta ^{2}[/tex] = 1

2.0625 = 3.0625[tex]\beta ^{2}[/tex]

[tex]\beta ^{2}[/tex] = 0.67

β = 0.819

substitute for  [tex]\beta = V/c[/tex]

V/c = 0.819

V = c x 0.819

V = 3 x 10^8 x 0.819 = 2.46 x 10^8 m/s

Answer:

d = 6.38 x 10⁻³ m = 6.38 mm

Explanation:

Since, the no. of bright fringes is 34 in a centimeter, therefore, the fringe spacing must be equal to:

Fringe Spacing = Δx = 1 cm/34

Δx = 0.0294 cm = 2.94 x 10⁻⁴ m

But, the formula for fringe spacing in a double slit experiment is:

Δx = λL/d

where,

λ = wavelength of light = 605 nm = 6.05 x 10⁻⁷ m

L = Distance between screen and slits = 3.1 m

d = slit separation = ?

Therefore,

2.94 x 10⁻⁴ m = (6.05 x 10⁻⁷ m)(3.1 m)/d

d = (18.755 x 10⁻⁷ m²)/(2.94 x 10⁻⁴ m)

d = 6.38 x 10⁻³ m = 6.38 mm

Answer:

The work done by the system is 550 J

Explanation:

Given;

heat added to the system, Q = 550 J

Apply the first law of thermodynamics;

ΔU = Q - W

Where;

ΔU is change in internal energy

Q is the heat added to the system

W is the work done by the system

During an isothermal process, the temperature of the system is constant for the entire process. During this process, the change in the internal energy is zero.

0 = Q - W

W = Q

W = 550 J

Therefore, the work done by the system is 550 J

Answer:

3.67°

Explanation: Given that λ=640nm , m = 1

Considering the slit separation

d = 1cm/1000

= 1.000×10^-3cm

= 1.000×10-5m

We then have

Sinθ = mλ/d

Sinθ= (1×640×10^-9)/1.000×10-5m

Sinθ = 0.064

θ= sin-1 0.064

θ= 3.669°

= 3.67°

Answer:

34°

Using the relation

θᶜ = sin^-1(n₂/n₁),

where n1= the refractive index of light is propagating from a medium

And n2 = refractive index of medium into which light is entering

So we know that

refractive index of diamond at 589nm = 2.41= n₁

refractive index of ethanol at 589nm and 20°C = 1.36= n₂

Thus. θᶜ = sin^-1(1.361/2.417) = 0.58radians = 34°

Explanation:

Answer:

Explanation:

a )

focal length of convex spherical mirror

f = 36/2  cm = 18 cm

object distance u = - 25 cm

mirror formula

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

[tex]\frac{1}{v} + \frac{1}{- 25} = \frac{1}{18}[/tex]

[tex]\frac{1}{v} = \frac{1}{25} + \frac{1}{18}[/tex]

v = 6.28  cm .

It is positive hence the image will be erect / upright  and formed on the back of the mirror.

For object distance of 47 cm

u = - 47 cm

Putting the values in the mirror formula

[tex]\frac{1}{v} + \frac{1}{- 47} = \frac{1}{18}[/tex]

[tex]\frac{1}{v} = \frac{1}{ 47} + \frac{1}{18}[/tex]

v = 13  cm

It is positive hence the image will be erect / upright and formed on the back of the mirror.

Answer:

0.09 x10^-10m

Explanation:

Using wavelength=( 12.27 A)/√V

= 12.27 x 10^-10/ √1.6x10^2

= 0.09x10^-10m