The sound source of a ship’s sonar system operates at a frequency of 22.0 kHz . The speed of sound in water (assumed to be at a uniform 20∘C) is 1482 m/s . What is the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling straight toward the ship at 4.95 m/s ? Assume that the ship is at rest in the water.

Your target variable is Δf, the magnitude of the difference in frequency between the waves emitted from the sonar device and the waves received by the device after reflecting off the whale. Write an expression for Δf in terms of the relevant frequencies using the subscript notation introduced above.

Express your answer in terms of some or all of the variables fLe, fLr, fSe, and fSr.

Δf =_______________.

This is a complex thermodynamics problem about a steam power plant's ideal reheat Rankine cycle. It requires calculation of pressure at reheat stage, total heat input rate and thermal efficiency by using correct thermodynamic practices. Due to the complexity, expert understanding and use of steam tables is necessary.

This is a thermodynamics problem associated with the ideal reheat Rankine cycle in a steam power plant. Due to the complex nature of the problem, the aid of thermodynamics and steam table reference books is required to solve it.

Under these ideal cycle conditions, calculating assumed pressure drops and using the steam tables, we can estimate the reheat pressure during the cycle. The exact figures would be subject to critical examination and calculation based on precise cycle parameters following real-life engineering practices.

For part (b), the total rate of heat input can be calculated using the mass flow rate and specific enthalpies at different stages of the cycle. The thermal efficiency for part (c) can be obtained by dividing the net work output by the total heat input.

An actual T-s diagram for the Rankine cycle would aid in visualizing the process but cannot be drawn here. Basically, the cycle is plotted with entropy(s) on the x-axis and temperature(T) on the y-axis, showing the expansion, reheat, and condensation stages of the steam.

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The Ideal Reheat Rankine Cycle is a model for determining efficiency in steam power plants. The pressure at which reheating takes place is typically assumed to be at the midpoint of the high and low-pressure limits. The total heat rate input in the boiler and thermal efficiency cannot be determined without more detailed specification of the conditions.

This question is related to the concepts of thermodynamics in the field of Mechanical Engineering. The Ideal Reheat Rankine Cycle is a model used to predict the performance of steam turbine systems, and we will use principles from this model to answer your questions.

(a) The pressure at which reheating takes place cannot be definitively stated without more specific information like the temperature at the exit of the high-pressure turbine or the entropy at key points in the cycle. However, it’s commonly assumed in practice to occur at the mid-point of the high and low-pressure limits, which would be 7.5 MPa or 7500 kPa.

(b) The total rate of heat input in the boiler cannot be definitively stated without more specific information such as the specific enthalpies at key points in the cycle.

(c) Thermal efficiency of the cycle also requires further specific information such as the enthalpy or temperature at key points in the cycle to compute.

Moreover, drawing a T-s (Temperature vs Entropy) diagram with respect to the saturation lines would need a graphical interface, so it's not possible to illustrate it here.

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Answer:

300000 N

Explanation:

We are given that

Mass of jumbo jet=300,000kg

Acceleration of jet=[tex]4m/s^2[/tex]

We have to find the force generated by each of its four engines.

We know that

Force,F =ma

Total force exert by four engines=4F

[tex]4F=300000\times 4[/tex]

[tex]F=\frac{300000\times 4}{4}=300000N[/tex]

Hence, the force generated by each of its four engines=300000 N

Answer:

Electric force will be equal to [tex]2\times 10^{-4}N[/tex]

Explanation:

We have given charge [tex]q=2\mu C=2\times 10^{-6}C[/tex]

Electric field will be [tex]E=100N/C[/tex]

We have to find the magnitude of force

Electric force is the multiplication of electric field and charge

So electric force [tex]F=qE=2\times 10^{-6}\times 100=2\times 10^{-4}N[/tex]

Electric force will be equal to [tex]2\times 10^{-4}N[/tex]

Answer:

(a) the net charge inside the closed surface.

Explanation:

In Gauss' Law, Qencl refers to the net charge inside the Gaussian surface. This surface is usually taken as a symmetric geometric surface, but this is merely for simplicity. Gauss' Law holds for any closed surface. Inside this surface there can be insulators as well as conductors. Regardless of the geometry or the materials inside, Qencl refers to the net charge inside the closed surface. The charge outside the surface is irrelevant for Gauss' Law, therefore all the charge in the physical system is not included in Gauss' Law.

A) Intensity: [tex]4.8 W/m^2[/tex]

B) Intensity: [tex]2.1 W/m^2[/tex]

C) Total intensity: [tex]13.8 W/m^2[/tex]

D) Distance: [tex]1.38\cdot 10^5 m[/tex]

Explanation:

A)

The relationship between intensity of a sound and power emitted is given by

[tex]I=\frac{P}{A}[/tex]

where

I is the intensity

P is the power

A is the surface area at the distance considered

For the speaker in this problem:

P = 60 W

The distance is r = 1.0 m, so the area to consider is the surface of a sphere with this radius:

[tex]A=4\pi r^2 = 4\pi(1.0)^2=12.6 m^2[/tex]

Therefore, the intensity is

[tex]I=\frac{60}{12.6}=4.8 W/m^2[/tex]

B)

For this problem, we can use the same equation we used before:

[tex]I=\frac{P}{A}[/tex]

where in this case, we have:

P = 60 W is the power of the speaker

r = 1.5 m is the distance considered

Therefore, the area of the spherical surface is

[tex]A=4\pi r^2 = 4\pi(1.5)^2=28.3 m^2[/tex]

And so, the intensity here is

[tex]I=\frac{60}{28.3}=2.1 W/m^2[/tex]

C)

In this problem, we have to consider 4 speakers. In order to find the total intensity, we have to add the intensity of each speakers.

For the two front speakers, we have

[tex]P=60 W[/tex]

r = 1.0 m

So we have already calculated their intensity in part A), and it is

[tex]I_1 = I_2 = 4.8 W/m^2[/tex]

For the two rear speakers, we have

[tex]P=60 W[/tex]

r = 1.5 m

So their intensity has been calculated in part B),

[tex]I_3 = I_4 = 2.1 W/m^2[/tex]

Therefore, the total intensity is

[tex]I=I_1 + I_2 + I_3 + I_4 = 4.8+4.8+2.1+2.1=13.8 W/m^2[/tex]

D)

In this case, we want to find the distance r at which the intensity is

[tex]I=10^{-12} W/m^2[/tex]

Using four speakers with power

P = 0.06 W

Since we have 4 speakers, the intensity due to each speaker at the location considered must be

[tex]I'=\frac{I}{4}=\frac{10^{-12}}{4}=2.5\cdot 10^{-13} W/m^2[/tex]

Using the usual equation, we find the area:

[tex]A=\frac{P}{I'}=\frac{0.06}{2.5\cdot 10^{-13}}=2.4\cdot 10^{11} m^2[/tex]

And so, we can find what is the corresponding distance:

[tex]A=4\pi r^2\\r=\sqrt{\frac{A}{4\pi}}=\sqrt{\frac{2.4\cdot 10^{11}}{4\pi}}=1.38\cdot 10^5 m[/tex]

So, the person must be at 138 km.

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The intensity of sound waves can be computed by using the equation I = P / (4πr²). For the minimum discernible intensity, we employ a rearranged version of the same formula to calculate the distance from the car stereo at the threshold of hearing.

The question is about the calculation of sound intensity produced by a car stereo featuring four speakers, each rated at 60 Watts, at various distances. To calculate the intensity (I) of the sound waves at different distances, we use the equation I = P / (4πr²) where P represents power and r is the distance.

For part D, to find the distance (d) at which sound from the stereo could still be discerned, we rearrange the intensity equation to solve for distance, d = √(P / (4πI)). We substitute P with the sound produced (0.06 W) and I with the minimum discernible intensity (10-12 W/m²). Disclaimer: Since external factors like absorption or diffusion are not taken into account, and the car stereo is not treated as a perfect point source emitter, these values serve as approximation.

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Answer

given,

weight = 1000 lbf

g = 32.174 ft/s²

mass =[tex] \dfrac{1000}{32.174}[/tex]

m = 31 slug

1 slug = 14.593 kg

m = 31 x 14.593

m = 452.383 Kg

b) weight on moon

  W = m g

   W = 452.383 x 1.62

   W= 732.86 N

c) we know,

   F = m  a

  400 lbf = 31 slugs x a

  a = 12.90 ft/s²

1 ft = 0.304 m

  a = 3.92 m/s²

Final answer:

This answer covers calculating mass in kg, weight on the moon, and acceleration with a force on both Earth and the moon.

Explanation:

Mass Calculation:

Weight on Moon:

Acceleration with Force:

Answer:

b

Explanation:

Answer:

B

Explanation:

egde test 2023

Answer:

a)[tex]p=1.89x10^{-27}kg.m.s^{-1}[/tex]

b)[tex]v=0.565\frac{m}{s}[/tex]

Explanation:

First, we need to obtain the linear momentum of the photons of wavelength 350nm.

We are going to use the following formula:

[tex]\lambda=\frac{h}{p}\\Where:\\\lambda=wavelength\\h=placnk's\_constant\\p=Linear\_momentum[/tex]

So the linear momentum is given by:

[tex]p=\frac{h}{\lambda}\\\\p=\frac{6.626x10^{-34}J.s}{350x10^{-9}m}\\\\p=1.89x10^{-27}kg.m.s^{-1}[/tex]

Having the linear momentum of the photon, we can calculate the speed of the hydrogen molecule to have the same momentum, we can use the classic formula for that:

[tex]p=m.v[/tex]

[tex]where:\\m=mass\\v=speed\\p=linear\_momentum[/tex]

The mass of the hydrogen molecule is given by:

[tex]m=2*(1.0078x10^{-3}\frac{kg}{mol}})x\frac{1}{6.022x10^{23}mol}[/tex]

[tex]3.35x10^{-27}kg[/tex]

What we've done here is to use the molecular weight of the hydrogen, and covert it kilograms, we had to multiply by two because the hydrogen molecule is found in pairs.

so:

[tex]v=\frac{p}{m}\\\\v=\frac{1.89x10^{-27}kg.m.s^{-1}}{3.35x10^{-27}kg}\\\\v=0.565\frac{m}{s}[/tex]

(a) The linear momentum of the photon is 1.89 x 10⁻²⁷ kgm/s.

(b) The speed of hydrogen atom with same momentum is 2,079.35 m/s.

The linear momentum of the photon is calculated as follows;

P = h/λ

P = (6.63 x 10⁻³⁴) / (350 x 10⁻⁹)

P = 1.89 x 10⁻²⁷ kgm/s

p = mv

v = p/m

v = (1.89 x 10⁻²⁷ ) / (9.11 x 10⁻³¹)

v = 2,079.35 m/s

Thus, the speed of hydrogen atom with same momentum is 2,079.35 m/s.

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Answer:

84%

Explanation:

g = Acceleration due to gravity = 9.81 m/s²

[tex]y_0=1\ m[/tex]

x = 10 m

t = Time taken

[tex]v_0[/tex] = 3.5 m/s (assumed, as it is not given)

[tex]A_0=\pi 1.5^2[/tex]

We have the equation

[tex]y=y_0+ut+\dfrac{1}{2}gt^2\\\Rightarrow 0=y_0-\dfrac{1}{2}gt^2\\\Rightarrow t=\sqrt{\dfrac{2y_0}{g}}\\\Rightarrow t=\sqrt{\dfrac{2\times 1}{9.81}}\\\Rightarrow t=0.45152\ s[/tex]

[tex]x=x_0+vt\\\Rightarrow 10=0+v0.45152\\\Rightarrow v=\dfrac{10}{0.45152}\\\Rightarrow v=22.14741\ m/s[/tex]

From continuity equation we have

[tex]Av=A_0v_0\\\Rightarrow A=\dfrac{A_0v_0}{v}\\\Rightarrow A=\dfrac{\pi 1.5^2\times 3.5}{22.14741}\\\Rightarrow A=1.11706\ cm^2[/tex]

Fraction is given by

[tex]f=\dfrac{A_0-A}{A_0}\times 100\\\Rightarrow f=\dfrac{\pi 1.5^2-1.11706}{\pi 1.5^2}\times 100\\\Rightarrow f=84.196\ \%\approx 84\ \%[/tex]

The fraction is 84%

A fraction of the cross-sectional area of the hose hole that Isabella must cover is 84%.

Given the following data:

Vertical distance = 1.0 meters.

Horizontal distance = 10.0 meters.

Radius = 1.5 cm.

Vertical speed = 3.5 m/s.

The time taken to reach a maximum height is given by this formula:

[tex]H=\frac{1}{2} gt^2\\\\t=\sqrt{\frac{2H}{g} } \\\\t=\sqrt{\frac{2\times 1.0}{9.8} }[/tex]

t = 0.452 seconds.

For the velocity required, we have:

[tex]x=x_o+Vt\\\\10=0+V0.452\\\\V=\frac{10}{0.452}[/tex]

V = 22.12 m/s.

From continuity equation, we have:

[tex]A=\frac{A_0V_0}{V} \\\\A=\frac{\pi r^2V_0}{V}\\\\A=\frac{\pi1.5^2 \times 3.5}{22.12} \\\\A=\frac{24.7433}{22.12}[/tex]

A = 1.118 cm^2.

Now, an expression for the fraction of the cross-sectional area is given by:

[tex]F=\frac{A_0-A}{A_0} \times 100\\\\F=\frac{7.0695-1.118}{7.0695} \times 100\\\\F=\frac{5.9515}{7.0695} \times 100\\\\F=0.8419 \times 100[/tex]

F = 84.19 ≈ 84%.

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Answer:

42.9 cm

Explanation:

given,

speed of sound, v = 340 m/s

Frequency of tuning fork, f = 198 Hz

The length of the shortest air column closed at one end.

this is the case of the standing wave.

L = N λ

N = the number of complete sine waves in the standing wave.

The standing wave in the problem is the first harmonic of a pipe open at one end.

N = 1/4

we know,

v = f λ

340 = 198 x λ

λ = 1.717 m

now,

L = N λ

[tex]L = \dfrac{1}{4}\times 1.717[/tex]

[tex]L = 0.429\ m[/tex]

   L = 42.9 cm

minimum length of the required pipe is 42.9 cm.

did you find the answer?

From Doppler effect we have that the frequency observed for the relation between the velocities is equivalent to the frequency observed. That is mathematically,

[tex]F_r = \frac{v}{v+v_s}F_s[/tex]

Here,

Speed of sound in water [tex]v = 1522m/s[/tex]

The Dolphin swims directly away from the observer with a velocity [tex]v_s = 8.5m/s[/tex]

Observed frequency of the clicks produced by the dolphin [tex]F_r = 2770Hz[/tex]

Replacing we have,

[tex]F_r = \frac{v}{v+v_s}F_s[/tex]

[tex]F_s = \frac{v+v_s}{v}[/tex]

[tex]F_s = 2770 (\frac{1522}{1522+8.5})[/tex]

[tex]F_s = 2754.61Hz[/tex]

Therefore the frequency emitted by the dolphin is 2754.61Hz

Answer:

The charged balloon’s mass will be almost equal to the original mass

Explanation:

When an electrically neutral balloon is rubbed on cloth, it losses some electron and becomes positively charged.

The balloon becomes positively charged by the removal of electrons (electrons from the cloth repels electron in the balloon).

The mass of positively charged balloon, will be equal to the original mass minus the mass of electrons removed.

Since Electrons have negligible mass, the removal of electrons from the neutral balloon will have little effect on the original mass of the balloon.

Therefore, the charged balloon’s mass will be almost equal to the original mass

Answer:

1008.33 W.

Explanation:

Power: This can be defined as the rate at which energy is consumed or dissipated. The S.I unit of power is Watt (W).

P = E/t.......................... Equation 1

Where P = Energy, E = Energy, t = time.

But from the question,

E = 1/2mΔv²................... Equation 2

where m = mass of the sprinter, Δv = change in velocity of the sprinter = final velocity - initial velocity.

Substitute equation 2 into equation 1

P = 1/2mΔv/t....................... Equation 3

Given: m = 50 kg, Δv = 11-0 = 11 m/s, t = 3.0 s.

Substitute into equation  3

P = 1/2(50)(11)²/3

P = 25(121)/3

P = 1008.33 W.

Thus the power output = 1008.33 W.

Final answer:

The power output of a 50-kg sprinter who accelerates from 0 to 11 m/s in 3.0 s is 1008.33 Watts or approximately 1.35 horsepower.

Explanation:

To calculate the power output of a 50-kg sprinter who accelerates from 0 to 11 m/s in 3.0 s, we use the work-energy principle and the definition of power. The work done on the sprinter is equal to the change in kinetic energy, and power is the work done per unit time.

The kinetic energy (KE) at the start is 0 since the sprinter starts from rest. The kinetic energy at the end is KE = 1/2 x mass x velocity² = 1/2 x 50 kg x (11 m/s)². After calculating the kinetic energy, we get KE = 1/2 x 50 x 121 = 3025 Joules.

Now, we find the power by dividing the work by the time interval: Power = Work / Time = 3025 J / 3.0 s = 1008.33 Watts.

To convert watts to horsepower, use the conversion 1 horsepower = 746 watts. Therefore, Power in horsepower = 1008.33 W / 746 W/hp = approximately 1.35 hp.

Answer:

The magnitude of the magnetic field vector is 1.91T and is directed towards the east.

The steps to the solution can be found in the attachment below.

Explanation:

For the charge to remain in the the earth' gravitational field the magnetic force on the charge must be equal to the earth's gravitational force on the charge and must act opposite the direction of the earth's gravitational force.

Fm = Fg

qvBSin(theta) = mg

Where q = magnitude of charge

v = magnitude of the velocity vector = 4 x10^4 m/s

B = magnitude of the magnetic field vector

theta = the angle between the magnetic field and velocity vectors = 90°

m = mass of the charge = 0.195g

g = acceleration due to gravity =9.8m/s²

On substituting the respective values of all variables in the equation (1) above

B = 1.91T

The direction of the magnetic field vector was found by the application of the right hand rule: if the thumb is pointed in the direction of the magnetic force and the index finger is pointed in the direction of the velocity vector, the middle finger points in the direction of the magnetic field.

Below is the step by step procedure to the solution.

Final answer:

The magnitude of the minimum magnetic field that will keep the particle moving in the Earth's gravitational field in the same horizontal, northward direction can be calculated using the equation for magnetic force. We need to find the minimum value of B that produces a force greater than or equal to the gravitational force acting on the particle. By setting up the equation qvBsinθ ≥ mg and solving for B, we can find the minimum magnetic field strength required.

Explanation:

The magnitude of the minimum magnetic field that will keep the particle moving in the Earth's gravitational field in the same horizontal, northward direction can be calculated using the equation for magnetic force. The force on a moving charged particle in a magnetic field is given by the equation F = qvBsinθ, where F is the magnetic force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field. In this case, we can assume that the angle between the velocity and the magnetic field is 90 degrees, as the particle is moving horizontally northward. Therefore, to find the minimum magnetic field that keeps the particle moving in this direction, we need to find the minimum value of B that produces a force greater than or equal to the gravitational force acting on the particle.

Let's take the example given in Example 22.1, where a glass rod with a positive charge of 20 nC is thrown with a horizontal velocity of 10 m/s due west in a place where the Earth's magnetic field is due north parallel to the ground. The force on the rod due to the Earth's magnetic field can be calculated using the equation F = qvBsinθ, where q is the charge of the rod (20 nC), v is the velocity of the rod (10 m/s), B is the magnetic field strength (unknown), and θ is the angle between the velocity and the magnetic field (90 degrees). The force on the rod should be equal to or greater than the gravitational force acting on it to keep it moving in the same horizontal, northward direction. Therefore, we can set up the equation F ≥ mg, where F is the force on the rod, m is the mass of the rod, and g is the acceleration due to gravity. Substituting the values, we get qvBsinθ ≥ mg. Solving for B, we get B ≥ mg / qvsinθ. Plugging in the given values, we can find the minimum magnetic field strength required to keep the particle moving in the Earth's gravitational field in the same horizontal, northward direction.

Answer:

2.92 x 10¹² electrons

Explanation:

given,

distance between two plastic ball, r = 17 cm

                                      r = 0.17 m

Force of attraction = F = 68 mN

                F = 0.068 N

number of electron transferred from one ball to another.

using Coulomb Force equation

[tex]F = \dfrac{kq^2}{r^2}[/tex]

[tex]0.068 = \dfrac{9\times 10^9\times q^2}{0.17^2}[/tex]

q² = 2.1835 x 10⁻¹³

q = 4.67 x 10⁻⁷ C

now, number of electron

 [tex]N = \dfrac{q}{e}[/tex]

e is the charge of electron which is equal to 1.6 x 10⁻¹⁹ C

  [tex]N = \dfrac{4.67\times 10^{-7}}{1.6\times 10^{-19}}[/tex]

       N = 2.92 x 10¹² electrons

electrons were transferred from one ball to the other is 2.92 x 10¹²

Field strength is directly proportional to the square of charge. The charge on the given plastic ball is [tex]4.67 \times 10^{-7} \rm \ C[/tex]

[tex]F = \dfrac {kQ^2}{r^2}[/tex]

Where,

[tex]F[/tex]- field strength = 68 mN = 0.06 N

[tex]Q[/tex]- charge

[tex]r[/tex]- distance =  17 cm =0.17 m

[tex]k[/tex]- constant = 9x10⁹

Put the values in the formula,

[tex]0.068 = \dfrac{9\times 10^9 \rimes Q^2}{0.017^2}\\\\q^2 = 2.1835 \times 10^{-13}\\\\q = 4.67 \times 10^{-7} \rm \ C[/tex]

Therefore, the charge on the given plastic ball is [tex]4.67 \times 10^{-7} \rm \ C[/tex].

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Answer:

[tex]13.5 rad/s^2[/tex]

Explanation:

39 revolutions = 39 * 2π = 245 rad

Let [tex]\omega_0[/tex] be the initial angular velocity of the wheel before the 10 s interval. We have the following equation of motion for angular velocity

[tex]\omega = \omega_0 + \alpha t[/tex]

where [tex]\omega = 92 rad/s[/tex] is the final angular velocity of the rotating wheel. [tex]\alpha[/tex] is the constant angular acceleration of the wheel, which we are looking for, and t = 10s is the duration time that the wheel rotates

[tex]92 = \omega_0 + 10\alpha[/tex]

[tex]\omega_0 = 92 - 10\alpha[/tex]

We also have the following equation of motion for angles

[tex]\theta = \omega_0t + \alpha t^2/2[/tex]

where [tex]\theta = 245 rad[/tex] is the total angles rotated

we can also substitute [tex]\omega_0 = 92 - 10\alpha[/tex]

[tex]245 = 10(92 - 10\alpha) + \alpha 10^2/2[/tex]

[tex]245 = 920 - 100\alpha + 50\alpha[/tex]

[tex]50\alpha = 675 [/tex]

[tex]\alpha = 675 / 50 = 13.5 rad/s^2[/tex]

Answer:

318K

113°F

Explanation:

45°C = 45 + 273K = 318K

45°C = (45 × 9/5) + 32 = 81 + 32 = 113°F

Answer:

The maximum potential energy of the system is 0.2 J

Explanation:

Hi there!

When the spring is stretched, it acquires potential energy. When released, the potential energy is converted into kinetic energy. If there is no friction nor any dissipative forces, all the potential energy will be converted into kinetic energy according to the energy conservation theorem.

The equation of elastic potential energy (EPE) is the following:

EPE = 1/2 · k · x²

Where:

k = spring constant.

x = stretching distance.

The elastic potential energy is maximum when the block has no kinetic energy, just before releasing it.

Then:

EPE = 1/2 · 40 N/m · (0.1 m)²

EPE = 0.2 J

The maximum potential energy of the system is 0.2 J

The maximum potential energy of the spring system, given a spring constant of 40 N/m and a displacement of 0.1 m, is calculated using the formula PEmax = (1/2)kx2, and the result is 0.2 J.

When dealing with a spring system in physics, we use Hooke's Law, which states the force exerted by a spring is directly proportional to the amount it is stretched or compressed and is given by F = -kx, where k is the spring constant and x is the displacement from equilibrium. The potential energy stored in such a system can be calculated using the formula PEmax = (1/2)kx2.

In this case, given a spring constant k = 40 N/m and a maximum displacement x = 0.1 m, the potential energy at maximum compression or stretch is:

PEmax = (1/2)kx2 = (1/2)(40 N/m)(0.1 m)2 = (1/2)(40)(0.01) = 0.2 J.

Therefore, the maximum potential energy of the oscillating system is 0.2 J.

Answer:

The following are true:

A satellite's motion is independent of its mass.

The launch speed of a satellite determines the shape of its orbit around Earth.

Explanation:

A satellite's motion is independent of its mass.

The speed of a satellite can be determined by means of the Universal law of gravity:

[tex]F = G\frac{M\cdot m}{r^{2}}[/tex] (1)

Where G is the gravitational constant, M and m are masses of the two objects and r is the distance between them.

In equation 1, Newton's second law can be replaced:

[tex]F = m\cdot a[/tex]

[tex]m. a = G\frac{M\cdot m}{r^{2}}[/tex]   (2)

Since it is a circular motion, the centripetal acceleration can be used:

[tex]a = \frac{v^{2}}{r}[/tex] (3)

Then, equation 3 can be replaced in equation 2:

[tex]m\frac{v^{2}}{r} = G\frac{M\cdot m}{r^{2}}[/tex]  (4)

In this case, m is the satellite's mass and M is the Earth mass. Therefore, v can be isolated from equation 4:

[tex]v^{2} = G\frac{M\cdot m r}{mr^{2}}[/tex]

[tex]v^{2} =\frac{G M}{r}[/tex]

[tex]v = \sqrt{\frac{G M}{r}}[/tex]

Where G is the gravitational constant, M is the mass of the Earth and r is the orbital radius of the satellite.

Notice, how the speed of the satellite does not depend in its mass, only in the Earth mass and its orbital radius.

The launch speed of a satellite determines the shape of its orbit around Earth.

Depending on the launch speed the satellite can reach a lower or higher height above the surface of the Earth and, therefore, its orbital radius will be bigger or smaller according with that height.

Remember that the orbital radius for the satellite will be the sum of the Earth radius and the height above the surface.      

Key term:

Geosynchronous satellite: It is a satellite with the same orbital period as Earth rotation period (24 hours).  

Answer:

R=12 m

Explanation:

I have drawn a vector form which I attached here.Please first go through that

Given Data

y (Tree Taller) = 9.0 m

x(Distance from center to edge is)= 8.5 m

To find

R(magnitude of the butterfly's displacement

)

Solution

[tex]R=\sqrt{x^{2} +y^{2} }\\R=\sqrt{9^{2}+8.5^{2}  }\\ R=12.379m[/tex]

Convert to two significant figures

R=12 m

The butterfly's displacement, when it moves from the tree to the flower, is approximately 19m. This is determined using the Pythagorean theorem, which is applied to the '9m' height difference between the tree and flower, and '17m' width of the garden.

To calculate the magnitude of the butterfly's displacement, we need to use the Pythagorean theorem, which establishes a relationship in any right triangle. The vertical height of the tree is 9m, which forms one side of the right triangle. The horizontal distance across the garden (or width of the garden) is 17m, forming the other side of the right triangle.

Applying the Pythagorean theorem (a^2 + b^2 = c^2), where 'a' and 'b' are the sides and 'c' is the hypotenuse (in this case, the butterfly's displacement), we get:

Displacement = √[(9m)^2 + (17m)^2]

So, the displacement of the butterfly is approximately 19 m, when rounded to two significant figures.

Learn more about Displacement here:

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Answer:

[tex]d=2.5367\times 10^{-6}\ cm[/tex]

Explanation:

Given:

Now the distance moved by the tectonic plate in the stipulated times:

[tex]d=v.t[/tex]

[tex]d=\frac{1}{365\times 12\times 3600} \times 80[/tex]

[tex]d=2.5367\times 10^{-6}\ cm[/tex]

Tectonic plates are the mass rock from of the earth's uppermost mantle and the crust which show similar behavior of movement with respect to the other such groups of lithosphere.

Answer:

156.67 m/s

0.45676 times the speed of sound

Explanation:

Distance from the ground = 23.5 km = 23500 m

Time taken by the blast waves to reach the ground = [tex]2\ minutes\ 30\ seconds=2\times 60+30=150\ s[/tex]

Spedd of the wave would be

[tex]Speed=\dfrac{Distance}{Time}\\\Rightarrow v_b=\dfrac{23500}{150}\\\Rightarrow v-b=156.67\ m/s[/tex]

The velocity of the blast wave is 156.67 m/s

v = Velocity of sound = 343 m/s

[tex]\dfrac{v_b}{v}=\dfrac{156.67}{343}\\\Rightarrow v_b=v\dfrac{156.67}{343}\\\Rightarrow v_b=0.45676v[/tex]

The blast wave is 0.45676 times the speed of sound

The average velocity of the blast wave can be calculated using the distance traveled and time taken, resulting in 156.7 m/s. This velocity is less than half the speed of sound at sea level.

The average velocity of the blast wave can be calculated by dividing the distance traveled by the time taken. The distance is the altitude where the explosion occurred, 23.5 km. Converting 2 minutes 30 seconds to seconds gives a time of 150 seconds.

So, velocity = distance / time = 23.5 km / 150 s = 0.1567 km/s = 156.7 m/s.Comparing this to the speed of sound at sea level, which is 343 m/s, the blast wave's velocity of 156.7 m/s is less than half the speed of sound.

Answer:

250 kg/m3

Explanation:

The total volume of the raft is length times width times height

V = lwh = 2 * 3 * 0.5 = 3 m cubed

The volume of the raft that is submerged in water is 1/4 of total volume

3 /4 = 0.75 m cubed

Let water density = 1000 kg/m cubed and g = 10 m/s2

The buoyant force is equal to the weight of water displaced by the raft

F = 0.75 * 1000 * 10 = 7500 N

This force is balanced by the raft weight, so the weight of the raft is also 7500N

Mass of raft is 7500 / g = 7500 / 10 = 750 kg

Raft density is mass divided by volume = 750 / 3 = 250 kg/m3

Final answer:

To determine the actual rate of heat input to the geothermal power plant, calculate the heat input using the provided formula. The actual thermal efficiency can be found by dividing the net power output by the heat input. The actual rate of heat rejection can then be calculated as the difference between the heat input and the net power output. To determine the power output if the geothermal water leaves the plant at a different temperature while maintaining its thermal efficiency, use the provided formula with the appropriate values.

Explanation:

The actual rate of heat input to the geothermal power plant can be calculated using the formula:

Heat input = mass flow rate * specific heat capacity * (hot water temperature - environment temperature)

Given that the mass flow rate is 210 kg/s, the specific heat capacity is 4.186 J/g°C, the hot water temperature is 150°C, and the environment temperature is 25°C, we can substitute these values into the formula to find the heat input.

The actual thermal efficiency of the power plant can be calculated using the formula:

Thermal efficiency = (Net power output / Heat input) * 100%

Given that the net power output is 8000 kW and we have already calculated the heat input, we can substitute these values into the formula to find the actual thermal efficiency. The maximum possible thermal efficiency can be calculated as the Carnot efficiency, which is the maximum possible efficiency for a heat engine operating between two temperatures.

The actual rate of heat rejection from the power plant can be calculated as the difference between the heat input and the net power output.

To find the power output if the geothermal water leaves the plant at 40°C and maintain its thermal efficiency, we can use the formula:

Power output = (Heat input - Heat rejection) * (Net power output / Heat input)

Substituting the appropriate values into the formula will give us the desired power output.

To solve this problem we will apply the concepts related to balance. Since the force applied is 3 times the weight, and the weight is defined as the multiplication between mass and gravity, we will have that the dynamic equilibrium ratio would be given by the relation,

[tex]\sum F = ma[/tex]

[tex]3mg-mg = ma[/tex]

Rearranging to find a,

[tex]a = 2g[/tex]

Using the linear motion kinematic equations, which express that the final velocity of the body, and in the absence of initial velocity, is equivalent to the product between 2 times the acceleration by the distance traveled, that is

[tex]v^2 = 2as[/tex]

[tex]v^2 = 2(2g)(0.18)[/tex]

[tex]v^2 = 2(2*9.8)(0.18)[/tex]

[tex]v = 2.66m/s[/tex]

Therefore the upward speed is 2.66m/s

Answer:

D

Explanation:

Ball A is a non positively charged non metal while ball B is metal ball.

Given: The ball B positive charge of small magnitude

To prove: Balls will attract each other

IN this condition because of induction negative charges on the sphere B move to the side closer to sphere A,(induction charging) while the positive charges move to the side further away from sphere A. The polarization of charge on B will cause a greater attractive force than the repulsion of the like charges.

Hence the correct answer will be D .

Answer:

The force constant of the spring is 317.8 N/m.

Explanation:

Given that,

Frequency [tex]f=7.0\times10^{13}\ Hz[/tex]

We need to calculate the reduced mass

Using formula of reduced mass

[tex]\mu=\dfrac{m_{H}m_{I}}{m_{H}+m_{I}}[/tex]

Where, [tex]m_{H}[/tex]= atomic mass of H

[tex]m_{I}[/tex]= atomic mass of I

Put the value into the formula

[tex]\mu=\dfrac{1\times126.9}{1+126.9}[/tex]

[tex]\mu=0.99\ u[/tex]

[tex]\mu=0.99\times1.66\times10^{-27}\ Kg[/tex]

[tex]\mu=1.643\times10^{-27}\ kg[/tex]

We need to calculate the force constant of the spring

Using formula of frequency

[tex]f=\dfrac{1}{2\pi}\times\sqrt{\dfrac{k}{\mu}}[/tex]

[tex]k=f^2\times 4\pi^2\times\mu[/tex]

Put the value into the formula

[tex]k=(7.0\times10^{13})^2\times4\pi^2\times1.643\times10^{-27}[/tex]

[tex]k=317.8\ N/m[/tex]

Hence, The force constant of the spring is 317.8 N/m.

Answer:

The force constant of the spring is 317.8 N/m.

Explanation:

hope it helped <3

To solve this problem we will apply the concepts related to the Electrostatic Force given by Coulomb's law. This force can be mathematically described as

[tex]F = \frac{kq_1q_2}{d^2}[/tex]

Here

k = Coulomb's Constant

[tex]q_{1,2} =[/tex] Charge of each object

d = Distance

Our values are given as,

[tex]q_1 = 1 \mu C[/tex]

[tex]q_2 = 6 \mu C[/tex]

d = 1 m

[tex]k =  9*10^9 Nm^2/C^2[/tex]

a) The electric force on charge [tex]q_2[/tex] is

[tex]F_{12} = \frac{ (9*10^9 Nm^2/C^2)(1*10^{-6} C)(6*10^{-6} C)}{(1 m)^2}[/tex]

[tex]F_{12} = 54 mN[/tex]

Force is positive i.e. repulsive

b) As the force exerted on [tex]q_2[/tex] will be equal to that act on [tex]q_1[/tex],

[tex]F_{21} = F_{12}[/tex]

[tex]F_{21} = 54 mN[/tex]

Force is positive i.e. repulsive

c) If [tex]q_2 = -6 \mu C[/tex], a negative sign will be introduced into the expression above i.e.

[tex]F_{12} = \frac{(9*10^9 Nm^2/C^2)(1*10^{-6} C)(-6*10^{-6} C)}{(1 m)^{2}}[/tex]

[tex]F_{12} = F_{21} = -54 mN[/tex]

Force is negative i.e. attractive

To develop this problem we will apply the relationship of density, such as the unit of mass per unit volume of a body. For this relationship we will use the known constants of the value of the land's mass and its respective radius. These values will be converted from kilograms to grams and meters to centimeters respectively. We will find the volume through the geometric relationship of the sphere using the radius of the earth.

The mass of the Earth is given as

[tex]m_E = 5.9722*10^{24}kg (\frac{1000g}{1kg}) = 5.9722*10^{27}g[/tex]

The radius of the Earth is

[tex]r_E = 6.3781*10^6m (\frac{100cm}{1m}) = 6.3781*10^8cm[/tex]

Using the geometric value of volume for a sphere, and using the radius of the earth, as the radius of that sphere we have to

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

Replacing,

[tex]V_E = \frac{4}{3} \pi (6.3781*10^8)^3[/tex]

[tex]V_E = 1.09*10^{27}cm^3[/tex]

The expression for the density of the Earth is

[tex]\rho = \frac{m_E}{V_E}[/tex]

Replacing,

[tex]\rho = \frac{5.9722*10^{27}}{1.09*10^{27}}[/tex]

[tex]\rho = 5.48g/cm^3[/tex]

Therefore the average density of the earth is [tex] 5.48g/cm^3[/tex]

The answer provides the speed of the putty just before striking the ceiling and the time it takes for the putty to reach the ceiling. The speed is found to be 5.79 m/s and the time taken is calculated to be 1.5 seconds.

The speed of the putty just before it strikes the ceiling:

Using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is acceleration, and s is displacement, the speed is found to be 5.79 m/s.

The time it takes for the putty to reach the ceiling:

By using the equation v = u + at, where t is time, a is acceleration, u is initial velocity, and v is final velocity, the time taken is calculated to be 1.5 seconds.