A block of mass 10 kg moves from position A to position B shown in the figure above. The speed of the block is 10 m/s at A and 4.0 m/s at B. The work done by friction on the block as it moves from A to B is most nearly
A block of mass 10 kg moves from position A to position B shown in the figure above. The speed of the block is 10 m/s at A and 4.0 m/s at B. The work done by friction on the block as it moves from A to B is most nearly

Answer:

3. converging lens

Explanation:

When the rays of light coming parallel to principle axis after refraction through the lens passes through a point called focus, since it converge all the ray at one point, that is why it is said to be converging lens.

The following statements are true:

- In region I, the magnetic field is into the page and is never zero.

- In region II, the field is into the page and can be zero.

- In region III, it is possible for the field to be zero.

The magnetic field produced by a current-carrying wire follows the right-hand rule. When two parallel wires carrying currents in opposite directions are considered, the magnetic field in the regions around the wires can be determined.

In region I, the magnetic field is between the two wires. According to the right-hand rule, the magnetic field produced by the current in wire I1 is into the page, while the field produced by the current in wire I2 is out of the page. These fields add up to create a net magnetic field into the page. Since the currents are non-zero, the magnetic field in region I is never zero.

In region II, the magnetic field is outside the wires. The fields produced by the currents in wires I1 and I2 are still into the page and out of the page, respectively. However, at certain points between the wires, the magnitudes of these fields can cancel each other out, resulting in a net magnetic field of zero. Therefore, in region II, the field can be zero.

In region III, which is outside both wires, the magnetic field produced by each wire individually decreases with distance. At a certain distance from the wires, the magnetic fields can cancel each other out, resulting in a net magnetic field of zero. Therefore, in region III, it is possible for the magnetic field to be zero.

In summary, in the given scenario of two long, parallel wires carrying currents in opposite directions, the magnetic field is into the page in region I and can be zero in regions II and III. This understanding is based on the right-hand rule and the superposition principle for magnetic fields.

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If a node is observed at a point 0.340 m from one end, in what mode and with what frequency is it vibrating . The correct answer is B. The frequency is the third state at 18.2 Hz.

To determine the mode and frequency of vibration for a node observed at a point 0.340 m from one end, we need to consider the fundamental frequency and the harmonics of the vibrating system. The fundamental frequency is the lowest natural frequency at which the system can vibrate. It corresponds to the first harmonic mode of vibration. The harmonics are integer multiples of the fundamental frequency.

To find the fundamental frequency, we can use the formula:

F₁ = v / (2L)

Where f₁ is the fundamental frequency, v is the velocity of the wave, and L is the length of the vibrating medium.

Since the node is observed at a point 0.340 m from one end, the length of the vibrating medium is twice that distance, which is 0.680 m.

Now, we need to examine the options and determine if any of them match the calculated fundamental frequency or any of its harmonics.

A. The frequency is the fifth state at 30.3 Hz: This option does not match the calculated fundamental frequency or any of its harmonics.

B. The frequency is the third state at 18.2 Hz: This option matches the calculated fundamental frequency, as it is the first harmonic or third state.

C. The frequency is the fifteenth state at 18.2 Hz: This option does not match the calculated fundamental frequency or any of its harmonics.

D. The frequency is the fifth state at 15.2 Hz: This option does not match the calculated fundamental frequency or any of its harmonics.

Therefore, the correct option is B. The frequency is the third state at 18.2 Hz, corresponding to the fundamental frequency or first harmonic of the vibrating system

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Answer:

Explanation:

The autonomic nervous system has two components, the sympathetic nervous system and the parasympathetic nervous system. The sympathetic nervous system functions like a gas pedal in a car. It triggers the fight-or-flight response, providing the body with a burst of energy so that it can respond to perceived dangers.

The minimum angular separation resolvable for a 200-m radio telescope investigating sources emitting a 21-cm wavelength is 0.073°.

The angular resolution of a telescope is determined by the ratio of the wavelength of the radiation being observed to the diameter of the telescope. In this case, the telescope has a diameter of 200 meters, and the wavelength being observed is 21 cm (or 0.21 m).

The formula for calculating the angular resolution is given by θ = λ/D, where θ is the angular resolution, λ is the wavelength, and D is the diameter of the telescope. Substituting the given values into the formula, we get θ = 0.21 m / 200 m = 0.00105 radians.

To convert this to degrees, we multiply by (180/π), which gives us approximately 0.073°. Therefore, the minimum angular separation resolvable for this system is 0.073°.

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True. The Sun radiates at an effective temperature of 5780 K and has a radius of about 696,000 km.

The Sun's effective temperature refers to the temperature at which a black body (an idealized object that absorbs all incident radiation) would emit the same amount of radiation as the Sun. This value is approximately 5780 K, representing the temperature of the Sun's photosphere, the visible surface. Regarding the Sun's radius, it has an estimated average radius of about 696,000 km. This measurement defines the distance from the center of the Sun to its outer edge. The Sun is classified as a G-type main-sequence star, and its size is relatively large compared to other stars, making it an important reference point for understanding stellar characteristics.

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I agree with Student 2: The frequency of the wave will remain the same as it is only dependent on the source, while the wavelength will increase as the wave moves into medium 2.

The equation that relates the velocity (v), frequency (f), and wavelength (λ) of a wave is:

v = f * λ

According to this equation, if the velocity increases in medium 2 compared to medium 1, and the frequency remains constant (as stated by Student 2), then the only way to maintain the equation is for the wavelength to increase in medium 2.

This behavior can be explained by the fact that different media have different properties, such as density and elasticity, which affect the propagation of the wave. When a wave travels from one medium to another, the speed of the wave can change. However, the frequency of the wave is determined by the source and remains constant. Therefore, in order to maintain the equation v = f * λ, the wavelength must adjust to compensate for the change in velocity.

In summary, Student 2 is correct in stating that the frequency of the wave will remain the same, while the wavelength will increase as the wave moves into medium 2 to keep the equation of the wave velocity valid.

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Answer:

Shear stress  is 50.63 Pascal

Explanation:

As we know shear stress = [tex]\frac{\rho V^2 f}{8} \\[/tex]

Rho is the density

V is the velocity

f is the value from Moody's chart

We will know determine Reynolds number  to determine the flow type and then the f value

[tex]R_e = \frac{ \rho*V*D}{u}[/tex]

[tex]R_e = \frac{1000*3*0.0254}{0.001} = 76200[/tex]

This is a turbulent flow and hence the roughness index is [tex]\frac{E}{D} = 0.0157[/tex], From this we get f = 0.045

Now shear stress = [tex]\frac{1000 * 3^2 * 0.045}{8} = 50.63[/tex] Pa

To determine the mass of air in the tank, we need to convert the given parameters and apply the ideal gas law. The mass of air in the tank is approximately 5.04 kg.

To determine the mass of air in the tank, we need to consider the ideal gas law and convert the given parameters to appropriate units.

Given:

Volume of air (V) = 2 m³

Temperature (T) = -93°C

Gauge pressure (P) = 1.4 MPa

Local atmospheric pressure (P_atm) = 1 atm

First, let's convert the temperature from Celsius to Kelvin:

T = -93°C + 273.15 = 180.15 K

Next, we need to convert the gauge pressure to absolute pressure by adding the atmospheric pressure:

P_abs = P + P_atm = 1.4 MPa + 1 atm = 2.4 MPa

Now, we can use the ideal gas law equation to calculate the mass of air (m):

PV = nRT

Where:

P = absolute pressure

V = volume

n = number of moles of air

R = ideal gas constant

T = temperature

Rearranging the equation to solve for mass (m):

m = (n * M) / N_A

Where:

M = molar mass of air

N_A = Avogadro's number

To find the number of moles (n), we can use the equation:

n = PV / RT

Given that the molar mass of air is approximately 28.97 g/mol, and the ideal gas constant R is 8.314 J/(mol·K), we can calculate the mass of air.

Calculations:

n = (P_abs * V) / (R * T)

m = (n * M) / N_A

Substituting the values:

n = (2.4 MPa * 2 m³) / (8.314 J/(mol·K) * 180.15 K)

m = (n * 28.97 g/mol) / 6.022 x 10^23 mol⁻¹

Calculating the mass of air (m):

m ≈ 5.04 kg

Therefore, the mass of air in the tank is approximately 5.04 kg.

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Answer:

Velocity can be directly added or subtracted.

For example, if a boat has a velocity V in still water.

And now you put the boat in a river with a current that has a velocity V'

The total velocity of the boat in that river is just the addition of these two velocities.

Velocity in the river  = V + V'

Where the only tricky part is that the velocity is a vector, so you need to take in account the directions of each vector.

In this case, we have a plane with a maximum velocity of 160km, let's assume a direction for this velocity, let's say that is in the positive x-direction.

Then we can write the velocity in the vector form:

velocity  = (vel in x-axis, vel in y-axis)

The velocity of the plane can be written as:

v = (160km/h, 0)

Now we add a crosswind of 30km/h

crosswind means that it is perpendicular, then it acts on the y-axis.

Then the total velocity of the plane will be:

velocity = (160km/h, 0) + (0, 30km/h)

velocity = (160km/h, 30km/h)

Now you can compute the total velocity of the airplane as the module of that vector.

Remember that for a vector (x, y) the module is:

mod = √(x^2 + y^2)

Then the module of the velocity is:

v = √( (160km/h)^2 + (30km/h)^2) = 162.8 km/h

To attenuate the signal by only 5%, the width-to-length ratio (W/L) of the NMOS transistor should be approximately 13.125.

To determine the required W/L ratio, we need to calculate the voltage gain of the circuit and find the value of W/L that corresponds to a 5% attenuation.

First, let's analyze the circuit. We have an NMOS transistor connected in a common-source configuration, where Vin is the input voltage, Va is the gate voltage, and Vout is the output voltage.

               _______________

              |               |

  Vin -------|               |

              |               |

              |               |

              |     NMOS      |------ Vout

              |               |

              |               |

              |               |

              |_______________|

The voltage gain (Av) of the NMOS transistor in the common-source configuration can be approximated as:

Av = -k' * (W/L) * (Vin - VTh) * (1 + λ * Vout)

where k' is the transconductance parameter, W/L is the width-to-length ratio, Vin is the input voltage, VTh is the threshold voltage, λ is the channel-length modulation parameter, and Vout is the output voltage.

Since the question states that Vin is very small, we can assume that the voltage drop across R is negligible. Therefore, Va will be approximately equal to Vin.

Va = Vin

We want the circuit to attenuate the signal by only 5%. This means the output voltage (Vout) should be 95% of the input voltage (Vin).

Vout = 0.95 * Vin

Substituting Va = Vin and Vout = 0.95 * Vin into the voltage gain equation, we get:

0.95 * Vin = -k' * (W/L) * (Vin - VTh) * (1 + λ * 0.95 * Vin)

Rearranging the equation, we have:

-k' * (W/L) * (Vin - VTh) * (1 + λ * 0.95 * Vin) = 0.95 * Vin

Simplifying, we get:

-k' * (W/L) * (1 + λ * 0.95 * Vin) = 0.95

Since Vin is very small, we can assume that λ * 0.95 * Vin is negligible compared to 1. Therefore, we can approximate the equation as:

-k' * (W/L) = 0.95

Now, let's substitute the given values:

k' = 800 A/V^2

VTh = 0.5 V

-800 * (W/L) = 0.95

Solving for W/L, we find:

W/L = 0.95 / -800 ≈ -0.0011875

The W/L ratio cannot be negative, so we take the absolute value:

W/L ≈ 0.0011875

Finally, we can calculate the width (W) for a given length (L). Assuming L = 1 (arbitrary units), we have:

W = (W/L) * L ≈ 0.0011875 * 1 ≈ 0.0011875

To attenuate the signal by only 5%, the width-to-length ratio (W/L) of the NMOS transistor should be approximately 0.0011875 (or 13.125 if the length is assumed to be 1 unit).

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The wavelength of the observed Lyman-alpha line from this quasar with a redshift of z = 3.7 will be approximately 444 nm.

The formula to calculate the observed wavelength (λ_obs) of an object with redshift (z) is given by:

λ_obs = λ_rest * (1 + z)

In this case, we are interested in the Lyman-alpha line, which has a rest wavelength (λ_rest) of 121.6 nm.

Substituting the values into the formula, we have:

λ_obs = 121.6 nm * (1 + 3.7)

λ_obs = 121.6 nm * 4.7

λ_obs ≈ 570.32 nm

However, it's important to note that the Lyman-alpha line falls in the ultraviolet (UV) region of the electromagnetic spectrum, not in the visible part.

Since the question specifically mentions that it is in the visible part, it suggests a typographical error or some other contextual discrepancy.

The wavelength of the observed Lyman-alpha line from this quasar, assuming a redshift of z = 3.7, is approximately 570.32 nm.

However, the Lyman-alpha line is in the ultraviolet (UV) region, not the visible part of the electromagnetic spectrum.

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a) The wavelength of electromagnetic radiation needed to excite the electron to the n = 3 state is approximately 1808.26 nm.

b) The width of the square well is approximately 904.13 nm.

To find the wavelength of electromagnetic radiation needed to excite the electron to the n = 3 state, we can use the formula:

λ = hc / ΔE

where λ is the wavelength, h is Planck's constant (6.626 × 10⁻³⁴ J·s), c is the speed of light (2.998 × 10⁸ m/s), and ΔE is the energy difference between the two states.

First, let's convert the energy difference ΔE from electron volts (eV) to joules (J):

ΔE = (3² - 1²) x e₁

ΔE = (9 - 1) x 0.86 eV

ΔE = 8 x 0.86 eV

ΔE = 6.88 eV

Next, let's convert the energy difference ΔE from eV to joules (J):

1 eV = 1.602 × 10⁻¹⁹ J

ΔE = 6.88 x 1.602 × 10⁻¹⁹ J

ΔE ≈ 1.101376 × 10⁻¹⁸ J

Now we can calculate the wavelength λ:

λ = (hc) / ΔE

λ = (6.626 × 10⁻³⁴ J·s x 2.998 × 10⁸ m/s) / (1.101376 × 10⁻¹⁸ J)

λ ≈ 1.80826 × 10⁻⁶ m

Finally, let's convert the wavelength from meters (m) to nanometers (nm):

1 m = 1 × 10⁹ nm

λ ≈ 1.80826 × 10⁻⁶ m x 1 × 10⁹ nm/m

λ ≈ 1808.26 nm

Therefore, the wavelength of electromagnetic radiation needed to excite the electron to the n = 3 state is approximately 1808.26 nm.

To find the width of the square well, we can use the formula:

L = λ / 2

where L is the width of the square well.

Using the value we calculated for λ in part (a):

L = 1808.26/2 nm

L = 904.13 nm

Therefore, the width of the square well is approximately 904.13 nm.

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Answer:

D. Newton's first law

Explanation:

Newton's first law of inertia says that an object will remain how it is, unless affected by an outside force. In this case, the plates want to remain stationary(not moving). Therefore, if you pull the table cloth fast enough, the force of friction produced will be small enough so that the Inertia of the plates will overcome the force of friction.

The magnetic field lines pοint tοwards the East (A).

Magnetic field lines are a visual representatiοn used tο depict the directiοn and strength οf the magnetic field arοund a magnet οr a current-carrying cοnductοr. They indicate the path that a hypοthetical magnetic nοrth pοle wοuld take if placed in the vicinity οf the magnetic field.

The prοtοn is a pοsitively charged particle and is traveling due nοrth. Since the electric field lines pοint due west, the electric fοrce οn the prοtοn is directed tοwards the west. In οrder fοr the prοtοn tο cοntinue traveling in a straight line due nοrth, the magnetic fοrce οn the prοtοn must be directed tοwards the east. This can be achieved if the magnetic field lines pοint tοwards the east.

Therefοre, the magnetic field lines pοint tοwards the East directiοn which is οptiοn A.

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The density of the N nucleus can be calculated by dividing its mass by its volume, the binding energy per nucleon E of the lithium isotope Li is [tex]5.6 MeV/nucleon[/tex], the energy needed to remove a proton from the nucleus of the potassium isotope K is [tex]289.77 MeV[/tex]

The mass number of N is 14 and its atomic number is 7. The number of neutrons in the N nucleus is given by [tex]14 - 7 = 7[/tex] neutrons.

The mass of one neutron is about 1.008665 atomic mass units (amu) or [tex]1.67493 \times 10^{-27} kg[/tex].

The mass of the N nucleus = [tex]7(1.008665) + 7.016004 = 14.04273 $ amu[/tex]. Thus, the density of the N nucleus can be calculated by dividing its mass by its volume.

The binding energy per nucleon E of the lithium isotope Li is 5.6 MeV/nucleon. To find its atomic mass of this isotope, the mass defect of the nucleus is calculated using the formula:

Mass defect = (Zmp + Nmn) - M

where

The mass of a proton is approximately [tex]1.00728 amu[/tex], while the mass of a neutron is approximately [tex]1.00866 amu[/tex].

The energy needed to remove a proton from the nucleus of the potassium isotope K can be calculated using the formula:

Binding energy = [tex]E \times A[/tex]

where E is the binding energy per nucleon, A is the mass number. Binding energy of K isotope = 7.43 MeV/nucleon (given)

Thus, the energy needed to remove a proton from the nucleus of the potassium isotope K is [tex]289.77 MeV[/tex].

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(B) The angle of refraction when light enters glass from air will be equal to the angle of incidence. This is in accordance with Snell's law, which relates the angles and refractive indices of the media involved.

According to Snell's law, the relationship between the angle of incidence (θ₁), the angle of refraction (θ₂), and the refractive indices of the two media is given by:

n₁ sin(θ₁) = n₂ sin(θ₂),

where n₁ and n₂ are the refractive indices of the initial medium (air) and the second medium (glass), respectively.

When light travels from air to glass, the refractive index of air (n₁) is smaller than the refractive index of glass (n₂). As a result, the sine of the angle of refraction (θ₂) will be smaller than the sine of the angle of incidence (θ₁), given that the angles are measured with respect to the normal.

Since sin(θ₂) < sin(θ₁), the only way for Snell's law to hold true is if θ₂ is smaller than θ₁. Therefore, the angle of refraction will be equal to the angle of incidence, option B.

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The maximum electrical force that these protons will exert on each other is 2.48 x 10^-13 N.

The electrical force between two charged particles can be calculated using Coulomb's Law:

F = (k * q1 * q2) / r^2

Where:

F is the electrical force,

k is the electrostatic constant (k ≈ 8.99 x 10^9 N m^2/C^2),

q1 and q2 are the charges of the particles (in this case, both are protons, so each charge is q = 1.6 x 10^-19 C),

and r is the distance between the particles (assuming they are in contact, r ≈ 2 x 10^-15 m).

To find the maximum electrical force, we need to calculate the force when the protons are closest to each other. This occurs when they are just about to collide, so their separation distance is equal to the sum of their radii (r ≈ 2 x 10^-15 m).

Plugging the values into the formula, we have:

F = (8.99 x 10^9 N m^2/C^2) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (2 x 10^-15 m)^2

F ≈ 2.48 x 10^-13 N

The maximum electrical force that these protons will exert on each other is approximately 2.48 x 10^-13 N. This force arises due to the interaction between their positive charges and is inversely proportional to the square of the distance between them.

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Answer:

  The wavelength of the wave is [tex]1.06\times10^6 m[/tex]  

Explanation:

Lets calculate

We know an electromagnetic wave is propagating through an insulating magnetic material of dielectric constant K and relative permeability [tex]K_m[/tex] ,then the speed of the wave in this dielectric medium is [tex]\nu[/tex] is less than the speed of the light c and is given by a relation

               [tex]\nu=\frac{c}{\sqrt{KK_m} }[/tex]  --------- 1

In case the electromagnetic  wave propagating through the insulating magnetic material , the amplitudes of electric and  magnetic fields are related as -

             [tex]E_m_a_x= \nu B_m_a_x[/tex]

The magnitude of the 'time averaged value' of the pointing vector is called the intensity of the wave and is given by a relation

                       [tex]I = S_a_v[/tex]

                        [tex]\frac{E_m_a_xB_m_a_x}{2K_m\mu0}[/tex]----------- 3

now , we will find the speed of the propagation of an electromagnetic wave by using equation 1

[tex]\nu=\frac{c}{\sqrt{KK_m} }[/tex]

Putting the values ,

   =[tex]\nu= \frac{3.00\times10^8}{\sqrt{(3.64)(5.18)} }[/tex]

 =[tex]0.6908\times10^8m/s[/tex]

 = [tex]6.91\times10^7m/s[/tex]

Now , using this above solution , we will find the wavelength of the wave -

     [tex]\lambda=\frac{\nu}{f}[/tex]

    Putting the values from above equations -

  [tex]\frac{6.91\times10^7m/s}{65.0Hz}[/tex]

        [tex]\lambda= 1.06\times10^6 m[/tex]

Hence , the answer is [tex]\lambda= 1.06\times10^6 m[/tex]

When comparing the camera and the human eye, the film of the camera functions as the retina. The correct option is A.

A camera is a device that records and captures images. A camera, whether digital or film, relies on the same basic technology to work: light enters a camera and is focused onto a photosensitive surface that converts the light into an electrical signal.

The human eye is a sensory organ that helps people to see. The eye is comprised of several components that work together to allow light to enter the eye, focus it, and create an image that is sent to the brain. The retina, the part of the eye that corresponds to the film of the camera, is responsible for capturing the image that is formed by the eye’s lens. In comparison, the film of the camera functions as the retina.

The retina is located at the back of the eye and contains photoreceptor cells that detect light and convert it into neural signals that are sent to the brain. Similarly, the film in a camera captures the image created by the camera’s lens and converts it into an image that can be viewed or printed.Both the human eye and a camera are complex systems that work together to create images.

However, the processes that occur within the eye and the camera are quite different. The human eye relies on biological processes to create images, while a camera uses electronic and mechanical processes to capture and record images. The correct option is A.

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The height (in feet) of the weight above the ground as a function of time will be given by the equation h = -16t² + 20t + 186. The weight will reach its zenith at t = 0.625 seconds at a height of 197.125 feet above the ground.

The given problem is a classic example of projectile motion where an object is thrown from a height and lands on the ground. The height (in feet) of the weight above the ground as a function of time will be given by the equation h = -16t² + 20t + 186, where h represents the height of the weight above the ground and t represents the time in seconds.The zenith is the highest point of the weight, i.e., the point where the weight stops moving upward and starts moving downward. To find the zenith, we need to find the time when the vertical component of the weight's velocity becomes zero, i.e., when it stops moving upwards. This can be found by differentiating the equation for height with respect to time and setting it equal to zero, which gives us the time when the vertical velocity is zero. This time is t = 0.625 seconds.

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Answer:

[tex]Pressure = 29723.1\ N/m^2[/tex]

Explanation:

Given

[tex]Force = 8694N[/tex]

[tex]Length = 0.45m[/tex]

[tex]Width = 0.65m[/tex]

Required

The force exerted on the floor by the box

First, calculate the area covered by the box (i.e. the base area)

[tex]Base\ Area = Length * Width[/tex]

[tex]Base\ Area = 0.45m * 0.65m[/tex]

[tex]Base\ Area = 0.2925m^2[/tex]

Pressure is calculated as:

[tex]Pressure = \frac{Force}{Area}[/tex]

[tex]Pressure = \frac{8694N}{0.2925m^2}[/tex]

[tex]Pressure = 29723.0769231\ N/m^2[/tex]

[tex]Pressure = 29723.1\ N/m^2[/tex] --- approximated

Answer:

They would all most likely have the same weight

Explanation:

Think about it the smaller the person or object the smaller the weight. But theyre all the same height now. And its not like you don't have any weight in the moon. So in conclusion they would all be the same weight

(a) The radial velocity and tangential velocity exiting from the impeller tip are 3.768 m/s and 10.472 m/s respectively.

(b) The stagnation temperature out of the diffuser (To₃) is 400 × [tex](P_3 / 400)^{0.4[/tex].

(c) The overall pressure ratio (Po₃/Po₁) is (P₃ / P₁) × [tex](To_3 / To_1)^{(y/(y-1))[/tex].

(d) The axial Mach number entering the eye region is √((2 / (1.4 - 1)) × [tex]((Po_1 / 100)^{((1.4-1)/1.4) - 1))[/tex]

Given:

Inner diameter (root) of the eye region: 0.15 m

Outer diameter (tip) of the eye region: 0.3 m

y = 1.4

Cp = 1 kJ/(kg K)

Impeller tip diameter: 0.5 m

Impeller height: 0.05 m

Impeller speed: N = 200 rev/s

Number of impeller blades: 12

Slip factor: σ = 1 - (0.63π / n)

Power input factor: n = 1.04

Isentropic efficiency: nc = 0.95

The static temperature at the impeller tip (station 2): T2 = 400 K

Static pressure at impeller tip (station 2): P2 = 400 kPa

Pressure at station 1 (eye region): P₁ = 100 kPa

The temperature at station 1 (eye region): To₁ = 300 K

(a) Radial velocity (Vr₂):

Vr₂ = (π × D₂ × N) / (60 × σ × n)

Vr₂ = (π × 0.5 × 200) / (60 × (1 - (0.63π / 1.04)))

Vr₂ ≈ 3.768 m/s

Tangential velocity (Vt₂):

Vt₂ = (π × D₂ × N) / 60

Vt₂ = (π × 0.5 × 200) / 60

Vt₂ ≈ 10.472 m/s

(b) Stagnation temperature out of the diffuser (To₃):

To₃ / To₂ = [tex](P_3 / P_2)^{((y-1)/y)[/tex]

To₃ / 400 = [tex](P_3 / 400)^{(0.4)[/tex]

To₃ = 400 × [tex](P_3 / 400)^{0.4[/tex]

(c) Overall pressure ratio (Po₃ / Po₁):

Po₃ / Po₁ = (P₃ / P₁) × [tex](To_3 / To_1)^{(y/(y-1))[/tex]

(d) Axial Mach number entering the eye region (M₁):

M₁ = √((2 / (y - 1)) × [tex]((Po_1 / P_1)^{((y-1)/y) - 1))[/tex]

M₁ = √((2 / (1.4 - 1)) × [tex]((Po_1 / 100)^{((1.4-1)/1.4) - 1))[/tex]

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Option (A) t = 6 , is the correct option .

The object changes direction at t = 6. The given velocity equation is v = -5t + 30, where v represents velocity and t represents time.

To determine when the object changes direction, we need to find the time at which the velocity becomes zero. The given velocity equation is v = -5t + 30, where v represents velocity and t represents time.

Setting the velocity equation equal to zero, we have:

-5t + 30 = 0

To solve for t, we can isolate t by subtracting 30 from both sides of the equation:

-5t = -30

Next, divide both sides of the equation by -5 to solve for t:

t = -30 / -5

t = 6

The object changes direction at t = 6. At this time, the velocity becomes zero.

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Answer:

Due to lower risk of injury or damage.

Explanation:

The high divers would choose to enter the water from the feet first because there is low risk of injury. The brain is the most important part of the body which very sensitive to any small injury. Small injury to brain leads to big problems in life. High divers can reach speeds of nearly 60 mph and enters about 28m into the water in about three seconds which can damage the head region if comes in contact with the ground so this is the reason the high divers avoid of entering in the water through their heads and choose entering through their feet.

The moment of inertia of the rider, box, and rocket about the pole is 170 kg * (6 m)^2 = 6120 kg · m^2.  The initial angular acceleration of the rider is 0.098 rad/s^2.

A) The moment of inertia of the rider, box, and rocket about the pole can be calculated using the formula for the moment of inertia of a point mass rotating around an axis. The moment of inertia (I) is given by the product of the mass (m) and the square of the distance (r) from the axis of rotation:

I = m * r^2

Since the mass of the rider, box, and rocket is given as 170 kg and the rod is neglected, the moment of inertia will be the same for all components. Therefore, the moment of inertia of the rider, box, and rocket about the pole is 170 kg * (6 m)^2 = 6120 kg · m^2.

B) The initial angular acceleration of the rider can be determined using Newton's second law of rotational motion, which states that the torque (τ) is equal to the moment of inertia (I) multiplied by the angular acceleration (α). The torque can be calculated as the product of the force (F) applied perpendicular to the path of the rider and the distance (r) from the axis of rotation:

τ = F * r

Rearranging the formula and substituting the given values:

α = τ / I = (98 N * 6 m) / 6120 kg · m^2 = 0.098 rad/s^2

Therefore, the initial angular acceleration of the rider is 0.098 rad/s^2.

C) The relationship between angular velocity (ω) and time (t) is given by the equation ω = α * t. Rearranging the formula to solve for time:

t = ω / α

The rider's velocity can be converted to angular velocity using the formula v = r * ω. Rearranging the formula to solve for angular velocity:

ω = v / r = 5 m/s / 6 m = 0.8333 rad/s

Substituting the values into the equation, we get:

t = 0.8333 rad/s / 0.098 rad/s^2 = 8.5 s

Therefore, the time required for the rider's velocity to reach 5 m/s is 8.5 seconds.

D) To find the mass per second that must leave the rocket to develop the given thrust (F), we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (dp/dt). In this case, the force is equal to the thrust of the rocket, and the change in momentum is the mass per second leaving the rocket (dm/dt) multiplied by the exit velocity (v):

F = dm/dt * v

Rearranging the formula and substituting the given values:

dm/dt = F / v = 98 N / 390 m/s = 0.2513 kg/s

Therefore, the mass per second that must leave the rocket to develop the thrust of 98 N is 0.2513 kg/s.

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Answer:

The coin is denser than any of the liquids, and will sink through everything. The oil is the least dense liquid, so it will float on the water, and the syrup is the densest liquid, so it will sink below the water.

Explanation:

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You can use the information below to calculate it :)

Density of water: 1000 kg/m3.

Density of the coin: copper 8.96   g/cm^3

nickel   8.90   g/cm^3

1 kg = 1000 g

All you have to do now is convert it and thats it

The increase in the time period of the pendulum with the increased length is 0.1 times or 10% of the initial time period.

What is a time period?

The time period of a periodic motion refers to the time it takes for one complete cycle or oscillation to occur. It is the time interval between two successive identical points in the motion.

The time period (T) of a simple pendulum is given by the equation:

T = 2π√(L/g)

where L is the length of the pendulum and g is the acceleration due to gravity.

Let's assume the initial length of the pendulum is L and the increased length is L + 0.21L = 1.21L (as it is increased by 21%).

The new time period (T') of the pendulum with the increased length can be calculated using the same equation:

T' = 2π√((1.21L)/g)

To find the increase in the time period, we subtract the initial time period (T) from the new time period (T'):

ΔT = T' - T

= 2π√((1.21L)/g) - 2π√(L/g)

= 2π(√(1.21L/g) - √(L/g))

= 2π(√(1.21)√(L/g) - √(L/g))

= 2π(1.1√(L/g) - √(L/g))

= 2π(0.1√(L/g))

Therefore, the increase in the time period of the pendulum with the increased length is 0.1 times the initial time period:

ΔT = 0.1T

Hence, the increase in the time period is 10% of the initial time period.

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The amplitude of the motion is 0.02 m. The maximum speed attained by the object is 0.352 m/s.

a.

In simple harmonic motion (SHM), the displacement of an object from its equilibrium position can be described by the equation:

x(t) = A * cos(ωt + φ)

where:

x(t) is the displacement at time t,

A is the amplitude of the motion,

ω is the angular frequency,

t is the time, and

φ is the phase constant.

The speed of the object is given by:

v(t) = A * ω * sin(ωt + φ)

Mass of the object, m = 2.7 kg

Spring constant, k = 310 N/m

Displacement from equilibrium position, x = 0.02 m

Speed of the object, v = 0.55 m/s

We can relate the angular frequency (ω) to the mass and spring constant using the equation:

ω = sqrt(k / m)

Let's calculate ω first:

ω = sqrt(310 N/m / 2.7 kg) ≈ 8.064 rad/s

To find the amplitude (A), we can use the given displacement:

0.02 m = A * cos(0 + φ)

cos(0) = 1

Therefore, we have:

A = 0.02 m

The amplitude of the motion is 0.02 m.

b.

The maximum speed in simple harmonic motion occurs when the displacement is zero (i.e., at the equilibrium position). At this point, the speed is at its maximum value.

Amplitude of the motion, A = 0.02 m

We can find the maximum speed (v_max) using the equation:

v_max = A * ω

Substituting the values:

v_max = 0.02 m * 8.064 rad/s ≈ 0.352 m/s

Conclusion:

The maximum speed attained by the object is 0.352 m/s.

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