Using a density of air to be 1.21kg/m3, the diameter of the bottom part of the filter as 0.15m (assume circular cross-section), and the power fit of your Trendline equation,calculate the drag coefficient. Solve for it first (see video) and then plug in the values.

Answers

Answer 1

Answer:

The  drag coefficient is  [tex]D_z = 1.30512[/tex]  

Explanation:

From the question we are told that

     The density of air is  [tex]\rho_a = 1.21 \ kg/m^3[/tex]

     The diameter of bottom part is  [tex]d = 0.15 \ m[/tex]

The  power trend-line  equation is mathematically represented as

      [tex]F_{\alpha } = 0.9226 * v^{0.5737}[/tex]

let assume that the velocity is  20 m/s

Then

      [tex]F_{\alpha } = 0.9226 * 20^{0.5737}[/tex]

       [tex]F_{\alpha } = 5.1453 \ N[/tex]

The drag coefficient is mathematically represented as

      [tex]D_z = \frac{2 F_{\alpha } }{A \rho v^2 }[/tex]

Where  

     [tex]F_{\alpha }[/tex] is the drag force

      [tex]\rho[/tex] is the density of the fluid

       [tex]v[/tex] is the flow velocity

       A is the area which mathematically evaluated as

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

substituting values

     [tex]A = 3.142 * \frac{(0.15)^2}{4}[/tex]

     [tex]A = 0.0176 \ m^2[/tex]

Then

   [tex]D_z = \frac{2 * 5.1453 }{0.0176 * 1.12 * 20^2 }[/tex]

   [tex]D_z = 1.30512[/tex]  


Related Questions

Two parallel plates having charges of equal magnitude but opposite sign are separated by 21.0 cm. Each plate has a surface charge density of 39.0 nC/m2. A proton is released from rest at the positive plate. (a) Determine the magnitude of the electric field between the plates from the charge density.

Answers

Answer:

E = 3.45*10^-19 N/C

Explanation:

a) The electric field between two parallel plates id given by the following formula:

[tex]E=\frac{\sigma}{\epsilon_o}[/tex]           (1)

where:

σ: surface charge density of the plates = 39.0nC/m^2

εo: dielectric permittivity of vacuum = 8.85*10^-12 C/Nm^2

You replace these values in the equation (1):

[tex]E=\frac{39.0*10^{-9}C/m^2}{8.85*10^{-12}C^2/Nm^2}\\\\E=3.45*10^{-19}\frac{N}{C}[/tex]

The electric field in between the parallel plates is 3.45*10^-19 N/C

In a Venn diagram, the separate circles contain characteristics unique to each compared and the intersection contains characteristics that are common to both items being compared. This Venn diagram compares the inner and outer planets. What belongs in the center section?
a. -Revolve around the Sun
-Rotate on an axis
-Generally have rings
b. -Revolve around the Sun
-Rotate on axis
-Generally have moons
c. -Rotate around the Sun
-Revolve on an axis
-Generally have moons
d. -Rotate around the Sun
-Revolve on an axis
-Generally have rings

Answers

Answer:

B. revolve around the sun

   rotate on an axis

   generally have moons

Explanation:

edge 2021

A 0.25 kg steel ball is tied to the end of a string and then whirled in a vertical circle at a constant speed v. The length of the string is 0.62 m, and the tension in the string when the ball is at the top of the circle is 4.0 N. What is v

Answers

Answer:

Explanation:

Let the tension in the string be T . At the top of the circle , total force acting on them = T + mg . This will provide centripetal force

T + mg = m v² / r

4 + .25 x 9.8 = .25 x v² / .62

6.45 = .25 v² / .62

v² = 16

v = 4 m /s .

In a circuit, a 100.-ohm resistor and a 200.-ohm resistor are connected in parallel to a 10.0-volt battery.
Calculate the equivalent resistance of the circuit. [Show all work, including the equation and substitution with units.]

Answers

Answer:

Explanation:

                                                                           

The equivalent resistance of resistor connected parallel in the circuit is [tex]66.66 ohm[/tex]

What is equivalent resistance?

The equivalent resistance is the total resistance measured in a parallel or series circuit. If several resistors are connected together and connected to a battery, the current supplied by the battery depends on the equivalent resistance of the circuit.

What is equivalent resistance in series?

Resistors are in series whenever the current flows through the resistors sequentially. It is given by

[tex]R_{eq} = R_{1} + R_{2} + ....[/tex]

What is equivalent resistance in parallel?

Resistors are in parallel when one end of all the resistors are connected by a continuous wire and the other end of all the resistors are also connected to one another through a continuous wire.

The equivalent resistance is the total resistance measured in a parallel. It is given by

[tex]\frac{1}{R_{eq} } = \frac{1}{R_{1} } + \frac{1}{R_{2} }+ ....[/tex]

Given:

Resistor, [tex]R_{1} = 100 ohm[/tex]

Resistor, [tex]R_{2} = 200 ohm[/tex]

Voltage, [tex]V = 10 Volt[/tex]

Since, resistors are connected in parallel, the equivalent resistor is given by,

[tex]\frac{1}{R_{eq} } = \frac{1}{R_{1} } + \frac{1}{R_{2} }[/tex]

[tex]\frac{1}{R_{eq} } = \frac{1}{100 } + \frac{1}{200 }[/tex]

[tex]R_{eq} = \frac{100*200}{100+200} \\R_{eq} = 66.66 ohm[/tex]

Hence, the equivalent resistor is [tex]66.66 ohm[/tex].

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Calculate the energy released by the electron-capture decay of 5727Co. Consider only the energy of the nuclei (ignore the energy of the surrounding electrons). The following masses are given:
5727Co: 56.936296u
5726Fe: 56.935399u
Express your answer in millions of electron volts (1u=931.5MeV/c2) to three significant figures.
A negligible amount of this energy goes to the resulting 5726Fe atom as kinetic energy. About 90 percent of the time, after the electron-capture process, the 5726Fe nucleus emits two successive gamma-ray photons of energies 0.140MeV and 1.70 102MeV in decaying to its ground state. The electron-capture process itself emits a massless neutrino, which also carries off kinetic energy. What is the energy of the neutrino emitted in this case?
Express your answer in millions of electron volts.

Answers

Answer:

Explanation:

⁵⁷Co₂₇  + e⁻¹  =  ²⁷Fe₂₆

mass defect = 56.936296 + .00055 - 56.935399

= .001447 u

equivalent energy

= 931.5 x .001447 MeV

= 1.3479 MeV .

= 1.35 MeV

energy of gamma ray photons = .14  + .017

= .157 MeV .

Rest of the energy goes to neutrino .

energy going to neutrino .

= 1.35 - .157

= 1.193 MeV.

6. When a positive charge is released and moves along an electric field line, it moves to a position of A) lower potential and lower potential energy. B) lower potential and higher potential energy. C) higher potential and lower potential energy. D) higher potential and higher potential energy.

Answers

Answer:

Since you would have to do work on the charge to bring it back to its original position, the charge moves to a position of lower potential and lower potential energy.

The positive charge is released from a point such that it will move along an uniform electric field to the position of lower potential and lower potential energy. Therefore, option (A) is correct,

When a positive charge (say +Q) is released from a point (say A) and moves in an uniform electric field to reach the point (say B), then some work is done on the charge. This work done is given as,

[tex]W=+Q(V_{A}-V_{B})[/tex]

Here, [tex]V_{A}[/tex] and [tex]V_{B}[/tex] are the potential differences between the points A and B respectively..

This means the charge is moving from higher potential to lower potential. And since it is moving along the uniform electric field, therefore the electric potential energy of charged system is decreased.

Thus, we conclude that on releasing the positive charge from a point, it starts moving along the electric field towards the direction of lower electric potential and lower electric potential energy. Hence, option (A) is correct.

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A train starts from rest and accelerates uniformly, until it has traveled 5.6 km and acquired a velocity of 42 m/s. The train then moves at a constant velocity of 42 m/s for 420 s. The train then slows down uniformly at 0.065 m/s^2, until it is brought to a halt. What is the acceleration during the first 5.6 km of travel?

Answers

Answer:

0.1575 m/s^2

Explanation:

Solution:-

- Acceleration ( a ) is expressed as the rate of change of velocity ( v ).

- We are given that the trains starts from rest i.e the initial velocity ( vo ) is equal to 0. Then the train travels from reference point ( so = 0 ) to ( sf = 5.6 km ) from the reference.

- During the travel the train accelerated uniformly to a speed of ( vf =42 m/s ).

- We will employ the use of 3rd kinematic equation of motion valid for constant acceleration ( a ) as follows:

                         [tex]v_f^2 = v_i^2 + 2*a*( s_f - s_o )[/tex]

- We will plug in the given parameters in the equation of motion given above:

                         [tex]42^2 = 0^2 + 2*a* ( 5600 - 0 )\\\\1764 = 11,200*a\\\\a = \frac{1,764}{11,200} \\\\a = 0.1575 \frac{m}{s^2}[/tex]

Answer: the acceleration during the first 5.6 km of travel is 0.1575 m / s^2

If a light is moved twice (2x) as far from a surface, the area the light covers is ___ as big.

- 2x
- 1/4
- 1/2
- 4x

Answers

Answer:

The correct option is;

- 4x

Explanation:

From the inverse square law, as the distance from the source of a physical quantity increases, the intensity of the source is spread over an area proportional to the square of the distance of the object from the source

The inverse square law can be presented as follows;

[tex]I = \dfrac{S}{4\times \pi \times r^2 }[/tex]

As the distance, r, increases, the surface it covers also increases by the power of 2

Therefore, where the distance increases from r to 2·r, we have;

When, I, remain constant

[tex]I = \dfrac{4\times S}{4\times \pi \times (2\cdot r)^2 } = I = \dfrac{4\times S}{4\times 4\times \pi \times r^2 } = \dfrac{S}{4\times \pi \times r^2 }[/tex]

The surface increases to 4·S by the inverse square law

Therefore, the correct option is 4 × x.

A block is supported on a compressed spring, which projects the block straight up in the air at velocity VVoj The spring and ledge it sits on then retract. You can win a prize by hitting the block with a ball. When should you throw the ball and in what direction to be sure the ball hits the block?
A. At the instant when the block is at the highest point, directed at the spring.
B. At the instant when the block is at the highest point, directed at the block.
C. At the instant when the block leaves the spring, directed at the spring.
D. At the instant when the block leaves the spring, directed at the block.
E. When the block is back at the spring's original position, directed at that position.

Answers

Answer:

the correct answer is B

Explanation:

We analyze this exercise a little, the block goes into the air and is under the acceleration of gravity. The ball is fired by the hand and is describing a parabolic movement, subjected to the acceleration of gravity.

For the ball to hit the block we must have the distance the ball goes up equal to the distance the block moves, therefore we must shoot the ball at the block at its highest point.

Let's write the kinematic equation for the two bodies

The block. At the highest point of the path

      y = - ½ g t2

The ball, in its vertical movement

     y = vo t - ½ g t2

therefore the correct answer is B

"A trooper is moving due south along the freeway at a speed of 28 m/s. At time t = 0, a red car passes the trooper. The red car moves with constant velocity of 40 m/s southward. At the instant the trooper's car is passed, the trooper begins to speed up at a constant rate of 2.9 m/s2. What is the maximum distance ahead of the trooper that is reached by the red car?"

Answers

Answer:

24.83 m

Explanation:

Applying the equation of motion;

d = vt + 0.5at^2 ......1

Where;

d = distance

v = velocity

t = time

a = acceleration

For the trooper;

v = 28 m/s

a = 2.9 m/s^2

Substituting into equation 1;

d1 = 28t + 0.5(2.9t^2)

d1 = 28t + 1.45t^2

For the red car;

v = 40 m/s

a = 0

Substituting into equation 1

d2 = 40t

The difference in distance is;

d = d2 - d1

d = 40t - (28t + 1.45t^2)

d = 12t - 1.45t^2

The maximum distance is at d(d)/dt = 0

differentiating d;

d' = 12 - 2.9t = 0

2.9t = 12

t = 12/2.9 = 4.137931034482

t = 4.138 s

Substituting t into function d;

d(max) = 12(4.138) - 1.45(4.138^2)

d(max) = 24.8275862 = 24.83 m

the maximum distance ahead of the trooper that is reached by the red car is 24.83 m

The red giant Betelgeuse has a surface temperature of 3000 K and is 600 times the diameter of our sun. (If our sun were that large, we would be inside it!) Assume that it radiates like an ideal blackbody.a) If Betelgeuse were to radiate all of its energy at the peak-intensity wavelength, how many photons per second would it radiate?b) Find the ratio of the power radiated by Betelgeuse to the power radiated by our sun (at 5800 K).

Answers

Answer:

Explanation:

a )

Radius of the sun = .69645 x 10⁹ m .

600 times = 600 x .69645 x 10⁹ m

= 4.1787 x 10¹¹ m .

surface area A = 4π (4.1787 x 10¹¹)²

= 219.317 x 10²²

energy radiated E = σ A Τ⁴

= 5.67 x 10⁻⁸ x 219.317 x 10²² x (3000)⁴

= 100695 x 10²⁶ J

To know the wavelength of photon emitted

[tex]\lambda_mT= b[/tex]

[tex]\lambda_m= \frac{b}{T}[/tex]

= 2.89777 x 10⁻³ / 3000

= 966 nm

= 1275 /966 eV

1.32 x 1.6 x 10⁻¹⁹ J

= 2.112 x 10⁻¹⁹ J

No of photons radiated = 100695 x 10²⁶ / 2.112 x 10⁻¹⁹

= 47677.5 x 10⁴⁵

= .476 x 10⁵⁰ .

b )

energy radiated by our sun per second

E₂ = σ A 5800⁴

energy radiated by Betelgeuse per second

E₁ = σ  x 600²A x  3000⁴

E₁ / E₂  = σ  x 600²A x  3000⁴ / σ A 5800⁴

= 36 X 10⁴ x 3⁴ x 10¹² / 58⁴ x 10⁸

= 25.76 x 10⁸ x 10⁻⁵

= 25760 times .

Which of the following statements is true of a gas?
It has a fixed volume, but not a fixed shape
It has closely packed molecules
It can change into a liquid by adding heat
It takes the shape and size of a container

Answers

Answer:

it takes the shape and size of the container that it is in

Explanation:

Answer:

it takes the shape and size of a container

A swimmer heading directly through a 200m wide river reaches the opposite shore in 6 min 40s. She is washed downstream 480 m. How fast can you swim in calm water?

Answers

Answer :v=480m400s=1.2ms

2002+4802=H2  

The hypotenuse  H=520m  

A quicker way to get the length of the hypotenuse is to recognize that this is a simple 5–12–13 triangle where the sides are multiples of 5, 12, and 13:

5(40) = 200m, 12(40)= 480m, 13(40)= 520m

We know that the swimmer travelled 520 m in 400 seconds, so her average speed was:

VR=520m400sec=   1.3ms

hope i got it right!! xx

Explanation:

An LC circuit has a 6.00 mH inductor. The current has its maximum value of 0.570 A at t =0s. A short time later the capacitor reaches its maximum potential difference of 66.0 V. What is the value of the capacitance?

Answers

Answer:

C = 44.75 x 10⁻⁸ F

Explanation:

Assuming no loss of energy between capacitor and inductor

energy in inductor initially = 1/2 Li₀² where L is inductance and i₀ is peak current .

= .5 x 6 x 10⁻³ x .57²

= .97 x 10⁻³ J .

This energy is transferred to capacitor .

energy of capacitor = 1/2 CV²

= .5 x C x 66²

= 2178 C

2178C = .97 x 10⁻³

C = 44.75 x 10⁻⁸ F .

The magnetic energy stored in the inductor is transformed into electrical energy stored in the capacitor. The value of capacitance for the given circuit is 44.75 x 10⁻⁸ F

Finding the capacitance:

According to the law of conservation of energy, the magnetic energy stored in the inductor will be gradually lost and this energy will be stored in the capacitor as electrical energy.

Initially, the energy in the inductor is:

E = 1/2 Li₀²

where L is inductance

and i₀ is peak current.

E = 0.5 × 6 × 10⁻³ × (0.57)²

E = 0.97 × 10⁻³J

This energy is transformed into electrical energy stored in the capacitor.

So the capacitor energy is:

E = 1/2 CV²

where C is the capacitance

E = 0.5 × C × 66²

E = 2178 C

0.97 x 10⁻³ = 2178 C

C = 44.75 x 10⁻⁸ F

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A ship can float on water as long as it weighs less than water.
O A. True
O B. False

Answers

Answer:

It's true

Explanation:

Because the ship is mafe up of aluminium, which is a light metal.

Answer:

False

Explanation:

Took The Quiz

Can someone help me with this question

Answers

Answer:

hypothesis , hope it helps

Explanation:

Answer:

Inference

Explanation:

Inference is something you predict after testing that's a result after an hypothesis has been made. Hypothesis is an intelligent guess based on some observed phenomena which can be subjected to further testing.

One car travels 40. meters due east in 5.0 seconds, and a second car travels 64 meters due west in 8.0 seconds. During their periods of travel, the cars definitely had the same

Answers

Answer:

They had the same speed.

Explanation:

It won't be velocity, because velocity is a vector quantity. Speed is scalar.

Velocity is the rate of change of displacement. During their periods of travel, the cars definitely had the same velocity.

What is Velocity?

Velocity is the directional speed of a moving object as an indicator of its rate of change in location as perceived from a certain frame of reference and measured by a specific time standard.

Given that the first car travels 40 meters due east in 5 seconds. Therefore, we can write,

Distance = 40 meters

Time = 5 seconds

Velocity = Distance / Time = 40 meter/ 5 sec = 40 m/sec

Also, given that the second car travels 64 meters due west in 8 seconds. Therefore, we can write,

Distance = 64 meters

Time = 8 seconds

Velocity = Distance / Time = 64 meter/ 8 sec = 8 m/sec

Hence, During their periods of travel, the cars definitely had the same velocity.

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The self-referencing effect refers to ________.

Answers

The self-reference effect is the tendency an individual to have better memory for information that relates to oneself than information that is not personally relevant.

You are moving a desk that has a mass of 36 kg; its acceleration is 0.5 m / s 2. What is the force being applied

Answers

Answer:

18 N

Explanation:

Force can be found using the following formula.

f= m*a

where m is the mass and a is the acceleration.

We know the desk has a mass of 36 kilograms. We also know that its acceleration is 0.5 m/s^2.

m= 36 kg

a= 0.5 m/s^2

Substitute these values into the formula.

f= 36 kg * 0.5 m/s^2

Multiply 36 and 0.5

f=18 kg m/s^2

1 kg m/s^2 is equivalent to 1 Newton, or N.

f= 18 Newtons

The force being applied is 18 kg m/s^2, Newtons, or N

Three identical 6.0-kg cubes are placed on a horizontal frictionless surface in contact with one another. The cubes are lined up from left to right and a force is applied to the left side of the left cube causing all three cubes to accelerate to the right at 2.0 m/s2. What is the magnitude of the force exerted on the middle cube by the left cube in this case

Answers

Answer:

24 Newtons

Explanation:

The force exerted in the middle cube needs to be enough to move the middle cube and the right cube with an acceleration of 2 m/s2.

The mass of those two cubes combined is 6 + 6 = 12 kg

So, using the following equation, we can find the force:

Force = mass * acceleration

Force = 12 * 2

Force = 24 Newtons

A solid sphere has a temperature of 556 K. The sphere is melted down and recast into a cube that has the same emissivity and emits the same radiant power as the sphere. What is the cube's temperature in kelvins

Answers

Answer:

Cube temperature = 526.83 K

Explanation:

Volume of the cube and sphere will be the same.

Now, volume of cube = a³

And ,volume of sphere = (4/3)πr³

Thus;

a³ = (4/3)πr³

a³ = 4.1187r³

Taking cube root of both sides gives;

a = 1.6119r

Formula for surface area of sphere is;

As = 4πr²

Also,formula for surface area of cube is; Ac = 6a²

Thus, since a = 1.6119r,

Then, Ac = 6(1.6119r)²

Ac = 15.5893r²

The formula for radiant power is;

Q' = eσT⁴A

Where;

e is emissivity

σ is Stefan boltzman constant = 5.67 x 10^(-8) W/m²k

T is temperate in kelvin

A is Area

So, for the cube;

(Qc)' = eσ(Tc)⁴(Ac)

For the sphere;

(Qs)' = eσ(Ts)⁴(As)

We are told (Qc)' = (Qs)'

Thus;

eσ(Tc)⁴(Ac) = eσ(Ts)⁴(As)

eσ will cancel out to give;

(Tc)⁴(Ac) = (Ts)⁴(As)

Since we want to find the cube's temperature Tc,

(Tc)⁴ = [(Ts)⁴(As)]/Ac

Plugging in relevant figures, we have;

(Tc)⁴ = [556⁴ × 4πr²]/15.5893r²

r² will cancel out to give;

(Tc)⁴ = [556⁴ × 4π]/15.5893

Tc = ∜([556⁴ × 4π]/15.5893)

Tc = 526.83 K

A student throws a set of keys vertically upward to his fraternity brother, who is in a window 3.60 m above. The brother's outstretched hand catches the keys 1.60 s later. (Take upward as the positive direction. Indicate the direction with the sign of your answer.)With what initial velocity were the keys thrown?

Answers

Answer:

[tex]v_{i}=10.10 m/s[/tex]

Explanation:

The equation of the position is:

[tex]y=y_{i}+v_{i}t-0.5gt^{2}[/tex]

Where:

v(i) is the initial velocity

The initial position y(i) will be zero and the final position y = 3.60 m.

So, we just need to solve this equation for v(i).

[tex]v_{i}=\frac{y+0.5gt^{2}}{t}[/tex]

[tex]v_{i}=\frac{3.6+0.5*9.81*1.6^{2}}{1.6}[/tex]

[tex]v_{i}=10.10 m/s[/tex]

Therefore, the initial velocity is 10.10 m/s upwards.

I hope it helps you!

You have a suction cup that creates a circular region of low pressure with a 30 mm diameter. It holds the pressure to 85 % of atmospheric pressure. What "holding force" does the suction cup generate in N

Answers

Answer:

Force = 60.08 N

Explanation:

Given that

Diameter d = 30 mm  

Holding pressure = 85 %  of Atmospherics pressure

Solution

As we know that  here 1 atm = 10⁵ N/m²

and pressure is known as force per unit area

pressure = [tex]\frac{F}{A}[/tex]   ................1

put here value and we will get

F = [tex]0.85\times 10^5\times \frac{\pi}{4}\times 0.03^2\ N[/tex]

solve it we get

Force = 60.08 N

Convert from standard form to scientific notation:
0.00000013


A)1.3 x 10-7
B)13 x 108
C)1.3 x 107
D)13 x 10-8

Answers

The answer is
A) 1.3 x 10-7

What caused the disappearance of land bridges?
A. Volcanic outgassing
B. Shrinking of the polar ice caps
C. Beginning of an ice age
D. A mass extinction​

Answers

Answer: B

Explanation:

I would say the shrinking of the polar ice caps because in order for ice caps to shrink, they would have to obviously melt. This will cause the sea level and total volume of sea water to rise and cover up the land bridges

Answer:B :)

Explanation:

A mass m at the end of a spring vibrates with a frequency of 0.72 Hz . When an additional 700 g mass is added to m, the frequency is 0.64 Hz . Part A What is the value of m? Express your answer using two significant figures.

Answers

Answer:

The value of m is 2635.294 grams.

Explanation:

Let suppose that mass-spring system has a simple harmonic motion, to this respect the formula for frequency is:

[tex]f = \frac{\omega}{2\pi}[/tex]

Where [tex]\omega[/tex] is the angular frequency, measured in radians per second.

For a mass-spring system under simple harmonic motion, the angular frequency is:

[tex]\omega = \sqrt{\frac{k}{m} }[/tex]

Where:

[tex]k[/tex] - Spring constant, measured in newtons per meter.

[tex]m[/tex] - Mass, measured in kilograms.

The following equation is obtained after replacing angular frequency in frequency formula:

[tex]f = \frac{1}{2\pi}\cdot \sqrt{\frac{k}{m} }[/tex]

As this shows, frequency is inversely proportional to the square root of mass. Hence, the following relationship is deducted:

[tex]f_{1}\cdot \sqrt{m_{1}} = f_{2} \cdot \sqrt{m_{2}}[/tex]

If [tex]m_{2} = m_{1} + 700\,g[/tex], [tex]f_{1} = 0.72\,hz[/tex] and [tex]f_{2} = 0.64\,hz[/tex], the resulting expression is simplified and then initial mass is found after clearing it:

[tex]f_{1} \cdot \sqrt{m_{1}} = f_{2} \cdot \sqrt{m_{1}+700\,g}[/tex]

[tex]f_{1}^{2} \cdot m_{1} = f_{2}^{2}\cdot (m_{1} + 700\,g)[/tex]

[tex]\left(\frac{f_{1}}{f_{2}} \right)^{2}\cdot m_{1} = m_{1} + 700\,g[/tex]

[tex]\left[\left(\frac{f_{1}}{f_{2}}\right)^{2} - 1\right]\cdot m_{1} = 700\,g[/tex]

[tex]m_{1} = \frac{700\,g}{\left(\frac{f_{1}}{f_{2}} \right)^{2}-1}[/tex]

[tex]m_{1} = \frac{700\,g}{\left(\frac{0.72\,hz}{0.64\,hz} \right)^{2}-1}[/tex]

[tex]m_{1} = 2635.294\,g[/tex]

The value of m is 2635.294 grams.

When you "crack" a knuckle, you suddenly widen the knuckle cavity, allowing more volume for the synovial fluid inside it and causing a gas bubble suddenly to appear in the fluid. The sudden production of the bubble, called "cavitation", produces a sound pulse---the cracking sound. Assume that the sound is transmitted uniformly in all directions and that it fully passes from the knuckle interior to the outside, at a distance of 0.29 m from your ear. If the pulse has a sound level of 61 dB at your ear, what is the rate at which energy is produced by the cavitation

Answers

Answer:If a wave y(x, t) = (6.0 mm) sin(kx + (600 rad/s)t + Φ) travels along a string, how much time does any given point on the string take to move between displacements y = +2.0 mm and y = -2.0 mm?

Explanation:

Calculate the potential difference across a 25-Ohm. resistor if a 0.3-A current is flowing through it.


V

Answers

Answer:7.5V

Explanation:

Ohm's law, V=IR

so, V=0.3×25

V=7.5V

Answer:

7.5 V

Explanation:

A spherical balloon has a radius of 7.40 m and is filled with helium. Part A How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 990 kg ? Neglect the buoyant force on the cargo volume itself. Assume gases are at 0∘C and 1 atm pressure (rhoair = 1.29 kg/m3, rhohelium = 0.179 kg/m3).

Answers

Answer:

The mass of the cargo is [tex]M = 188.43 \ kg[/tex]

Explanation:

From the question we are told that

    The radius of the spherical balloon is  [tex]r = 7.40 \ m[/tex]

     The mass of the balloon is  [tex]m = 990\ kg[/tex]  

The volume of the spherical balloon is mathematically represented as

     [tex]V = \frac{4}{3} * \pi r^3[/tex]

substituting values

      [tex]V = \frac{4}{3} * 3.142 *(7.40)^3[/tex]

      [tex]V = 1697.6 \ m^3[/tex]

The total mass  the balloon can lift is mathematically represented as

     [tex]m = V (\rho_h - \rho_a)[/tex]

where [tex]\rho_h[/tex] is the density of helium with a  value of

       [tex]\rho_h = 0.179 \ kg /m^3[/tex]

and  [tex]\rho_a[/tex] is the density of air with a value of

        [tex]\rho_ a = 1.29 \ kg / m^3[/tex]

substituting values

          [tex]m = 1697.6 ( 1.29 - 0.179)[/tex]

         [tex]m = 1886.0 \ kg[/tex]

Now the mass of the cargo is mathematically evaluated as

        [tex]M = 1886.0 - 1697.6[/tex]

        [tex]M = 188.43 \ kg[/tex]

       

Water flows at 0.850 m/s from a hot water heater, through a 450-kPa pressure regulator. The pressure in the pipe supplying an upstairs bathtub 3.70m above the heater is 414-kPa. What's the flow speed in this pipe?

Answers

Answer:

The velocity is  [tex]v_2= 0.45 \ m/s[/tex]

Explanation:

From the question we are told that

      The initial speed of the hot water is  [tex]v_1 = 0.85 \ m/s[/tex]

     The pressure from the heater  [tex]P_1 = 450 \ KPa = 450 *10^{3} \ Pa[/tex]

      The height of the hot water before flowing is  [tex]h_1 = 0 \ m[/tex]

      The height of bathtub above the heater is [tex]h_2 = 3.70 \ m[/tex]

       The pressure in the pipe is [tex]P_2 = 414 KPa = 414 *10^{3} \ Pa[/tex]

       The density of water is [tex]\rho = 1000 \ kg/m^3[/tex]

Apply Bernoulli equation

      [tex]P_1 + \rho gh_1 +\frac{1}{2} \rho v_1^2 = \rho g h_2 + \frac{1}{2}\rho v_2 ^2[/tex]

Substituting values

     [tex](450 *10^{3}) + (1000 * 9.8 * 0) + (0.5 * 1000 * 0.85^2) = (1000 * *9.8*3.70) + (0.5*1000*v_2^2 )[/tex]

=>   [tex]v_2^2 = \frac{ (450 *10^{3}) + (1000 * 9.8 *0 ) + (0.5 * 1000 * 0.85^2) -[ (1000 * *9.8*3.70) ]}{0.5*1000}[/tex]

=>   [tex]v_2= \sqrt{ \frac{ (450 *10^{3}) + (1000 * 9.8 * 0) + (0.5 * 1000 * 0.85^2) -[ (1000 * *9.8*3.70) ]}{0.5*1000}}[/tex]

=>    [tex]v_2= 0.45 \ m/s[/tex]

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