15. A parallel-plate capacitor, with air between the plates, is connected across a voltage source. This source establishes a potential difference between the plates by placing charge of magnitude 4.15 x 10-6 C on each plate. The space between the plates is then filled with a dielectric material, with a dielectric constant of 7.74. What must the magnitude of the charge on each capacitor plate now be, to produce the same potential difference between the plates as before? (Input your answer in 3 significant figures without unit. For example, if the answer is 1.356 x 10-6 C; then just input 1.37)

Answer:

Snell's law says that

n1*sin(a1) = n2*sin(a2)

n1 < n2

son n2/n1 > 1

then:

sin(a1) = (n2/n1)sin(a2)

the maximum possible value of sin(x) is 1 when x =90°

total internal reflection means that a2= 90°

but as the coefficient that is multiplying sin(a2) is bigger than 1, we can not have a2 = 90°, because the right side will be greater than 1 and the left side can not be bigger than 1, so we can not have a2 = 90°, so we can not have total internal reflection

The maximum possible value of sin(x) is 1 when x =90°total internal reflection means that a2= 90°.

Snell's law asserts that the ratio of the sines of the angle of incidence 1 and angle of refraction 2 for a given set of media is equal to the ratio of phase velocities (v1 / v2) in the two media, or equivalently, the refractive indices (n2 / n1).

If n1*sin(a1) = n2*sin(a2) and n1 n2 son n2/n1 > 1 according to Snell's law, then:

(n2/n1)sin = sin(a1) (a2)

When x =90°, the maximum feasible value of sin(x) is 1.

Total internal reflection indicates a2=90°, but because the coefficient multiplying sin(a2) is more than 1, we can't have a2 = 90° because the right side will be greater than 1 and the left side will be smaller than 1, therefore we can't have a2 = 90°. so we dont have total reflection.

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Answer:

The initial velocity is 38.46 m/s.

Explanation:

The horizontal distance travel by the tennis ball = 13 m  

The height at which the tennis ball dropped = 56 cm

Now calculate the initial speed of tennis ball.

The vertical velocity is zero.

Below is the calculation. Here, first convert centimetre into kilometre. So, height at which ball dropped is 0.56 km.

[tex]v = \sqrt{2 \times 9.8 \times 0.56} = 3.32 m/s \\[/tex]

[tex]t = \frac{3.32}{9.8} = 0.338s \\[/tex]

[tex]Ux \times t = 13 \\[/tex]

[tex]Ux = \frac{13}{0.338} = 38.46 m/s = Initial velocity.[/tex]

Answer:Reflection

Explanation:

The throwing back of a sound wave without absorbing it is called reflection

In acoustic reflection of sound is termed as echo i.e. sound arrived at the listener after a particular delay depending upon the position of barrier to the observer.

The reflection of sound is used in many devices like megaphone, trumpets, etc. It is also used in auditorium such that the ceiling of the auditorium is curved for multiple reflections of sound so that sound can be reached at every corner of the auditorium.

Answer:

a) Beth will reach before Alan

b)Beth has to wait 20 min for Alan to arrive

Explanation:

let 'd' be distance b/w Los Angeles and San  Francisco i.e 400 mi

considering ,

Alan's speed [tex]v_A[/tex]=50mph

Beth's speed [tex]v_B[/tex]=60mph

->For Alan:

The time required [tex]t_A[/tex]= d/[tex]v_A[/tex]= 400/50 => 8h

-> For beth:

The time required [tex]t_B=\frac{d}{v_B} =\frac{400}{60} =>6\frac{2}{3} h[/tex] => 6h 40m

Alan will reach at 8:00 a.m +8h = 4:00p.m.

Beth will reach at 9:00 a.m +6h 40m= 3:40p.m.

a) Beth will reach before Alan

b)Beth has to wait 20 min for Alan to arrive

The rate of heat loss, in watts, does this achieve is 37.66 W

It leads in cooling since water absorbs heat equivalent to mass times latent heat of evaporation to get converted into vapor .

So,

latent heat of evaporation of water = 2260 x 10³ J / kg or 2260 J / g

Now

in the evaporation of 1 g of water , heat lost = 2260 J

And,

heat lost per minute = 2260 J

So,

heat lost per second = 2260 / 60

= 37.66 J /s

= 37.66 W

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Answer:

The total resistance is more than the largest resistor.

Explanation:

In series connection of resistors, the total resistance of the connection is the sum of all the resistance of the resistors connected.

For example; let assume three resistors with resistance 3,4 and 5 ohms, the total resistance is;

Rt = 3+4+5 = 12 ohms

So, the total resistance is greater than the largest resistor since 12 ohms is greater than 5 ohms(largest resistor).

Answer:I=V/R

Explanation:

V=IR

Divide both sides by R

V/R=IR/R

V/R=I

I=V/R

The voltage in a circuit is given by the equation V= IR, in this equation v is the voltage Iis correct and R is the resistance the solution for the current is given as follows,

V= IR

I = V/R

Resistance is the obstruction of electrons in an electrically conducting material. The mathematical relation for resistance can be understood with the help of the empirical relation provided by Ohm's law.

V=IR

As for the given problem  if we have to solve for the current from the equation V=IR

V=IR

I = V/R

Let us suppose a 60-volt battery connected in a closed circuit with a resistor of 15 ohms then we have o find out the amount of current flowing in the circuit,

Voltage = 60V

Resistance = 15 Ohm

Current =?

By using Ohm,s Law,

V=IR

I = V/R

By substituting the respective values,

I = 60/15

I = 4 Ampere

Hence, we solved for the current from the equation V=IR.

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Answer:

C

Explanation:

Cereal made with refined grains is the healthiest type of carbohydrate.

A carbohydrate is defined as a bio-molecule which consists of carbon,hydrogen and oxygen atoms which are usually in the ratio of 2:1 with the empirical formula C[tex]_n[/tex](H₂O)[tex]_n[/tex].

This term is most commonly used in  field of biochemistry as a synonym of saccharide which is a group of sugars, starch and cellulose.

They perform various functions in living organisms. They serve as an energy source and as well as structural components . They are a key component in providing nutrition and are found in wide variety of natural as well as processed foods.

Carbohydrates occur as cellulose in the cell walls of plants and is one of the components of insoluble dietary fibers.

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Answer:

The deceleration is  [tex]a = - 76.27 m/s^2[/tex]

Explanation:

From the question we are told that

   The height above  firefighter safety net is [tex]H = 14 \ m[/tex]

   The length by which the net is stretched is [tex]s = 1.8 \ m[/tex]

From the law of energy conservation

    [tex]KE_T + PE_T = KE_B + PE_B[/tex]

 Where [tex]KE_T[/tex] is the kinetic energy of the person before jumping which equal to zero(because to kinetic energy at maximum height )

   and  [tex]PE_T[/tex] is the potential energy of the before jumping  which is mathematically represented at

          [tex]PE_T = mg H[/tex]

and  [tex]KE_B[/tex] is the kinetic energy of the person just before landing on the safety net  which is mathematically represented at

        [tex]KE_B = \frac{1}{2} m v^2[/tex]

and  [tex]PE_B[/tex] is the potential energy of the person as he lands on the safety net which has a value of zero (because it is converted to kinetic energy )

   So the above equation becomes

          [tex]mgH = \frac{1}{2} m v^2[/tex]

=>           [tex]v = \sqrt{2 gH }[/tex]

    substituting values

                [tex]v = 16.57 m/s[/tex]

Applying the equation o motion

             [tex]v_f = v + 2 a s[/tex]

Now the final velocity is zero because the person comes to rest

      So

         [tex]0 = 16.57 + 2 * a * 1.8[/tex]

            [tex]a = - \frac{16.57^2 }{2 * 1.8}[/tex]

            [tex]a = - 76.27 m/s^2[/tex]

Answer:

The volume of gas in an early diving bell full of air at sea level is halved at 10 m according to Boyle’s law

Explanation:

;at 20 m pressure is 300 kPa absolute and the gas is compressed into one third the volume.

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Answer:

a)5.88J

b)-5.88J

c)0.78m

d)0.24m

Explanation:

a) W by the block on spring is given by

W= [tex]\frac{1}{2}[/tex]kx² = [tex]\frac{1}{2}[/tex](530)(0.149)² =  5.88 J

b)  Workdone by the spring = - Workdone by the block = -5.88J

c) Taking x = 0 at the contact point we have U top = U bottom

So, mg[tex]h_o[/tex] = [tex]\frac{1}{2}[/tex]kx² - mgx

And, [tex]h_o[/tex]= ( [tex]\frac{1}{2}[/tex]kx² - mgx )/(mg) = [tex][\frac{1}{2} (530)(0.149^2)-(0.645)(9.8)(0.149)[/tex]]/(0.645x9.8)    

   [tex]h_o[/tex]=   0.78m            

d) Now, if the initial initial height of block is 3[tex]h_o[/tex]

[tex]h_o[/tex] = 3 x 0.78 = 2.34m

then, [tex]\frac{1}{2}[/tex]kx² - mgx - mg[tex]h_o[/tex] =0

[tex]\frac{1}{2}[/tex](530)x²  - [(0.645)(9.8)x] - [(0.645)(9.8)(2.34) = 0

265x² - 6.321x - 14.8 = 0  

a=265

b=-6.321

c=-14.8

By using quadratic eq. formula, we'll have the roots

x= 0.24 or x=-0.225

Considering only positive root:

x= 0.24m (maximum  compression of the spring)

Complete Question

A 0.025-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 150 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the displacement is x = 0.024 m, what is the kinetic energy of the block?

Answer:

The kinetic energy is  [tex]KE = 0.4368\ J[/tex]

Explanation:

From the question we are told that

   The mass of the block is [tex]m= 0.025\ kg[/tex]

   The spring constant is [tex]k = 150 N/m[/tex]

   The length of first  displacement  is [tex]x_1 = 0.80 \ m[/tex]

     The length of first  displacement  is [tex]x_2 = 0.024 \ m[/tex]

At the [tex]x_2[/tex] the kinetic energy is mathematically evaluated as

     [tex]KE = \Delta E[/tex]

Where [tex]\Delta E[/tex] is the change in energy stored on the spring which is mathematically represented as

            [tex]\Delta E = \frac{1}{2} k (x_1 ^2 - x_2^2)[/tex]

=>        [tex]KE = \frac{1}{2} k (x_1 ^2 - x_2^2)[/tex]

Substituting value

          [tex]KE = \frac{1}{2} * 150 * (0.08^2 - 0.024^2)[/tex]

          [tex]KE = 0.4368\ J[/tex]

Answer:

a:it speed up

b:it should be positive since final

velocity is larger than initial velocity

c:acceleration is approximately 4.5

m/s^2

Explanation:

initial velocity=u=4.47m/s

Final velocity=v=17.9m/s

Time=t=3 seconds

a:the car speed up since the velocity

increased

b:change in velocity is positive

because final velocity is larger than

initial velocity

17.9-4.47=13.43 m/s

c: acceleration=(v-u)/t

acceleration=(17.9-4.47)/3

acceleration=13.43/3

acceleration=4.5 m/s^2

If a car goes from a velocity u to a velocity v, the change in velocity is expressed as;

[tex]\triangle v =v-u[/tex]

Given

final velocity v = 17.9m/s

initial velocity u = 4.47m/s

[tex]\triangle v = 17.9-4.47\\\triangle v =13.43m/s[/tex]

a) Since the change in velocity is a positive value, this shows that the car speeds up.

b) The answer should be positive since the final velocity is greater than the initial velocity.

c) Acceleration is the change in velocity with respect to time

[tex]a=\frac{v-u}{t}\\a=\frac{17.9-4.47}{3} \\a=\frac{13.43}{3}\\a= 4.48m/s^2[/tex]

Hence the acceleration of the car is 4.48m/s²

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Answer:

as in motor generaror are connected to same shaft then both machines are working with same speed

but number of poles are different with same speed means both machines are working with different frequencies

we know

frequency F = N*P/120

speed N = 82120F/P

given

motor speed = generator speed

120F1/P1 = 120F2/P2

F1/P1 = F2/P2

output frequency is 25 which is obtained from generator so F2=25

input frequency is 60 which is given to motor soF1=60

60/P1 = 25/P2

60/25 = P!/P2

P1/P2 = 12/5

multiply and divided by 2 becuase poles are even

P1/P2 = 12*2/5*2

=24/10

P1= 24 poles a

P2 =10 poles we get 25 hz frequency from 60 hz frequency

Answer:

66.94N

Explanation:

To find the force you use the second Newton law, which is given by:

[tex]F=ma[/tex]   (1)

m: mass of the ball 5.85g

the acceleration is:

[tex]a=\frac{v_f-v_o}{t}[/tex]

vf: final velocity = 128mph = 57.21m/s

vo : initial velocity = 0m/s

t: time = 5ms =5*10^{-3}s

by computing the acceleration and replacing it in the equation (1) you obtain:

[tex]a=\frac{57.21m/s}{5*10^{-3}s}=11443.2\frac{m}{s^2}\\\\F=(5.85*10^{-3}kg)(11443.20m/s^2)=66.94N[/tex]

hence, the force applied by Serena on the ball is 66.94N

Answer:

3.4 rad/sec^2

Explanation:

rotational inertia = 2.5 kg-m^2   radius = 1.1 m   force = 7.7 N

t = rotational inertia * angular acceleration    equation 1

also t = force * radius

therefore to calculate angular acceleration equation 1 becomes

f * r = inertia * angular acceleration   hence

angular acceleration = f * r / inertia = [tex]\frac{7.7 * 1.1 }{2.5}[/tex]   8.47 / 2.5 = 3.388 ≈ 3.4 rad/sec^2

Answer:

......................

Answer:

(a) Ra = 9.25 kN; Rb = 5.75 kN

(b) 26.7 kN

Explanation:

(a) Draw a free-body diagram of the crane.  There are four forces:

Reaction Ra pushing up at A,

Reaction Rb pushing up at B,

Weight force 12.5 kN pulling down at G,

and weight force 2.5 kN pulling down at F.

Sum of moments about B in the counterclockwise direction:

∑τ = Iα

-Ra (0.66 m + 0.42 m + 2.52 m) + 12.5 kN (2.52 m + 0.42 m) − 2.5 kN ((3.6 m + 0.9 m) cos 30° − 2.52 m) = 0

-Ra (3.6 m) + 12.5 kN (2.94 m) − 2.5 kN (1.38 m) = 0

Ra = 9.25 kN

Sum of moments about A in the counterclockwise direction:

∑τ = Iα

Rb (0.66 m + 0.42 m + 2.52 m) − 12.5 kN (0.66 m) − 2.5 kN ((3.6 m + 0.9 m) cos 30° + 0.66 m + 0.42 m) = 0

Rb (3.6 m) − 12.5 kN (0.66 m) − 2.5 kN (4.98 m) = 0

Rb = 5.75 kN

Alternatively, you can use sum of the forces in the y direction as your second equation.

∑F = ma

Ra + Rb − 12.5 kN − 2.5 kN = 0

Ra + Rb = 15 kN

9.25 kN + Rb = 15 kN

Rb = 5.75 kN

However, you must be careful.  If you make a mistake in the first equation, it will carry over to this equation.

(b) At the maximum weight, Ra = 0.

Sum of the moments about B in the counterclockwise direction:

∑τ = Iα

12.5 kN (2.52 m + 0.42 m) − F ((3.6 m + 0.9 m) cos 30° − 2.52 m) = 0

12.5 kN (2.94 m) − F (1.38 m) = 0

F = 26.7 kN

Answer:

A fan pushes hot air out of a vent and into a room. The hot air displaces cold air in the room, causing the cold air to move closer to the floor.

The hot air displacing the cold air is an example of  transfer by

Explanation:

Answer:

3) False. It is expensive since it requires sophisticated equipment and very low temperatures

Explanation:

Nuclear magnetic resonance imaging measurements consist of magnetic resonance imaging to analyze tissues by the transition of the unpaired electron at carbon 13, giving information on the structure and composition of tissues. This information is processed in computers and transformed into images.

So the physical measurement is the MRN

Now we can analyze the statements in the problem

1) True by itself a magnetic measurement is non-invasive

2) True. Measuring carbon transitions has information about the soft tissue of the body

3) False. It is expensive since it requires sophisticated equipment and very low temperatures

4) Right. The applied magnetic field is high to be able to induce carbon transaction

Answer:

The answer is diffraction

Explanation:

Answer:

The answer is diffraction

Explanation:

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Your answer:

In Greek mythology, this constellation is related with the time the Olympian gods sought refuge in Egypt. Unfortunately, following their epic fighting with the Titans, peace did not closing for long, as the monster Typhon, son of the Titan Tartarus and Earth, sought revenge. Typhon was once a fearsome fire-breathing creature, taller than mountains and with palms which possessed dragons' heads in region of fingers. The Olympian gods sought to break out by way of adopting a number disguises: Zeus, a ram - Hera, a white cow, Bacchus (another model of the fable suggests Pan) a goat. As Typhon approached, Bacchus/Pan threw himself into the Nile but, in a panic, solely succeeded in altering part of his body, ending up with a goat's physique and the tail of a fish. Meanwhile, Zeus had been dismembered via Typhon, however was saved when Bacchus/Pan let out an ear-splitting yell, distracting the monster lengthy ample for an agile Hermes to gather the supreme god's limbs and cautiously fix him. In gratitude, Zeus transferred Bacchus/Pan to the heavens.

Answer:

Located in the Southern Hemisphere, Capricornus represents a creature that is a blend of fish and goat; the name means "goat horn" in Latin. While it is one of the Zodiac constellations identified by the Greek astronomer Ptolemy in the 2nd century, Capricornus is often used when referring to the constellation, while Capricorn is used in conjunction with the sign of the Zodiac.Locating Capricornus

Capricornus is among the faintest constellations, just brighter than Cancer. The 40th largest constellation, Capricornus measures 414 square degrees. It sits among the other constellations of the water genre, including the water-bearer Aquarius, the whale-like sea monster Cetus, the fishes Pisces, and the river Eridanus.

Right Ascension: 21.02 hours

Declination: -20 to -23 degrees

Visible: between latitudes 60 degrees and -90 degrees

Best viewed: During the month of September at 9 p.m.

To find the arrowhead-shaped Capricornus in the sky, look for the Summer Triangle and make a line from Vega through Altair to the lower southern sky.

The tropic of Capricorn the place where the sun appears overhead at noon on the winter solstice originally sliced right through its namesake constellation, but the line has since shifted to go through the constellation .

The constellation has its roots in the cultures of Sumeria — which identified it with a mythical figure that was half goat and half fish — and Babylonia, which portrayed it as a goat-human hybrid.

The Greeks associate the constellation with Pan, the god of nature. Part of Pan's lore was that he helped Zeus fight the Titans to earn his spot in the heavens. He escaped the monster Typhon by jumping into the Nile, but only half of his body was submerged, so he was a fish in the part of his body that remained underwater. Other spins on the tale have the constellation associated with Amalthaea, the mythical goat that acted as a foster mother to Zeus as an infant.

Answer:

Explanation:

The mass of cube = 700 kg

volume = 1 m³

density = 700 kg / m²

Its density is less than that of water so it will try to float on the surface .

Tension in rope will be equal to net upward force

upthrust = volume x density of water x g

= 1 x 10³ x 9.8

= 9800 N

weight of cube = mass x g

= 700 x 9.8

= 6860 N .

Net upward force = 9800 - 6860

= 2940 N.

Tension in the rope = 2940 N.

Rope will hold the cube inside and not allow it to go outside water .

b )

If rope is cut , cube being lighter , will float on surface of water .

Part of cube inside water while floating

= 6860 / 9800

= .7

.7 m will remain inside water

part floating outside

= 1 - 0.7

= 0.3 m .

Carbon dioxide is the most abundant greenhouse gas in the atmosphere.

Answer:C

Explanation:

Carbon dioxide is the most abundance greenhouse gas in The atmosphere.

Answer:

The velocity just before hitting the ground is [tex]v_f = 30 m/s[/tex]

Explanation:

From the question we are told that

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

    The final speed is  [tex]v = 30 \ m/s[/tex]

From the equations of motion we have that

      [tex]v^2 =u^2 + 2as[/tex]

Where s is the distance travelled which is the height of the cliff

  So making it the subject of the the formula  we have that

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

Where a is the acceleration due to gravity with a value  [tex]a = 9.8m/s^2[/tex]

       So

                  [tex]s = \frac{30^2 - 10^2 }{2 * 9.8 }[/tex]

                  [tex]s = 40.8 \ m[/tex]

Now we are told that was through horizontally with a speed of

      [tex]v_x =10 m/s[/tex]

Which implies that this would be its velocity horizontally through out the motion

    Now it final  velocity vertically can be mathematically evaluated as

            [tex]v_y = \sqrt{2as}[/tex]

Substituting values

             [tex]v_y = \sqrt{(2 * 9.8 * 40.8)}[/tex]

             [tex]v_y = 28.3 \ m/s[/tex]

The resultant final velocity is mathematically evaluated as

       [tex]v_f = \sqrt{v_x^2 + v_y^2}[/tex]

Substituting values

       [tex]v_f = \sqrt{10^2 + 28.3^2}[/tex]

       [tex]v_f = 30 m/s[/tex]

Answer:

Materials that allow electricity to pass through them are called conductors.

Copper wire is a good conductor. Materials that do not allow electricity to pass through them are called insulators.

Explanation:

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Answer:

B. add more loops of wire between the magnets

Explanation:

this would increase the magnetic force acting on the rod therefore increasing

By adding more loops of wire between the magnets the motor is changed to be able to lift a heavier box.

An electric motor is a mechanism that turns electricity into mechanical energy.

The interaction between the motor's magnetic field and electric current in a wire winding generates force in the form of torque imparted to the motor's shaft in most electric motors.

An electric generator is physically equivalent to an electric motor, but it converts mechanical energy into electrical energy using a reversed flow of power.

The load capacity in the motor can be increased by increasing the no of loops. So by adding more loops of wire between the magnets the motor is changed to be able to lift a heavier box.

Hence option B is correct.

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Answer:

Explanation:

Emf e generated in a coil with no of turn n and area A rotating in a magnetic field B  with angular speed of ω is given by the expression

e = e₀ sinωt

where e₀ = nωAB which is the maximum emf generated

Putting the given values

15.7 = 1000xω x 20 x 10⁻² x 5

ω = .0157

frequency of rotation

= ω / 2π

= .0157 / 2 x 3.14

= .0025 /s

9 rotation / hour .

Answer:

2.10 V

Explanation:

To find the potential difference across the ends of the bar, you take into account that when the bar moves with speed v, in a constant magnetic field, the charges in the wire feels a magnetic force that separate the opposite charges, generating an induced potential difference given by the following formula:

[tex]\epsilon=vBL[/tex]   (1)

v: speed of the bar = 11.5 m/s

B: magnitude of the magnetic field = 1.22 T

L: length of the bar = 15.0cm = 0.15m

You replace the values of v, B and L in the equation (1):

[tex]\epsilon=(11.5m/s)(1.22T)(0.15m)=2.10\ V[/tex]

hence, the induced potential difference is 2.10 V