slab of ice floats on water with a large portion submerged beneath the water surface. The slab is in the shape of a rectangular solid. The volume of the slab is 20 m3 and the surface area of the top is 14 m2. The density of ice is 900 kg/m3 and sea water is 1030 kg/m3. No need to show work. a) Calculate the percentage of the volume of the ice that is submerged. b) Calculate the height, in meters, of the portion of the ice that is submerged. c) Calculate the buoyant force acting on the ice. d) Assume a polar bear has a mass of 400 kg. Calculate the maximum number of polar bears that could be supported by the slab without the slab sinking below the surface of the water.

Answer:

Explanation:

Let θ be the inclination

downward acceleration on an inclined plane

= g sinθ

= 32 x sin6

a =  3.345 ft /s

a ) for knowing the speed at point B

v² = u² + 2 a s , v is final velocity , u is initial velocity , a is acceleration and s is distance travelled .

v² = 0 + 2 x 3.345 x 500

= 3345

v = 57.8 ft /s

from point B to C , the car decelerates so we shall find deceleration

v² = u² + 2 a s

0 = 3345 + 2 x a x 70      ( v becomes u here )

a = - 23.9 m /s²

net force on car during deceleration

= μmgcosθ - mg sinθ     where  μ is coefficient of static friction ,

= mg ( μcosθ -  sinθ )

deceleration = g ( μcosθ -  sinθ )

g ( μcosθ -  sinθ )  = 23.9

( μcosθ -  sinθ ) = .74

μcosθ = .74 + .104

= .8445

μ = .8445 / .9945

= .85 .

Final answer:

To calculate the maximum deceleration of a car heading down a 6° slope under different road conditions, we can use the coefficient of static friction. On dry concrete, the deceleration is approximately 2.12 m/s². On wet concrete, the deceleration is approximately 1.62 m/s². On ice, the deceleration is approximately 2.04 m/s².

Explanation:

To calculate the maximum deceleration of a car heading down a 6° slope, we need to consider the road conditions. Assuming the weight of the car is evenly distributed on all four tires, and that the tires are not allowed to slip during the deceleration, we can calculate the deceleration for different road conditions.

(a) On dry concrete, the coefficient of static friction can be calculated using the equation μs = tan(θ), where θ is the angle of the slope. In this case, the coefficient of static friction is approximately 0.105 and the maximum deceleration is approximately 2.12 m/s².

(b) On wet concrete, the coefficient of static friction is typically lower than on dry concrete. Let's assume a coefficient of 0.08. In this case, the maximum deceleration is approximately 1.62 m/s².

(c) On ice, assuming a coefficient of static friction of 0.100, the same as for shoes on ice, the maximum deceleration is approximately 2.04 m/s².

Answer:

A town interested in installing wind turbines to generate electricity measures the speed of the wind in the town over the course of a year. They find that most of the time, the wind speed is pretty slow, while only rarely does the wind blow very fast during a storm. What would be the best measure of the central wind speed they should report to the mayor?

The median is the best measure of the central wind speed they should report to the mayor because the distribution is not symmetric. The distribution of wind speeds is skewed.

Explanation:

Based on the scenario described in the question, the median is the best measure of the central wind speed they should report to the mayor because the distribution is not symmetric. The distribution of wind speeds is skewed.

Answer:

8 minutes sooner

Explanation:

Average speed of snail= 4cm/min

Distance to be covered = 160cm

Time taken for the journey = distance/speed

Time taken for the journey = 160/4

Time taken for the journey = 40 min

If it crawed an average speed of 5cm/min

Distance = 160 cm

Time for the journey = distance/speed

Time for the journey = 160/5

Time for the journey = 32 min

Its going to take the snail 40 min - 32 min to Kno how sooner it will taje it if the average speed is 5cm/min

40 min - 32 min = 8 min

The correct statements are: (b) All these technologies use radio waves, including high-frequency microwaves. (d) Microwave ovens emit in the same frequency band as some wireless Internet devices.

The correct statements that describe the various applications listed above are:

Statement a.) is incorrect because not all technologies listed use low-frequency microwaves. Statement c.) is incorrect because not all technologies listed use a combination of infrared waves and high-frequency microwaves. Statement e.) is incorrect because wireless Internet devices do not have the shortest wavelength among the technologies listed. Statement f.) is incorrect because the wavelengths of the technologies listed vary. Statement g.) is incorrect because the wavelengths of the technologies listed also vary.

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The correct answers are option (a) and option (d). All these technologies use radio waves, including low-frequency microwaves and Microwave ovens emit in the same frequency band as some wireless Internet devices.

The electromagnetic (EM) spectrum includes a wide range of frequencies, which are used in various modern technologies. Here are analyses correlating with the provided frequency ranges:

Answer:

Wavelength at which the light reflected by the film is brightest = 567.5 nm

Explanation:

We are given;

index of refraction n2 = 1.33

Thickness;(t) = 320 nm

Now the wavelength at which the light reflected by the film is brightest is gotten from the formula for path difference in critical interference as;

Path difference = (m + ½)(λ/n)

Where;

path difference = 2 x thickness = 2(320) = 640 nm

λ = Wavelength at which the light reflected by the film is brightest

n is Refractive index

m is an integer = 0,1,2,3...

Thus; at m = 0;

We have;

640 = (0 + ½)(λ/1.33)

640 = (λ/2.66)

λ = 640 x 2.66

λ = 1702.4 nm

at m = 1;

We have;

640 = (1 + ½)(λ/1.33)

640 = (3/2)(λ/1.33)

λ = 640 x 1.33 x 2/3

λ = 567.5 nm

at m = 2;

We have;

640 = (2 + ½)(λ/1.33)

640 = (5/2)(λ/1.33)

λ = 640 x 2 x 1.33/5

λ = 340.5 nm

Since we are told that the wavelength is between 400 – 690 nm.

Thus, the wavelength at which the light reflected by the film is brightest is the higher value gotten that is between 400nm and 690nm.

Thus, Wavelength at which the light reflected by the film is brightest = 567.5 nm

The light reflected by the water film will appear brightest to an observer at a wavelength of approximately 854.4 nm.

The wavelength of light in a medium is given by λn = λ/ʼn, where λ is the wavelength in vacuum and ʼn is the medium's index of refraction. In water, which has an index of refraction of n = 1.33, the range of visible wavelengths is 285 to 570 nm. When light is incident on the water film, it will reflect predominantly at the wavelengths where the film's thickness is an integer multiple of half the wavelength. The brightest reflection will occur when the film's thickness is such that the reflected wavelength is at its maximum in the range of visible light.

To find the wavelength of the brightest reflection, we can use the equation λn = 2nt, where λn is the wavelength in vacuum, n is the refractive index of the film, and t is the thickness of the film. Given the refractive index n2 = 1.33 and the thickness t = 320 nm, we can solve for λn.

Plugging in the values:

λn = 2nt = 2(1.33)(320 nm) ≈ 854.4 nm

Therefore, the wavelength of the light reflected by the film that appears brightest to an observer is approximately 854.4 nm.

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Answer:

a) v3 = 1 m/s

c) K3 < K1

d) p3 = p1

Explanation:

a) To solve this problem you use the conservation of the linear momentum in elastic collision.

In the first case you have:

[tex]p_i=p_f\\\\m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}[/tex]

but the second block is at rest, then v2i = 0m/s:

[tex]m_1v_{1i}=m_1v_{1f}+m_2v_{2f}[/tex]

Furthermore, you can assume that the first object stops just after the collision with the second one. From this last expression you obtain the value of the second object:

[tex]v_{2f}=\frac{m_1v_{1i}}{m_2}\\\\m_2=2m_1\\\\v_{2f}=\frac{m_1(4m/s)}{2m_1}=2\ m/s[/tex]

Then, you use the conservation of momentum for the second case, in which the second objects impact the third one:

[tex]m_2v'_{2i}+m_3v_{3i}=m_2v'_{2f}+m_3v_{3f}\\\\v_{3i}=0\\\\m_2v'_{2i}=m_2v'_{2f}+m_3v_{3f}\\\\v_{2f}=0\\\\m_2v'_{2i}=m_3v_{3f}\\\\v_{3f}=\frac{m_2v'_{2i}}{m_3}[/tex]

where again it has assumed that the second object stops, just after the impact with the third object. v'_2i = v_2f (in order to distinguish). BY using the fact m3 = 2m2 you obtain:

[tex]v_{3f}=\frac{m_2(2m/s)}{2m_2}=1\ m/s[/tex]

Then, you obtain that v3 < v2 < v1

c) The kinetic energy is given by:

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

you compute for all the three objects:

[tex]K_1=\frac{1}{2}m_1(4m/s)^2=8m_1\ m^2/s^2\\\\K_2=\frac{1}{2}m_2(2m/s)^2=\frac{1}{2}(2m_1)(4m^2/s^2)=4m_1\ m^2/s^2\\\\K_3=\frac{1}{2}m_3=(1m/s)^2=\frac{1}{2}(2m_2)(1\ m^2/s^2)=\frac{1}{2}(2(2m_1))(1 m^2/s^2)=2m_1\ m^2/s^2[/tex]

then, k3 < k2 < k1

d) For the momentum you have:

[tex]p_1=4m_1\ m/s\\\\p_2=m_2(2m/s)=(2m_1)(2m/s)=4m_1\ m/s\\\\p_3=m_3(1m/s)=(2m_2)(1m/s)=(2(2m_1))(1m/s)=4m_1\ m/s[/tex]

p1 = p2 = p3

Answer:

D. The object will continue to move with a constant velocity

Explanation:

According to Newton's first law also known as law of inertia, states that an object at rest will remain at rest or, if in motion, will remain in motion at constant velocity unless acted on by a net external force.

Therefore, An object moving in the absence of a net force will continue to move at a constant velocity

In the absence of a net force, an object will continue to move with a constant velocity.

The correct answer is D. The object will continue to move with a constant velocity. In the absence of a net force, an object will continue to move at a constant velocity. This means that the object will continue to move in a straight line at the same speed without slowing down or changing direction.

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Complete question:

A person uses 25.0 J of kinetic energy to push an object for 11.0 s How are work and power affected if the person uses the same amount of kinetic energy to push the object in less time ?

Answer:

The power will increase, and the amount of work will remain the same

Explanation:

Given;

Kinetic energy, K = 25.0 J

time of work, t = 11.0 s

Power = work / time = Energy / time

This equation shows that power is inversely proportional to time

Also, Energy is directly proportional to work (both are measured in Joules)

Since the person will use the same amount of kinetic energy to push the object in less time.

It means that energy will be constant (work done will not change) and the time will be reduced.

Power and time are inversely proportional, decrease in time means increase in power.

Thus, the power will increase, and the amount of work will remain the same

Answer:1960j

Explanation:

total input energy=2000j

98% of total input energy is useful

98% of 2000

98/100 x 2000

(98 x 2000) ➗ 100

196000 ➗ 100=1960

1960j is useful

The amount of useful transferred energy is  1960 J.

A body's capacity for work is measured in terms of energy. It cannot be produced or eliminated. There are numerous types of energy, including thermal, electrical, fusion, electrical, and nuclear. Energy has the ability to change its forms.

Efficiency is essentially a measurement of the amount of labour or energy that can be saved throughout a process. In other words, it's similar to comparing the energy input and output in any particular system. For instance, we observe that many processes result in the loss of effort or energy like vibration or waste heat.

Given parameters:

Total input energy; I =2000 Joule.

efficiency of the kettle; η = 98%.

We have to find useful output energy of the kettle: O = ?

We know that: output energy = efficiency × input energy

= 98% ×  2000 J.

 = 98/100 x 2000 J.

= (98 x 2000) ÷ 100 J.

= 196000 ÷ 100 J

= 1960 J.

Hence, the useful transferred energy is  1960 J.

Learn more about energy here:

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An impulse is the product of force and the time interval during which that force is applied, resulting in a change of an object's momentum. It can be described both mathematically (J = F⋅Δt) and visually (area under the force-time curve). An impulse leads to an object's acceleration or deceleration and affects both speed and direction.

An impulse acting on an object is a concept in physics that describes the effect of a force applied over a period of time. It is the product of the average force and the time duration during which the force acts, resulting in a change in the object's momentum. The impulse experienced by an object can result in acceleration or deceleration, dependent on the direction of the force. Moreover, impulse is not just about the magnitude of force, but also the duration over which it is applied. A key point is that an impulse can be delivered either by a large force over a short period or a smaller force over a longer period, tailored to the specifics of a situation.

Impulse is measured as the change in momentum, which is the mass of the object multiplied by its velocity (mv). The formula for impulse is typically represented as J = F⋅Δt, where J represents impulse, F the force, and Δt the change in time. If you graph force versus time, the area under the curve represents the impulse, visually demonstrating the relationship between force, time, and momentum change.

It is essential to understand that impulse not only influences the speed of an object but also its direction of motion. For example, when a tennis player hits a ball, the racket imparts an impulse to the ball changing its momentum. The total impulse given by multiple forces is considered the net impulse, which is the sum of all individual impulses over a specified time.

Answer:

7.44 m/s

Explanation:

Units

The first thing you must do is get the units.

The distance is in meters.

The time is in seconds.

Therefore the speed is going to be in meters/second.

Givens

d = 2345 meters

t = 315 seconds

Solution

s = d/t

s = 2345/315

s = 7.44 meters/second

Correct question is;

To regulate the intensity of light reaching our retinas, our pupils1 change diameter anywhere from 2 mm in bright light to 8 mm in dim light. Find the angular resolution of the eye for 550 nm wavelength light at those extremes. In which light can you see more sharply, dim or bright?

Answer:

We'll see more sharply in dim light

Explanation:

If we consider diffraction through a circular aperture, then angular resolution is given by;

θ = 1.22λ/D

where:

θ is the angular resolution (radians) λ is the wavelength of light

D is the diameter of the lens' aperture.

Thus,

at diameter = 2mm = 2 x 10^(-3) m = 2 x 10^(6) nm

θ = (1.22 * 550)/(2 x 10^(6))

θ = 335.5 x 10^(-6) radians

Now, we need to convert this to arc seconds.

Thus;

1 arc second = 4.85 x 10^(-6) radians

So,θ = 335.5 x 10^(-6) radians = [335.5 x 10^(-6)]/[4.85 x 10^(-6)]

= 69.18 arc seconds

at diameter = 8mm = 8 x 10^(-3) m = 8 x 10^(6) nm

θ = (1.22 * 550)/(8 x 10^(6))

θ = 83.875 x 10^(-6) radians

Now, we need to convert this to arc seconds.

Thus;

1 arc second = 4.85 x 10^(-6) radians

So,θ = 83.875 x 10^(-6) radians = [83.875 x 10^(-6)]/[4.85 x 10^(-6)]

= 17.3 arc seconds

From the values of angular resolution gotten, we see that sharpness of image increases with increasing angular resolution. Thus, objects are sharper in dim light.

Answer:

Tension maximum =1131.9 N

Tension minimum =868.28 N

Tension at 3/4= 1065.995 N

Explanation:

a)

Given Mass of wrecking ball M1=88.6 Kg

Mass of the chain M2=26.9 Kg

Maximum Tension Tension max=(M1+M2) × (9.8 m/s²)

=(88.6+26.9) × (9.8 m/s²)

=115.5 × 9.8 m/s²

Tension maximum =1131.9 N

b)

Minimum Tension Tension minimum=Mass of the wrecking ball only × 9.8 m/s²

=88.6 × 9.8 m/s²

Tension minimum =868.28 N

c)

Tension at 3/4 from the bottom of the chain =In this part you have to use 75% of the chain so you have to take 3/4 of 26.9

= (3/4 × 26.9)+88.9) × 9.8 m/s²

= (20.175+88.6) × 9.8 m/s²

=(108.775) × 9.8 m/s²

=1065.995 N

Final answer:

The maximum tension in the chain is 1131.9 N, occurring at the top, while the minimum tension is 263.62 N at the bottom. The tension at a point three-fourths the way up from the bottom is 935.465 N.

Explanation:

To find the maximum and minimum tension in the chain, we need to consider the system's configuration, and the force due to gravity. The maximum tension occurs at the top of the chain, where it supports the entire weight of the wrecking ball and the chain. The minimum tension occurs at the bottom of the chain, where it only needs to support the chain's weight. To find the tension at a point three-fourths of the way up from the bottom, we need to consider the weight of the portion of the chain below that point and the wrecking ball's weight.

Maximum tension (Tmax) is the sum of the weight of the wrecking ball and the entire chain:
Tmax = (mass of ball + mass of chain) × gravitational acceleration
Tmax = (88.6 kg + 26.9 kg) × 9.80 m/s²
Tmax = 115.5 kg × 9.80 m/s²
Tmax = 1131.9 N

Minimum tension (Tmin) is just the weight of the chain:
Tmin = mass of chain × gravitational acceleration
Tmin = 26.9 kg × 9.80 m/s²
Tmin = 263.62 N

Tension at three-fourths the way up:
We calculate the weight of the top one-fourth of the chain plus the wrecking ball:
Tension at three-fourths the way up = (mass of one-fourth of the chain + mass of ball) × gravitational acceleration
Tension at three-fourths = ((26.9 kg / 4) + 88.6 kg) × 9.80 m/s²
Tension at three-fourths = (6.725 kg + 88.6 kg) × 9.80 m/s²
Tension at three-fourths = 935.465 N

Answer:

9.2 amperes

Explanation:

Ohm's law states that the voltage V across a conductor of resistance R is given by [tex]V = R I[/tex]

Here, voltage V is proportional to the current I.

For voltage, unit is volts (V)

For current, unit is amperes (A)

For resistance, unit is Ohms (Ω)

Put R = 12.5 and V = 115 in V=RI

[tex]115=12.5I\\I=\frac{115}{12.5}\\ =9.2\,\,amperes[/tex]

Complete Question

The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leader–a physicist, naturally–immediately makes a determination of the acceleration due to gravity on the Pink Planet's surface by means of a simple pendulum of length 1.08m. She sets the pendulum swinging, and her collaborators carefully count 101 complete cycles of oscillation during 2.00×102 s. What is the result? acceleration due to gravity:acceleration due to gravity: m/s2

Answer:

The acceleration due to gravity is  [tex]g = 167.2 \ m/s^2[/tex]  

Explanation:

From the question we are told that

     The length of the simple pendulum is [tex]L = 1.081.08 \ m[/tex]

      The number of cycles is  [tex]N = 101[/tex]

       The time take is  [tex]t = 2.00 *10^{2 \ }s[/tex]

Generally the period of this oscillation is mathematically evaluated as

         [tex]T = \frac{N}{t }[/tex]

substituting values

         [tex]T = \frac{101}{2.0*10^2 }[/tex]

        [tex]T = 0.505 \ s[/tex]

The period of this oscillation is mathematically represented  as

               [tex]T = 2 \pi \sqrt{\frac{l}{g} }[/tex]

making g the subject of the formula we have

              [tex]g = \frac{L}{[\frac{T}{2 \pi } ]^2 }[/tex]

              [tex]g = \frac{4 \pi ^2 L }{T^2 }[/tex]

Substituting values

               [tex]g = \frac{4 * 3.142 ^2 * 1.08 }{505.505^2 }[/tex]

               [tex]g = \frac{4 * 3.142 ^2 * 1.08 }{0.505^2 }[/tex]  

              [tex]g = 167.2 \ m/s^2[/tex]  

Answer:

The the elongated length is [tex]\Delta L = 0.4 \ mm[/tex]

The change in diameter is  [tex]\Delta d = - 0.0136\ mm[/tex]

Explanation:

From the question we are told that

   The diameter of  the cylindrical bar is [tex]d = 21.0 \ mm = \frac{21}{1000} = 0.021 \ m[/tex]

     The length of the cylindrical bar is  [tex]L= 210 \ mm = 0.21 \ m[/tex]

      The force that deformed it is [tex]F = 46800 \ N[/tex]

       Elastic modulus is  [tex]E = 60.9 \ GPa = 60.9 *10^{9}Pa[/tex]

       The Poisson's ratio is  [tex]\mu = 0.34[/tex]

Generally elastic modulus is mathematically represented as

             [tex]E = \frac{\sigma }{\epsilon}[/tex]

Where

[tex]\epsilon[/tex] is the strain which is mathematically represented  as

            [tex]\epsilon = \frac{L}{\Delta L}[/tex]

Where [tex]\Delta L[/tex] is the elongation length

[tex]\sigma[/tex] is the stress on the cylinder which is mathematically represented as

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

Where F is the force and

 A is the area which is calculated as

               [tex]A = \frac{\pi} {4} d^2[/tex]

Substituting values

               [tex]A = \frac{\pi}{4} * (0.021)[/tex]

              [tex]A = 0.000346 \ m^2[/tex]

So the stress is

         [tex]\sigma = \frac{46800}{0.000346}[/tex]

        [tex]\sigma = 1.35 *10^{8} \ N \cdot m^2[/tex]

Thus the elastic modulus is  

        [tex]E = \frac{1.35 *10 ^{8}}{\frac{\Delta L}{L} }[/tex]

making [tex]\Delta L[/tex] the subject

       [tex]\Delta L = \frac{EL}{1.35 *10^{8}}[/tex]

Substituting values

      [tex]\Delta L = \frac{1.35 *10^{8} * 0.21}{1.35 *10^{8}}[/tex]

      [tex]\Delta L = \frac{1.35 *10^{8} * 0.21}{60.9*10^{9}}[/tex]        

       [tex]\Delta L = 0.0004 \ m[/tex]

      Converting to mm

   [tex]\Delta L = 0.0004 * 1000[/tex]    

  [tex]\Delta L = 0.4 \ mm[/tex]    

Generally the poisson ratio is mathematically represented as

        [tex]\mu = - \frac{\frac{\Delta d }{d} }{\frac{\Delta L }{L} }[/tex]

The negative sign indicate a decrease in diameter as a result of the force

making [tex]\Delta d[/tex] the subject

        [tex]\Delta d = - \mu * \frac{\Delta L }{L } * d[/tex]

Substituting values

        [tex]\Delta d = - 0.34 * \frac{0.0004 }{0.210 } * 0.021[/tex]

       [tex]\Delta d = - 1.36 *10^{-5} \ m[/tex]

      Converting to mm      

 [tex]\Delta d = - 0.0136\ mm[/tex]

Answer:

The number of molecules in the volume is  [tex]N_v = 2.27109* 10^{12}[/tex] molecules

Explanation:

From the question we are told that

    The pressure of the ultrahigh vacuum is [tex]P = 8.4*10^{-11} torr = 8.4*10^{-11} * 133 = 1.1172 *10^{-8}Pa[/tex]

     The molecular diameter of the gas molecules [tex]d = 2.2*10^{-10} m[/tex]

      The temperature is  [tex]T = 310 \ K[/tex]

      Avogadro's number is [tex]N = 6.02214 *10^{23}\ l/mol[/tex]

        The volume of the gas is [tex]V = 0.87 m^3[/tex]

From the ideal gas law[[tex]PV = nRT[/tex]] that the number of mole is mathematically represented as

           [tex]n = \frac{PV}{RT}[/tex]

Where R is the gas constant with a value  [tex]R = 8.314\ J/mol[/tex]

  Substituting values

              [tex]n = \frac{1.1172 *10^{-8} * 0.87}{8.314 * 310}[/tex]

             [tex]n = 3.771*10^{-12} \ mole[/tex]

The number of molecules is mathematically represented as

               [tex]N_v = n * N[/tex]

  Substituting values

              [tex]N_v = 3.771*10^{-12} * 6.02214 *10^{23}[/tex]

             [tex]N_v = 2.27109* 10^{12}[/tex] molecules

Answer:

a) 423.64 KJ / mole

Explanation:

The pictures below explains it all in the calculation and i hope it helps you

Answer:

a) 2.693*10^-4 C

b) 8.875*10^-5 s

c) 2.96 W

Explanation:

Given that

Inductance of the circuit, L = 4.24 mH

Capacitance of the circuit, C = 3.02 μF

Current in the circuit, I = 2.38 A

See attachment for calculations

Answer:

a) 0.269 mC

b) 0.355 ms

c) 1.39W

Explanation:

a) To find the charge off the capacitor you start by using the following expression for the charge in the capacitor:

[tex]q=Qsin(\omega t)[/tex]

next, you calculate the current I by using the derivative of q:

[tex]I=\frac{dq}{dt}=Q\omega cos(\omega t)\\\\for \ t= 0:\\\\I=Q\omega\\\\Q=\frac{I}{\omega}\\\\\omega=\frac{1}{\sqrt{LC}}\\\\Q=I\sqrt{LC}[/tex] ( 1 )

L: inductance = 4.24*10^{-3}H

C: capacitance = 3.02*10^{-6}F

I: current = 2.38 A

you replace the values of the parameters in (1):

[tex]Q=(2.38A)(\sqrt{(4.24*10^{-3}H)(3.02*10^{-6}F)})=2.69*10^{-4}C=0.269mC[/tex]

b) to find the time t you use the following formula for the energy of the capacitor:

[tex]u_c=\frac{q^2}{2C}=\frac{Q^2sin^2(\omega t)}{2C}[/tex]

the maximum storage energy in the capacitor is obtained by derivating the energy:

[tex]\frac{du_c}{dt}=\frac{2\omega Q^2sin(\omega t)cos(\omega t)}{2C}=0\\\\\frac{du_c}{dt}=\frac{\omega Q^2 sin(2\omega t)}{2C}=0\\\\sin(2\omega t)=0\\\\2\omega t= 2\pi\\\\t=\frac{\pi}{\omega}=\pi\sqrt{LC}=\pi\sqrt{(4.24*10^{-3}H)(3.02*10^{-6}F)}=3.55*10^{-4}s=0.355\ ms[/tex]

hence, the time is 0.355 ms

c) The greatest rate is obtained for duc/dt evaluated in t=0.355 ms:

[tex]\frac{du_c}{dt}=\frac{2Q^2sin(2\frac{t}{\sqrt{LC}})}{\sqrt{LC}}[/tex]

[tex]\frac{du_c}{dt}=\frac{(2.69*10^{-4}C)^2sin(2\frac{3.55*10^{-4}s}{\sqrt{(4.24*10^{-3}H)(3.02*10^{-6}C)}})}{2(3.02*10^{-6}C)\sqrt{(4.24*10^{-3}H)(3.02*10^{-6}C)}}=-1.39W[/tex]

Complete Question

 The complete question is shown on the first uploaded image  

Answer:

The total pressure is  [tex]P_T = 10.79*10^{5} N/m^2[/tex]

The temperature at the bottom is [tex]T_b = 284.2 \ K[/tex]

Explanation:

From the question we are told that

    The length of the glass tube is  [tex]L = 1.50 \ m[/tex]

      The length of water  rise at the bottom of the lake  [tex]d = 1.33 \ m[/tex]

     The depth of the lake is  [tex]h = 100 \ m[/tex]

     The air temperature is [tex]T_a = 27 ^oC = 27 +273 = 300 \ K[/tex]

      The atmospheric pressure is  [tex]P_a = 1.01 *10^{5} N/m[/tex]

      The density of water is [tex]\rho = 998 \ kg/m^3[/tex]

The total pressure at the bottom of the lake is mathematically represented as

                 [tex]P_T = P_a + \rho g h[/tex]

substituting values

               [tex]P_T = 1.01*10^{5} + 998 * 9.8 * 100[/tex]

               [tex]P_T = 10.79*10^{5} N/m^2[/tex]

According to ideal gas law

         At the surface the glass tube not covered by water at surface

             [tex]P_a V_a = nRT_a[/tex]

Where is the volume of

             [tex]P_a *A * L = nRT_a[/tex]

 At the bottom of the lake  

           [tex]P_T V_b = nRT_b[/tex]

Where [tex]V_b[/tex] is the volume of the glass tube not covered by water at bottom

          and  [tex]T_b[/tex] i the temperature at the bottom

  So the ratio between the temperature  at the surface to the temperature at the bottom is mathematically represented as

             [tex]\frac{T_b}{T_a} = \frac{d * P_T}{P_a * h}[/tex]

substituting values

           [tex]\frac{T_b}{27} = \frac{0.133 * 10.79 *10^5}{1.01 *10^{5} * 1.5}[/tex]

   =>     [tex]T_b = 284.2 \ K[/tex]

Answer:

1*10^6 N/m^2

Explanation:

Coefficient of Linear Expansion for Concrete = α = 1.2 x 10^-5 (°C)^-1

Change in temperature = ΔT

ΔT= T2 - T1

ΔT = 33 - 21

ΔT = 12°C

ΔL = α * L(i) * ΔT

ΔL = (1.2 x 10^-5 (°C)^-1) * L(i) * (12°C)

ΔL = 1.44 x 10^-4

Stress = F / A

Strain = ΔL / L

Strain = (1.44*10^-4) * (L) / L

Strain = 1.44*10^-4

Y = Stress / Strain

Stress = Y * Strain

Stress = (7.00*10^9 N/m^2) * (1.44*10^-4)

Stress = 1*10^6 N/m^2

Thus, the stress in the cement on a hot day of 33° is 1*10^6 N/m^2

Answer:

the color is green

the observation is that there is a change of visible color

Explanation:

A) wavelength of visible light that is most strongly reflected from a point on a soap

refraction n = 1.33

wall thickness (t) = 290 nm

2nt = (2m +1 ) ∝/2 -----equation 1

note when m = 0

therefore ∝ =  4nt/ 1 = 4 * 1.33 * 290 = 1542.8nm we will discard this

when m = 1

equation 1 becomes

∝ = 4nt/3 =( 4 * 1.33 * 290) /  3 = 1542.8 / 3 = 514.27 ( wavelength )

the color is green

B) the wavelength when the wall thickness is 340 nm

∝ = 4nt / 2m +1

where m = 1

∝ = (4 * 1.33 * 340 ) / 3  = 1808.8 / 3 = 602.93 nm  ( orange color )

the observation is that there is a change of visible color

Final answer:

The wavelength of visible light most strongly reflected for a soap bubble wall thickness of 290 nm and index of refraction of 1.33 is 770 nm, corresponding to the red color. For a thickness of 340 nm, the wavelength is 904 nm, which falls outside the visible spectrum, in the infrared range. As the thickness increases, the reflected wavelength shifts toward longer wavelengths.

Explanation:

The phenomenon described in the question is known as thin film interference, which is a physical effect that occurs when light waves reflected off the top and bottom surfaces of a thin film interfere with each other. To find the wavelength (λ) of visible light that is most strongly reflected, we use the formula for constructive interference in thin films:

2nt = mλ,

where n is the index of refraction of the film, t is the thickness of the film, and m is the order of the fringe (which is an integer).

For part (a), we have a soap bubble thickness of 290 nm and an index of refraction n = 1.33. Assuming the light is perpendicular to the surface (m = 1 for the first order of constructive interference), we calculate the wavelength using the given formula as follows:

λ = 2nt/m = 2 * 1.33 * 290 nm / 1 = 770 nm.

The wavelength of 770 nm corresponds to red light in the visible spectrum.

For part (b), with a wall thickness of 340 nm, we calculate the wavelength in a similar fashion:

λ = 2 * 1.33 * 340 nm / 1 = 904 nm.

However, a wavelength of 904 nm falls outside the visible spectrum and cannot be seen as a color. It is in the infrared range.

Comparing answers from (a) and (b), we observe that as the thickness of the soap bubble increases, the wavelength of light most strongly reflected shifts towards the longer wavelengths, moving out of the visible range into the infrared.

Complete Question

If a sound with frequency fs is produced by a source traveling along a line with speed vs and an observer is traveling with speed vo along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is

f_o = [(c+v_o)/(c-v_s)] f_s

where c is the speed of sound, about 332 m/s. (This is the Doppler effect). Suppose that, at a particular moment, you are in a train traveling at 34 m/s and accelerating at 1.2 m/s^2. A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.4 m/s^2, and sounds its whistle, which has a frequency of 460Hz. At that instant, what is the perceived frequency that you hear and how fast is it changing?

Answer:

The frequency the person hears is  [tex]f_o = 557 Hz[/tex]

The speed at which it is changing is [tex]\frac{df_o}{dt} = 4.655 Hz/s[/tex]

Explanation:

Form the question we are told that

       The frequency of the sound produced by source is  [tex]f_s[/tex]

        The speed of the source is  [tex]v_s[/tex]

         The speed of the observer

         The frequency of sound heard by observer  [tex]f_o =[ \frac{c + v_o }{c - v_s} ] * f_s[/tex]

          The speed of sound is  c  with value [tex]c = 332 m/s[/tex]

Looking the question we can deduce that the person in the first train is the observer so the

            [tex]v_o = 34 m/s[/tex]

and the acceleration is  [tex]\frac{dv_o}{dt} = 1.2 m/s^2[/tex]

The train the travelling in the opposite direction the blew the whistle

is the source

    So   [tex]v_s = 40 m/s[/tex]

    and  [tex]f_s = 460 Hz[/tex]

and the acceleration is  [tex]\frac{dv_s}{dt} = 1.4 m/s^2[/tex]  

   We are told that

           [tex]f_o =[ \frac{c + v_o }{c - v_s} ] * f_s[/tex]

Substituting values we have that  

          [tex]f_o =[ \frac{332 + 34 }{332 - v40} ] * 460[/tex]

        [tex]f_o = 557 Hz[/tex]

  Differentiating [tex]f_o[/tex]  using chain rule we have that

         [tex]\frac{d f_o}{dt} = \frac{df_o}{dt } * \frac{dv_o}{dt} + \frac{d f_o}{dv_s} * \frac{dv_s}{dt}[/tex]    

Now  

           [tex]\frac{df_o}{dt } = \frac{f_s}{c- v_s}[/tex]

           [tex]\frac{df_o}{dv_s} = \frac{c+ v_o}{c-v_s} f_s[/tex]

Substituting this into the equation

         [tex]\frac{df_o}{dt} = \frac{f_s}{c-v_s} * \frac{d v_o}{dt} + \frac{c+v_o}{(c-v_s)^2} f_s * \frac{dv_s}{dt}[/tex]

Now substituting values

         [tex]\frac{df_o}{dt} = \frac{460}{332 - 40} * (1.2) + \frac{332+ 34}{(332- 40)^2} 460 * 1.4[/tex]

          [tex]\frac{df_o}{dt} = 4.655 Hz/s[/tex]

The speed of the train can be calculated using the formula for the Doppler effect. Using the given frequencies and the speed of sound in air, the student can calculate the speed of the train to be approximately 8.7 m/s.

To calculate the speed of the train, we can use the formula for the Doppler effect. The formula is given by:

Δf/f = v/c

Where Δf is the change in frequency, f is the frequency observed when the train is at rest, v is the speed of the train, and c is the speed of sound in air.

Using the given frequencies of 491 Hz and 472 Hz, and the speed of sound in air of 343 m/s, we can calculate the speed of the train:

v = (Δf/f) * c = (491 - 472) / 491 * 343 = 8.7 m/s

Therefore, the student finds that the speed of the train is approximately 8.7 m/s.

https://brainly.com/question/15318474

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Given the observed frequencies of 491 Hz when approaching and 472 Hz when receding, the calculated speed of the train is approximately 6.66 m/s. This calculation assumes the speed of sound in air is 343 m/s.

The question involves using the Doppler Effect to calculate the speed of the train. The Doppler Effect formula for a source moving towards a stationary observer is:

[tex]f'_{approach} = f \times (v + v_o)/(v - v_s)[/tex]

and when the source is moving away:

[tex]f'_{recede} = f \times (v - v_o)/(v + v_s)[/tex]

where:

Given:

First, solve for the source frequency (f) using both equations.

For the approaching train:

[tex]491 = f \times (343) / (343 - v_s)[/tex]

For the receding train:

[tex]472 = f \times (343) / (343 + v_s)[/tex]

Divide the two frequency equations to eliminate f:

(491 / 472) = (343 + [tex]v_s[/tex]) / (343 - [tex]v_s[/tex])

Cross-multiplying and solving for [tex]v_s[/tex]:

491 × (343 - [tex]v_s[/tex]) = 472 × (343 + [tex]v_s[/tex])

491 × 343 - 491 × [tex]v_s[/tex] = 472 × 343 + 472 × [tex]v_s[/tex]

168313 - 491 × [tex]v_s[/tex] = 161896 + 472 × [tex]v_s[/tex]

168313 - 161896 = 491 × [tex]v_s[/tex] + 472 × [tex]v_s[/tex]

6417 = 963 × [tex]v_s[/tex]

[tex]v_s[/tex] = 6417 / 963

[tex]v_s[/tex] ≈ 6.66 m/s

Therefore, the student calculates the speed of the train to be approximately 6.66 m/s.

Answer:

A) i) at V_s = 5.6V

N_s = 6.53 turns

ii) at V_s = 12V, N_s = 14 turns

iii) at V_s = 480V, N_s = 560 turns

B) i) at V_s = 5.6V

I_s = 214.29A

ii) at V_s = 12V, I_s = 100A

iii) at V_s = 480V, N_s = 2.5A

Explanation:

A) The formula for calculating number of turns in the secondary coil is gotten from;

V_p/V_s = N_p/N_s

Making N_s the subject we have;

N_s =( V_s*N_p)/V_p

Where;

V_p is input voltage

V_s is output voltage

N_p is number of turns in primary coil

N_s is number of turns in secondary coil

We are given V_p = 240V and N_p = 280 turns

Thus;

i) at V_s = 5.6V,

N_s = (5.6*280)/240

N_s = 6.53 turns

ii) at V_s = 12V,

N_s = (12*280)/240

N_s = 14 turns

iii) at V_s = 480V,

N_s = (480*280)/240

N_s = 560 turns

B) The formula for calculating maximum output current in the secondary coil is gotten from;

I_s = (V_p*I_p)/V_s

Where;

I_s is maximum output current

V_p is input voltage

I_p is maximum input current

V_s is output voltage

We are given I_p = 5A

Thus;

i) at V_s = 5.6V,

I_s = (240*5)/5.6

I_s = 214.29 A

ii) at V_s = 12V

I_s = (240*5)/12

I_s = 100 A

iii) at V_s = 480V

I_s = (240*5)/480

I_s = 2.5 A

Final answer:

The number of turns in the secondary coil of the transformer to produce outputs of 5.60, 12.0, and 480 V are approximately 6.5, 14, and 560 turns respectively. The associated maximum output currents for each voltage, assuming 100% efficiency, are approximately 214.29 A for 5.60 V, 100.00 A for 12.0 V, and 2.50 A for 480 V.

Explanation:

The question involves a multipurpose transformer where the primary coil receives an input voltage of 240 V and has 280 turns, and we need to calculate the number of turns in the secondary to produce various output voltages of 5.60, 12.0, and 480 V. Secondly, we have to determine the maximum output currents for a maximum input current of 5.00 A using the transformer's power conservation principle.

(a) To find the number of turns in each part of the secondary coil, we can use the transformer equation:

VP / VS = NP / NS

For each output voltage, we can solve for NS (number of turns in the secondary):

For 12.0 V output: NS = (12.0 V / 240 V) × 280 turns = 14 turns

For 480 V output: NS = (480 V / 240 V) × 280 turns = 560 turns

(b) Power conservation in transformers (assuming 100% efficiency) indicates that PP = PS (power in primary equals power in secondary), so:

For 480 V: IS = (240 V × 5.00 A) / 480 V = 2.50 A

The horizontal distance (d) a block travels after being released from a slide is limited by the initial velocity from the slide and the time of flight from the table. Mathematical considerations of kinetic energy and projectile motion demonstrate why the distances h1 and h2 are crucial factors. On the Moon, the block would travel further due to reduced gravity.

The horizontal distance (d) that a block travels after sliding down a slide and falling off a table is dependent on both the vertical height dropped and the velocity with which it leaves the table. If we make height h1 (the slide) very small, the velocity of the block at the bottom of the slide and consequently at the end of the table would be small because it would have converted a smaller amount of potential energy into kinetic energy. This would result in a small horizontal distance (d) even though height h2 (the table) is large. Conversely, making height h2 (the table) very small would mean that the block doesn't have much height to fall from, which limits the total time it has to move horizontally, again resulting in a small d.

In analyzing both scenarios mathematically, the relationship between the horizontal distance and the heights would involve equations of motion and energy conservation. The step that supports reasoning in part (a)i would involve the equation for kinetic energy at the end of the slide (KE = 1/2 m[tex]v^2[/tex]), which is maximized when h1 is large. Similarly, the step supporting part (a)ii is Newton's equations of motion for projectile motion (particularly, time of flight = sqrt(2h2/g)), where increasing h2 increases the time the block spends in air and thus d.

When repeating the experiment on the Moon, the new landing distance d will be greater than the landing distance when performed on Earth. This is because the acceleration due to gravity on the Moon is less than on Earth, which increases the time the block spends in the air.

Answer:

The magnetic field required required for the beam not to be deflected  is [tex]B = 0.0036T[/tex]

Explanation:

From the question we are told that

    The charge on the particle is [tex]q = +2e[/tex]

    The mass of the particle is  [tex]m = 6.64 *10^{-27} kg[/tex]

    The potential difference is [tex]V_a = 1.8 kV = 1.8 *10^{3} V[/tex]

    The potential difference between the two parallel plate is  [tex]V_b = 120 V[/tex]

    The separation between the plate is  [tex]d = 8 mm = \frac{8}{1000} = 8*10^{-3}m[/tex]

The Kinetic energy experienced by the beam before entering the region of the parallel plate is equivalent to the potential energy of the beam  after the region having a potential difference of 1.8kV

               [tex]KE_b = PE_b[/tex]

Generelly

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

And      [tex]PE_b = q V_a[/tex]

 Equating this two formulas

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

making v the subject

           [tex]v = \sqrt{\frac{q V_a}{2 m} }[/tex]

Substituting value  

           [tex]v = \sqrt{\frac{ 2* 1.602 *10^{-19} * 1.8 *10^{3}}{2 * 6.64 *10^{-27}} }[/tex]

           [tex]v = 41.65*10^4 m/s[/tex]

Generally the electric field between the plates is mathematically represented as

                 [tex]E = \frac{V_b}{d}[/tex]  

Substituting value  

                 [tex]E = \frac{120}{8*10^{-3}}[/tex]              

                [tex]E = 15 *10^3 NC^{-1}[/tex]

the magnetic field  is mathematically evaluate    

                     [tex]B = \frac{E}{v}[/tex]

                   [tex]B = \frac{15 *10^{3}}{41.65 *10^4}[/tex]

                    [tex]B = 0.0036T[/tex]

Answer: A BIRD BRAINLIEST PLEASE

Explanation: If a plane was traveling at the same velocity as a bird, which would have the most kinetic energy (assuming the plane has more mass)? ... So if a 747 weighs 750,000 times as much as a bird, at the same velocity it will have 750,000 times the kinetic energy.

The two objects have the same speed, thus the plane will have more kinetic energy compared to the bird.

Kinetic energy is the energy acquired by a body during its motion. This kinetic energy depends on the speed and mass of the object.

The formula for estimating kinetic energy is given as;

K.E = ¹/₂mv²

where;

The mass of the plane should be greater than the mass of the bird. Since the two objects have the same speed, we can conclude that the plane will have more kinetic energy compared to the bird.

Learn more here:https://brainly.com/question/23503524

Answer:

Explanation:

On both sides of the film , the mediums have lower refractive index.

for interfering pattern from above , for constructive interference of reflected wave from both sides of the film , the condition is

2μt = ( 2n +1 ) λ / 2

μ is refractive index of film ,t is thickness of film λ is wavelength of light

n is order of fringe

for minimum thickness

n = 0

2μt =  λ / 2

t =  λ / 4μ

= 670 / 1.75 x 4

= 95.71 nm .