P7.36 A ship is 125 m long and has a wetted area of 3500 m2. Its propellers can deliver a maximum power of 1.1 MW to seawater at 20C. If all drag is due to friction, estimate the maximum ship speed, in kn.

Answer:

Explanation:

Resonant frequency is 240

4π² x 240² = 1 / LC

230400π² = 1 / LC

Let the required frequency = n

inductive reactance = 2 πn L

capacitative reactance = 1 /  2 π n C

inductive reactance / capacitative reactance

= 4π² x n ² x LC = 5.68

4π² x n ² = 1 / LC x 5.68

= 230400π²  x 5.68

4n ²= 230400 x 5.68

n ²= 57600 x 5.68

n ² = 327168

n = 572 approx

The generator's frequency in this RLC circuit, where the ratio of inductive to capacitive reactance is 5.68 and the resonant frequency is 240 Hz, is approximately 571 Hz.

To solve this problem, we need to use the relationship between inductive and capacitive reactance in an RLC circuit. Given that the ratio of the inductive reactance (XL) to the capacitive reactance (XC) is 5.68,

Reactance is frequency-dependent, with the following formulas for inductive and capacitive reactance:

Given the resonant frequency as 240 Hz, we start by calculating the resonance reactances:

Using the non-resonant frequency, we use the reactance ratio:

Rearranging gives us:

Since 240 Hz is the resonant frequency, substituting f:

Simplifying yields:

Therefore, the generator frequency is approximately 571 Hz.

Answer:

φ = -7.16 × 10⁴ Nm²/C

Explanation:

q = -3.80 × 10⁻⁶ C

ε₀ = 8.85 10⁻¹² C²/Nm²

By Gauss's law

φ = q/ε₀

as the cube has 6 faces so for one side the flux will

φ =1/6 ( q/ε₀)

φ = 1/6 ( -3.80 × 10⁻⁶ C / 8.85 10⁻¹² C²/Nm²)

φ = -71,563.088 Nm²/C

φ = -7.16 × 10⁴ Nm²/C

-7.00 x 10⁴Nm²/C

Let the single point charge of -3.80µC be Q

i.e

Q = -3.80µC = -3.80 x 10⁻⁶C

From Gauss's law, the total electric flux,φ, through an enclosed surface is equal to the quotient of the enclosed charge Q, and the permittivity of free space, ε₀. i.e;

φ = Q / ε₀     ----------------------(i)

Where;

ε₀ = known constant = 8.85 x 10⁻¹²F/m

Now, If the total flux through the enclosed cube is given by equation (i), then the flux, φ₁, through one of the six sides of the cube is found by dividing the equation by 6 and is given as follows;

φ₁ = Q / 6ε₀     --------------------(ii)

Substitute the values of  Q and ε₀ into equation (ii) as follows;

φ₁ = -3.80 x 10⁻⁶ / (6 x 8.85 x 10⁻¹²)

φ₁ = -0.07 x 10⁶

φ₁ = -7.00 x 10⁴

Therefore, the electric flux through one side of the cube is -7.00 x 10⁴ Nm²/C

Note:

The result (flux) above is negative to show that the electric field lines from the point charge points radially inwards in all directions.

This answer explains the calculation of turns in a transformer's secondary winding based on given voltage outputs and primary turns, along with determining maximum output currents for different voltage levels.

Input Voltage: 240 V

Primary Coil Turns: 280 turns

Secondary Parts Turns: 5.60 V - 77 turns, 12.0 V - 56 turns, 480 V - 7 turns

Maximum Output Currents: 5.60 V - 5 A, 12.0 V - 2.1 A, 480 V - 0.042 A

Final answer:

The question delves into advanced transformer analysis, focusing on impedance during a short circuit, input parameters at full load, and how voltage regulation varies with load. However, specific calculations for these scenarios are complex and require more detailed analysis beyond the provided data.

Explanation:

The student's question involves a complex analysis of a 60-Hz single-phase transformer under different loading conditions, focusing on electrical parameters such as impedance, current, power, and voltage regulation. It covers several fundamental concepts in electrical engineering, particularly those relating to transformers' performance and efficiency under load.

Total Input Impedance

To calculate the total input impedance when the secondary is shorted, we must consider the impedances in parallel and series as per the equivalent circuit of the transformer. However, given the specific data provided, a direct calculation isn't presented here.

Input Current, Voltage, Power, and Power Factor at Full Load

At full load (150 kW) with a power factor of 0.83 and a secondary voltage of 230 V, the input current, voltage, power, and power factor can be derived from the transformer's ratings and load characteristics. However, to accurately calculate these values, one would typically apply the transformer's equivalent circuit model, considering real and reactive power components.

Voltage Regulation vs. Load

The voltage regulation versus load plot and the determination of the load that produces 5% regulation require an analysis of how the secondary voltage varies with load, against rated conditions. This involves calculations and assumptions not fully detailed in the question.

Final answer:

To find the work done when stretching or compressing a non-Hookean spring by 0.050 m, we calculate the definite integral of the force function over the respective intervals. The work done for stretching is the integral from 0 to -0.050 m, and for compression, it is the integral from 0 to 0.050 m. The ease of stretching versus compressing depends on the non-linear force constants.

Explanation:

Work Done to Stretch or Compress a Non-Hookean Spring

To compute the work (W) required to stretch or compress the spring an amount x, we need to integrate the force function Fx = kx - bx2 + cx3 from the unstretched length (0) to the final position (x).

For stretching (x < 0), substitute the given constants (k = 100 N/m, b = 700 N/m2, c = 12,000 N/m3) and integrate from 0 to -0.050 m.

For compression (x > 0), use the same constants and integrate from 0 to 0.050 m.

Analyze the dependence of Fx on x to determine which process (stretching or compressing) requires less work.

The work done for both stretching and compressing can be calculated by evaluating the definite integral of Fx over the interval [0, x].

(a) Work done to stretch:

W = ∫0-0.050 (100x - 700x² + 12,000x3) dx

(b) Work done to compress:

W = ∫00.050 (100x - 700x² + 12,000x3) dx

(c) Comparison of ease:

The comparison is based on the shape of the force-displacement curve. With the given non-linear characteristics, it might be easier or harder to stretch or compress the spring depending on the values of b and c which affect the quadratic and cubic terms, respectively.

Answer:

The magnitude of F₁ is 3.7 times of F₂

Explanation:

Given that,

Time = 10 sec

Speed = 3.0 km/h

Speed of second tugboat = 11 km/h

We need to calculate the speed

[tex]v_{1}=\dfrac{3.0\times10^{3}}{3600}[/tex]

[tex]v_{1}=0.833\ m/s[/tex]

The force F₁is constant acceleration is also a constant.

[tex]F_{1}=ma_{1}[/tex]

We need to calculate the acceleration

Using formula of acceleration

[tex]a_{1}=\dfrac{v}{t}[/tex]

[tex]a_{1}=\dfrac{0.833}{10}[/tex]

[tex]a_{1}=0.083\ m/s^2[/tex]

Similarly,

[tex]F_{2}=ma_{2}[/tex]

For total force,

[tex]F_{3}=F_{2}+F_{1}[/tex]

[tex]ma_{3}=ma_{2}+ma_{1}[/tex]

The speed of second tugboat is

[tex]v=\dfrac{11\times10^{3}}{3600}[/tex]

[tex]v=3.05\ m/s[/tex]

We need to calculate total acceleration

[tex]a_{3}=\dfrac{v}{t}[/tex]

[tex]a_{3}=\dfrac{3.05}{10}[/tex]

[tex]a_{3}=0.305\ m/s^2[/tex]

We need to calculate the acceleration a₂

[tex]0.305=a_{2}+0.083[/tex]

[tex]a_{2}=0.305-0.083[/tex]

[tex]a_{2}=0.222\ m/s^2[/tex]

We need to calculate the factor of F₁ and F₂

Dividing force F₁ by F₂

[tex]\dfrac{F_{1}}{F_{2}}=\dfrac{m\times0.83}{m\times0.22}[/tex]

[tex]\dfrac{F_{1}}{F_{2}}=3.7[/tex]

[tex]F_{1}=3.7F_{2}[/tex]

Hence, The magnitude of F₁ is 3.7 times of F₂

Answer:

16.5 m

Explanation:

Given,

Magnetic field = 0.02 T

radius of electron = 9 mm

speed of electron  = speed of proton

radius of proton = ?

We know,

[tex]F_e = q_e vB[/tex].........(1)

[tex]F_p = q_p vB[/tex]

using newton second law

[tex]F = m a = m\dfrac{v^2}{r}[/tex]

equating Force due to electron and proton

[tex]F_e = F_p[/tex]

[tex]\dfrac{m_ev^2}{r_e}=\dfrac{m_pv^2}{r_p}[/tex]

[tex]\dfrac{m_e}{r_e} = \dfrac{m_p}{r_p}[/tex]

m_ e = 9.1 x 10⁻³¹ Kg    and m_p = 1.67 x 10⁻²⁷ Kg

[tex]r_p = \dfrac{m_p}{m_e}\times r_e[/tex]

[tex]r_p = \dfrac{1.67\times 10^{-27}}{9.1 \times 10^{-31}}\times 9 \times 10^{-3}[/tex]

[tex]r_p = 16.5 m[/tex]

Hence, the radius of proton is equal to 16.5 m.

Answer:

(a) 380.96 pC

(b) 3.25V

Explanation:

(a) Before immersion,

[tex]C_{air}[/tex] = [tex]\frac{E_{0}A }{d}[/tex]

⇒(8.85E-12× 25E-4× 260) ÷(0.0151)

= 380.96 pC

(b)   Charge on the plates after immersion can be calculated by,

  Q = ΔV×C

      = Δ[tex]V_{air}[/tex] ÷ K

where K is the constant for distilled water

      = 260 ÷ 80

      = 3.25V

Answer:

Explanation:

(a) Charge  on the plates before immersion

as we know that,

C = εA/d

C = 8.85×[tex]10^{-12}[/tex]× 25×[tex]10^{-4}[/tex]/ 1.51×[tex]10^{-2}[/tex]

   = 1.46×[tex]10^{-12}[/tex]

Q = CV

   = (1.46×[tex]10^{-12}[/tex]) (260)

   = 3.796×[tex]10^{-10}[/tex] C

(b) Charge on the plates after immersion

Q = 3.796×[tex]10^{-10}[/tex] C

The charge will remain the same, as the capacitor was disconnected before it was immersed.

The magnitude of the frictional force between the person and the wall is

[tex]\[ f = \frac{mv^2}{r} \][/tex]

To find the magnitude of the frictional force between the person and the wall, we can use the concept of centripetal force.

First, let's define the variables:

m = mass of the person

v = tangential velocity of the person

R = radius of the circular path (distance from the person to the axis of rotation, in this case, the distance from the person to the wall)

The centripetal force [tex](\( F_c \))[/tex] required to keep the person moving in a circular path is given by:

[tex]\[ F_c = \frac{{mv^2}}{R} \][/tex]

Since the person is held against the wall, the frictional force [tex](\( F_f \))[/tex] provides the centripetal force. Therefore,

[tex]\[ F_f = F_c \][/tex]

[tex]\[ F_f = \frac{{mv^2}}{R} \][/tex]

Therefore, the magnitude of the frictional force between the person and the wall is [tex]\( \frac{{mv^2}}{R} \)[/tex].

Answer:

[tex]6.68\times 10^{15}\ kg[/tex]

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

R = Radius of orbit = 45 km

T = Time period = 1.04 days

Mass of Eros would be given by the following equation

[tex]M=\dfrac{4\pi^2R^3}{GT^2}\\\Rightarrow M=\dfrac{4\pi^2\times (45\times 10^3)^3}{6.67\times 10^{-11}\times (1.04\times 24\times 3600)^2}\\\Rightarrow M=6.68\times 10^{15}\ kg[/tex]

The mass of Eros is [tex]6.68\times 10^{15}\ kg[/tex]

To find the initial speed of the football, you can use the kinematic equation. Given that the football is moving upward at 0.500 m/s and the displacement is 4.00 m, the equation can be used to find the initial velocity.

To find the initial speed of the football, we can use the kinematic equation that relates the final velocity, initial velocity, acceleration, and displacement: vf = vi + at. Given that the football is moving upward at 0.500 m/s and the displacement is 4.00 m, we can plug in the values to solve for the initial velocity:

0.500 m/s = vi + (-9.8 m/s2) x t

Since the football is thrown straight up, the acceleration due to gravity is negative. Let's assume the time taken for the football to reach a height of 4.00 m is t. Since the football goes up and then comes back down, the time taken to reach the height of 4.00 m in the upward direction will be half of the total time. Let's call this time tu. Since the motion is symmetric, the time taken to reach the height of 4.00 m on the way down will also be tu. Therefore, the total time taken for the football's motion is 2tu.

Given that the total time is 2tu, we can substitute it into the equation:

0.500 m/s = vi + (-9.8 m/s2) x 2tu

Now, we can solve for vi by isolating it:

vi = 0.500 m/s - (-9.8 m/s2) x 2tu

Since the time taken for the motion is unknown, we cannot determine the precise initial velocity without more information.

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Answer:

 V = k Q/l  ln [(l +√(l² + x²)) / x]

Explanation:

The electrical potential for a continuous distribution of charges is

      V = k ∫ dq / r

Let's apply this expression to our case, define a linear charge density for the bar

           λ = dq / dy

          dq = λ dy

The distance from a point on the bar to the x-axis is

            r = √ (x² + y²)

Let's replace

          V = K ∫ λ dy /√ (x² + y²)

We integrate

         V = k λ ln (y + √ (x² + y²))

Let's evaluate between y = 0 and y = l

         V = k λ [ ln (l +√(x² + l²) - ln x]

We substitute the linear density

           V = k Q/l  ln [(l +√(l² + x²)) / x]

Final answer:

To calculate the electric potential at a point on the x-axis due to a uniformly charged rod, we use the concept of charge density and integrate the contributions from each infinitesimal charge element along the rod with respect to the position.

Explanation:

The student is asking about the electric potential due to a uniformly charged rod on the x-axis. To find an expression for the electric potential at a point on the x-axis, we can imagine dividing the rod into infinitesimally small segments of charge dq. Given that the charge Q is evenly distributed along the rod of length L, the linear charge density λ is Q/L. The potential dV due to a small element dq at a distance x from the rod is given by Coulomb's law as dV = k * dq / r, where k is Coulomb's constant and r is the distance from the charge element to the point on the x-axis.

To find the total potential V, we integrate this expression from one end of the rod to the other. The distance r varies along the rod, so we integrate with respect to y, the position along the rod. Setting up the integral, we have V = k * ∫_{-L/2}^{L/2} (dq / √((L/2 - y)^2 + x^2)) where the limits of integration account for the rod's position along the y-axis with one end at the origin and λ = Q/L. After substituting dq with λdy, performing the integration, and simplifying, we obtain the electric potential V(x) as a function of position along the x-axis.

Answer:0.161 m

Explanation:

Given

mass of cube  [tex]m=0.49\ kg[/tex]

Spring constant [tex]k_1=606\ N/m[/tex]

compression in the spring [tex]x_1=0.1\ m[/tex]

When this cube is released then it will compress another spring of spring constant [tex]k_2=233\ N/m[/tex]

Conserving energy

[tex]\frac{1}{2}k_1x^2=\frac{1}{2}mv^2=\frac{1}{2}k_2x'^2[/tex]

[tex]\frac{x'}{x}=\sqrt{\frac{k_1}{k_2}}[/tex]

[tex]x'=0.1\times \sqrt{\frac{606}{233}}[/tex]

[tex]x'=0.1\times 1.61[/tex]

[tex]x'=0.161\ m[/tex]

Answer:

 ΔV = 2k λ ln (r₁ / r₂)

Explanation:

The electric potential is

         ΔV = - ∫ E. ds

The expression for the electric field of a charge line is given

           E = 2k λ / r

Let's replace and integrate

         ΔV = - 2k λ ∫ dr / r

         ΔV = -2 k λ ln r

Let's evaluate

       ΔV = - 2k λ ln r₂- ln r₁

       ΔV = -2k λ ln (r₂ / r₁)

       ΔV = 2k λ ln (r₁ / r₂)

Answer:

Potential difference = 245 V

Explanation:

First, we have to find velocity at which ionized molecules are accelerated into a magnetic field. Here, magnetic force acts as a centripetal force due to circular path of molecules towards detector slot.

Now, the magnetic force to the centripetal force equates as:

qvB = [tex]\frac{mv2}{r}[/tex] = [tex]\frac{mv2}{d/2}[/tex]

For Velocity (v) :

v = [tex]\frac{qBd}{2m}[/tex]

According to law of conservation of energy, we know that the initial potential energy of the molecules is converted into kinetic energy as they enter into the magnetic field. So,

[tex]qV=\frac{1}{2}mv2[/tex]

Substitute the value of v in above equation:

qV = [tex]\frac{1}{2}[/tex] m [tex]\frac{q2B2d2}{4m2}[/tex]

V = [tex]\frac{qB2d2}{8m}[/tex]

V= 245 V

Answer: A

Explanation: We can use the concept of conservation energy which implies that the kinetic energy of the froghoppers equals it potential energy from the ground level.

Where potential energy = mgh

Where m = mass of the object , g = acceleration due gravity and h = height from ground level.

The value of potential energy will reduce when the height is inclined at an angle.

Let us assume equal mass for both froghoppers, say m , g = 10 m/s^2 and a value of h.

For the first froghopper, potential energy = m×9.8×h = 9.8 mh

For the second froghopper, potential energy = m×9.8×hsin58 ( hsin58 is the vertical componet of height h inclined at angle 58),

potential energy = 8.3109 mh

As we can see , froghopper A has more potential energy than froghoppers B which implies that A has more kinetic energy than B

Final answer:

Both froghoppers experience the same change in kinetic energy, as the change in potential energy is the same for both due to reaching the same height.

Explanation:

To determine which froghopper experiences the greatest change in kinetic energy we can consider their jumps from an energy perspective. As both froghoppers are aiming for the same leaf at a height of 35 cm, the change in gravitational potential energy (UG) from the ground to the leaf will be the same for both, since potential energy depends only on the height and mass, which are constant for both froghoppers. Assuming that both froghoppers start at rest (kinetic energy Ki = 0), the change in kinetic energy during the jump (ΔK) will equal the change in potential energy (ΔUG) at the top of their trajectories where their velocity is zero.

If we follow the work-energy principle, the work done by the froghoppers' muscles will convert to potential energy at the peak of their jumps. Thus, the greatest change in kinetic energy will be equivalent to the potential energy gained at the leaf's height, which is same for both, meaning that neither froghopper experiences a greater change in kinetic energy than the other when reaching the leaf. The takeoff angle does not affect the change in kinetic energy in this case since both reached the same height.

Answer:

33,458.71 turns

Explanation:

Given: L = 37 cm = 0.37 m, B= 0.50 T, I = 4.4 A, n= number of turn per meter

μ₀ = Permeability of free space = 4 π × 10 ⁻⁷

Solution:

We have B = μ₀ × n × I

⇒ n = B/ (μ₀ × I)

n = 0.50 T / ( 4 π × 10 ⁻⁷ × 4.4 A)

n = 90,428.94 turn/m

No. of turn through 0.37 m long solenoid = 90,428.94 turn/m × 0.37

= 33,458.71 turns

Given Information:  

Diameter of solenoid = d = 1.8 cm = 0.018 m

Length of solenoid = L = 37 cm = 0.37 m

Current = I = 4.4 A  

Magnetic field = B = 0.50 T  

Required Information:  

Number of turns = N = ?  

Answer:  

Number of turns ≈ 33,498 or 33,458

Step-by-step explanation:  

The magnetic field at the center of the solenoid is given by

B = μ₀NI/√ (L²+4r²)

N = B√ (L²+4r²)/μ₀I

Where L is the length and r is the radius of the solenoid, N is the number of turns and B is the magnetic field.

r = d/2 = 0.018/2 = 0.009 m

N = 0.50√ (0.37)²+(4*0.009²)/4πx10⁻⁷*4.4

N ≈ 33,498 Turns

Please note that we can also use a more simplified approximate model for this problem since the length of the solenoid is much greater than the radius of the solenoid

L = 0.37 >> r = 0.009

The approximate model is given by

B = μ₀NI/L

N = BL/μ₀I

N = 0.50*0.37/4πx10⁻⁷*4.4

N ≈ 33,458 Turns

As you can notice the results with the approximate model are very close to the exact model.

Answer:

88.1 N

Explanation:

As shown in the free body diagram attached to the question, the only forces acting on the inner block include in the required vertical direction.

- Its Weight.

- Frictional forces as a result of the Two compression forces.

If the block is not to slip off, the weights must match the two frictional forces

Let the compressive forces be F and frictional force be Fr

Fr = μ F

Sum of force acting on the inner block in the y-direction

Fr + Fr - W = 0

μ F + μ F = mg

2 μF = 118

2(0.67) F = 118

F = 118/1.34

F = 88.1 N

Each of the compression forces is 88.1 N

Hope this Helps!!!

The magnitude of one of the compression forces acting on either side of the inner board in a vice setup is 88.1 N

Given that the coefficient of friction () between the inner and the outer boards is 0.67 and the normal force (weight of the inner board) is 118 N, we can use the relationship for static friction to find the frictional force. Since the inner board is at equilibrium and not moving, the magnitude of one of the compression forces that acts on either side of the inner board must be equal to the static frictional force.

Thus,

Let the compressive forces be F and the frictional force be Fr

Fr = μ F

The sum of force acting on the inner block in the y-direction

Fr + Fr - W = 0

μ F + μ F = mg

2 μF = 118

2(0.67) F = 118

F = 118/1.34

F = 88.1 N

1 hour = 3600 seconds

2 hrs = 7200 sec

(24 frame/sec) x (72 sec) =

172,800 frames.

If each frame of a motion picture film is 35 mm high, and 24 frames go by in a second, then the number of frames needed to show a two-hour-long movie would be 172800 frames

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis.

As given in the problem If each frame of a motion picture film is 35 mm high, and 24 frames go by in a second,

The number of seconds in 2 hours = 2 ×3600

                                                        =7200 seconds

The number of frames goes by in one second =  24 frames

the number of frames in a 2-hour movie = 24×7200

                                                                =172800 frames

Thus, the number of frames needed to show a two-hour-long movie would be 172800 frames

Learn more about multiplication here,

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After 9 seconds, an object dropped on the moon will have fallen 65.61 meters, be traveling at 14.58 meters per second, with an acceleration of 1.62 meters per second squared. The second derivative of the distance function represents the moon's gravitational acceleration.

An object is dropped on the moon from a height of 200 meters, and the distance function of free-fall due to lunar gravity is given by s(t)=0.81t^2. We are asked to determine various properties of the object's motion after 9 seconds.

a) Distance Fallen

To find how far the object has fallen, we plug t=9 into the distance function to get s(9)=0.81(9)^2=65.61 meters. This is the distance the object has fallen, not the distance from its starting height.

b) Velocity

The object's velocity can be determined by finding the derivative of the distance function, which gives us v(t) = 2(0.81)t = 1.62t. Substituting t=9, we find v(9) = 1.62(9) = 14.58 meters per second.

c) Acceleration

The acceleration of the object is constant and equal to twice the coefficient of t^2 in the distance function, which is 1.62 meters per second squared on the moon.

d) Meaning of the Second Derivative

The second derivative of the free-fall distance function represents the acceleration due to gravity on the moon. It's constant at 1.62 meters per second squared, indicating uniform acceleration during free-fall.

Answer:

Upper scale reads 4.4kg while lower scale reads 7.6 kg

Explanation:

The buoyant force of the water on the aluminum piece would equal to the weight of the water displaced by the aluminum.

The mass of the water displaced by aluminum is

[tex]m_w = V_w \rho_w = \frac{m_a}{\rho_a}\rho_w = \frac{7}{2700}1000 = 2.6 kg[/tex]

As 7kg aluminum piece is supported by 2.6 kg buoyant force, the scale that the aluminum is hung on would read

Mass of aluminum - mass of water displaced

7 - 2.6 = 4.4 kg

This buoyant force would also created a reaction on the lower scale of 2.6 kg (according to Newton's 3rd law). So the lower scale would read:

Mass of water + mass of bleak + mass of buoyant reaction force

3 + 2 + 2.6 = 7.6 kg

Answer:

a) Height of the antenna (in m) for a radio station broadcasting at 604 kHz = 124.17 m

b)Height of the antenna (in m) for radio stations broadcasting at 1,710 kHz =43.86 m

Explanation:

(a) Radiowave wavelength= λ = c/f

As we know, Radiowave speed in the air = c = 3 x 10^8 m/s

f = frequency = 604 kHz = 604 x 10^3 Hz

Hence, wavelength = (3x10^8/604x10^3) m

λ = 496.69 m

So the height of the antenna BROADCASTING AT 604 kHz =  λ /4 = (496.69/4) m

= 124.17 m

(b) As we know , f = 1710 kHz = 1710 x 10^3 Hz  (1kHZ = 1000 Hz)

Hence, wavelength =  λ = (3 x 10^8/1710 x 10^3) m

 λ= 175.44 m

So, height of the antenna =  λ /4 = (175.44/4) m

= 43.86 m  

Answer:

Area = 25km² in a century.

Explanation:

Given

Spread Rate = 5m/century

Length of rift = 5000km

Convert to metres

Length of rift = 5000 * 1000m

Length of rift = 5,000,000m

In one century, the additional area to Atlantis = (Rift Length) * (Spread rate) * 1 century

Atea = 5,000,000 m * 5m/century * 1 century

Area = 25,000,000m² in a century

----- Convert to km²

Area = 25,000,000km² * 1m²/1,000,000km²

Area = 25km² in a century.

Hence, the total area of new ocean floor created in the Atlantic each century is 25km²

Final answer:

The total area of new ocean floor created along the mid-Atlantic Rift each century is 5,000,000 m², or 25 km² of new oceanic crust formed every century.

Explanation:

The question asks how much new ocean floor is created in the Atlantic Ocean each century along the mid-Atlantic Rift, which is known to be 5000 km long, as Europe and North America drift apart by about 5 m per century.

To calculate the total area of the new ocean floor created, we consider the length of the rift (5000 km) and the rate of separation (5 m per century).

First, we need to convert kilometers to meters for uniform units:

5000 km * 1000 m/km = 5,000,000 m.

Now we can calculate the area:

Area = Length * Width

Area = 5,000,000 m * 5 m

Area = 25,000,000

So, every century, an area of 25,000,000 m2 of new ocean floor is created along the mid-Atlantic Rift. This is equivalent to 25 km2 of new oceanic crust, since 1 km2 = 1,000,000 m2.

Answer:

U = 12 J.

Explanation:

The potential energy in a spring is given by the following formula

[tex]U = \frac{1}{2}kx^2[/tex]

where k is the spring force constant and x is the displacement from the equilibrium.

If U = 3 J when x = 0.05 m, then k is

[tex]3 = \frac{1}{2}k(0.05)^2\\k = 2400~N/m[/tex]

Using this constant, we can calculate the potential energy at x = 0.10 m:

[tex]U = \frac{1}{2}(2400)(0.1)^2 = 12 ~J[/tex]

The potential energy when the mass is at [tex]\( x = 0.10 \)[/tex] m is 12 J.

The potential energy (U) of a mass-spring system is given by the equation:

[tex]\[ U = \frac{1}{2} k x^2 \][/tex]

Given that the potential energy is 3.0 J when \( x = 0.050 \) m, we can use this information to find the spring constant \( k \). Plugging the values into the equation, we get:

[tex]\[ 3.0 \, \text{J} = \frac{1}{2} k (0.050 \, \text{m})^2 \] \[ k = \frac{2 \times 3.0 \, \text{J}}{(0.050 \, \text{m})^2} \] \[ k = \frac{6.0 \, \text{J}}{0.0025 \, \text{m}^2} \] \[ k = 2400 \, \text{N/m} \][/tex]

Now that we have the spring constant, we can find the potential energy when [tex]\( x = 0.10 \)[/tex]m using the same formula:

[tex]\[ U = \frac{1}{2} k x^2 \] \[ U = \frac{1}{2} (2400 \, \text{N/m}) (0.10 \, \text{m})^2 \] \[ U = \frac{1}{2} (2400 \, \text{N/m}) (0.010 \, \text{m}^2) \] \[ U = 1200 \, \text{N/m} \times 0.010 \, \text{m}^2 \] \[ U = 12 \, \text{J} \][/tex]

Therefore, the potential energy when the mass is at[tex]\( x = 0.10 \)[/tex]m is 12 J."

Complete Question

The complete question is shown on the first uploaded image

Answer:

The slit width [tex]a = \frac{2L \lambda}{W}[/tex]

Explanation:

Assuming the unit on the graph is cm

Given that the slit to screen distance is D = 200 cm = 20 000 m

The wavelength [tex]\lambda[/tex]  = 633 nm = [tex]633*10^{-9}m[/tex]

                         slit width a = ?

 The width of the spot that is the width of the peak from the graph is

            W = 1.6 × 2 = 3.2 cm

Where the 1.6 is the distance from 0 to the right  end point of the peak

        The change in y i.e [tex]\Delta y[/tex] has a formula

                         [tex]\Delta y[/tex]  = Ltanθ

An the width of the spot is 2 × [tex]\Delta y[/tex]

                                       W = 2Ltanθ

Applying this formula qsinθ = m[tex]\lambda[/tex]

   where m = 1 because we a focused on the first zeros ,using small angle approximation we have y

              [tex]a\theta = (1) \lambda[/tex]

               [tex]\theta = \frac{\lambda}{a}[/tex]

Substituting this into W = 2ltanθ

         Using small angle approximation

                  W = 2ltanθ = 2Lθ

                  [tex]W = 2L\frac{\lambda}{a}[/tex]

                   [tex]a = \frac{2L \lambda}{W}[/tex] and this is the slit width

Answer:

The conditions are not given in the question. Here is the complete question.

High-altitude mountain climbers do not eat snow, but always melt it first with a stove. To see why, calculate the energy absorbed from a climber's body under the following conditions. The specific heat of ice is 2100 J/kg⋅C∘, the latent heat of fusion is 333 kJ/kg, the specific heat of water is 4186 J/kg⋅C∘

a) eat 1.0kg of -15 degrees Celsius snow which your body warms to body temperature of 37 degrees Celsius ?

b) melt 1.0kg of -15 degrees Celsius snow using a stove and drink the resulting 1.0kg of water at 2 degrees Celsius, which your body has to warm to 37 degrees Celsius ?

Explanation:

Let's calculate the heat required to convert ice from -15°C to 0°C and then the heat required to convert it into the water.

a)

Heat required to convert -15°C ice to 0°C.

  [tex]ms_{ice}[/tex]ΔT = (1.0)(2.100×10³)(15) = 3.150×[tex]10^{4}[/tex]J

Heat required to convert 1.0 kg ice to water.

    [tex]mL_{ice} = 1[/tex]×[tex]3.33[/tex]×[tex]10^{5}[/tex] = 3.33×[tex]10^{5}[/tex]J

Heat required to convert 1.0 kg water at 0°C to 37°C.

   [tex]ms_{water}[/tex]ΔT = 1×4.186×[tex]10^{3}[/tex]×37 = 1.548×[tex]10^{5}[/tex] J

Total heat required = 3.150×[tex]10^{4}[/tex] + 3.33×[tex]10^{5}[/tex] + 1.548×[tex]10^{5}[/tex]

                              = 5.19×[tex]10^{5}[/tex] J

b)

Heat required to warm 1.0 kg water at 2°C to water at 37°C.

[tex]ms_{water}[/tex]ΔT = 1×4.186×[tex]10^{3}[/tex]×35

                = 1.465×[tex]10^{5}[/tex]J

At the start of meiosis II, the cell exhibits characteristics of a haploid cell preparing for mitosis. It has one set of homologous chromosomes, each with two chromatids, equivalent to a haploid cell in the G₂ phase of interphase.

At the beginning of meiosis II, a cell appears much like a haploid cell preparing to undergo mitosis. After completion of meiosis I, the cell does not duplicate its chromosomes, so at the onset of meiosis II, each dividing cell has only one set of homologous chromosomes, each with two chromatids. This results in half the number of sister chromatids to separate out as a diploid cell undergoing mitosis. In terms of chromosomal content, cells at the start of meiosis II are similar to those of haploid cells in the G₂ phase of interphase, where they are preparing for mitosis.

https://brainly.com/question/10621150

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Answer:

Explanation:

We shall apply conservation of momentum  here because it is a case of inelastic collision

u₁ , u₂ initial velocity of knife and target . v₁ , v₂ be their final velocity.

m₁ u₁ + m₂u₂ = m₁v₁ + m₂v₂

u₂ will be negative as it is coming from opposite direction.

36 x 22.5 - 300 x 2.45 = 22.5 x v₁ + 0

810 - 735 = 22.5 x v₁

v₁ = 3.33 m /s

Answer:

0.2289

Explanation:

Power required to climb= Fv where F is force and v is soeed. We know that F= mg hence Power, P= mgv and substituting 700 kg for m, 9.81 for g and 2.5 m/s for v then

P= 700*9.81*2.5=17167.5 W= 17.1675 kW

To express it as a fraction of 75 kw then 17.1675/75=0.2289 or 22.89%

Answer:

0.2v

Explanation:

Data given,

Diameter=18.5cm

Hence we can calculate the radius as D/2=18.5/2=9.25cm

radius=9.25cm/100=0.0925m

The area is calculated as

[tex]area=\pi r^{2}\\Area=0.0925^{2}*\pi \\Area=0.02688m^{2}\\[/tex]

magnetic field, B=1.3T

time,t=0.18s

The flux is expressed as

[tex]flux=BAcos\alpha \\[/tex]

since the loop is parallel, the angle is 0

Hence we can calculate the flux as

[tex]flux=1.3*0.02688cos(0)\\flux=0.0349Wb\\[/tex]

to determine the emf induced in the loop, we use Faraday law

[tex]E=-N\frac{d(flux)}{dt}\\ E=-0.0349/0.18\\E=0.19V\\E=-0.2v[/tex]

Note the voltage is not negative but the negative sign shows the current flows in other to oppose the flux

Answer:

The boat is approaching the dock at a rate of 2.5 ft/s.

Explanation:

Let the rope length be 'l' at any time 't', the distance of boat from dock be 'b' at any time 't'.

Given:

The height of dock above water (h) = 6 feet

Rate of pull of rope or rate of change of rope is, [tex]\frac{dl}{dt}=2\ ft/s[/tex]

As clear from the question, the height is fixed and only the length 'l' and distance 'b' varies with time 't'.

Now, the above situation represents a right angled triangle as shown below.

Using Pythagoras Theorem, we have:

[tex]l^2=h^2+b^2\\\\l^2=6^2+b^2\\\\l^2=36+b^2----------(1)[/tex]

Now, differentiating the above equation with time 't', we get:

[tex]2l\frac{dl}{dt}=0+2b\frac{db}{dt}\\\\l\frac{dl}{dt}=b\frac{db}{dt}\\\\\frac{db}{dt}=\frac{l}{b}\frac{dl}{dt}------(2)[/tex]

Now, the distance 'b' can be calculated using 'l=10 ft' in equation (1). This gives,

[tex]b^2=10^2-36\\\\b=\sqrt{64}=8\ ft[/tex]

Now, substituting all the given values in equation (2) and solve for [tex]\frac{db}{dt}[/tex]. This gives,

[tex]\frac{db}{dt}=\frac{10}{8}\times 2\\\\\frac{db}{dt}=2.5\ ft/s[/tex]

Therefore, the boat is approaching the dock at a rate of 2.5 ft/s.

Answer:

A) v/ sq. rt. of 2

Explanation:

The speed of the wave in the string is defined as:

[tex]v=\sqrt{\frac{T}{\mu}}[/tex]

Where T is the tension on the string and [tex]\mu[/tex] is the linear density, that is, the mass per unit length:

[tex]\mu=\frac{m}{L}[/tex]

Where m is the mass of the string and L its length. We have [tex]m'=2m[/tex], [tex]T'=T[/tex] and [tex]L'=L[/tex]:

[tex]v'=\sqrt\frac{T'}{m'/L'}\\v'=\sqrt\frac{T}{2m/L}\\v'=\frac{1}{\sqrt2}\sqrt\frac{T}{m/L}\\v'=\frac{v}{\sqrt2}[/tex]

Explanation:

Below is an attachment containing the solution.