A spring with k = 35.5 N/m has a mass of 5.50 kg attached to it. An external force F = (4.40 N)sin[(6.80 s−1)t] drives the spring mass system so that it oscillates without any resistive forces. What is the amplitude of the oscillatory motion of the spring-mass system?

Answers

Answer 1

Answer:

A = 0.02 m

Explanation:

The spring constant, k = 35.5 N/m

The attached mass, m = 5.50 kg

The expression for the external force, F =  (4.40 N)sin[(6.80 s⁻¹)t].....(1)

The general expression for the external force, F = F₀ sin (wt).............(2)

Comparing equations (1) and (2):

The forced frequency, \(\omega = 6.80 rad/s\)

F₀ = 4.40 N

The natural frequency can be calculated using the formula:

\(\omega_0 = \sqrt{\frac{k}{m} } \\\\\omega_0 = \sqrt{\frac{35.5}{5.5} } \\\\\omega_0 = 2.54 rad/s\)

The amplitude of oscillation of a spring-mass system in the steady state:

\(A = \frac{F_0}{m(\omega^2 - \omega_o^2)} \\\\A = \frac{4.4}{5.5(6.8^2 - 2.54^2)} \\\\A = 0.02 m\)


Related Questions

How long has a victim been dead if his body temperature was 89.2°F?

Answers

The body loses 1.5 degrees of temperature per hour. Depending on the environment of course.
The body’s regular temperature is 98.6 so 98.6-89.2= 9.4
9.4 divided by 1.5 is about 6.2 hours.
But this is just what I know this is not a guaranteed solution.

A power plant burns coal to generate electricity. Suppose that 1000 J of heat (Q) from the coal fire enters a boiler, which is kept at a constant temperature of 900 C. That 1000 J is used to boil water in a boiler. The steam from the boiler is used to drive a turbine that creates electricity (work). The excess heat is put into a cooling tower at 5 C.
Carnot efficiency If everything is perfectly efficient,
• What is the maximum efficiency that the plant could operate at?
• How much work could be done starting from that 1000 J?

Answers

Answer:

The work done will be "763 J". A further explanation is given below.

Explanation:

The given values are:

\(Q_1=1000 \ J\)

Temperature,

\(T_1=900^{\circ} C\)

i.e,

    \(=1173\)

\(T_2=5^{\circ}C\)

i.e.,

    \(=278\)

As we know,

⇒  \(\eta =1-\frac{T_2}{T_1}\)

On substituting the values, we get

⇒     \(=1-\frac{278}{1173}\)

⇒     \(=\frac{1173-278}{1173}\)

⇒     \(=\frac{895}{1173}\)

⇒     \(=0.763\)

then,

⇒  \(W=\eta Q_1\)

⇒       \(=0.763\times 1000\)

⇒       \(=763 \ J\)

1. Who is Nancy Lieberman?

2. What were some of her accomplishments throughout her life?

3. How could her accomplishments motivate other women in their lives?

4. Describe how you think she felt at the peak of her success?


5. How did her success contribute to women’s sports?


who can help me with that 5 questions please, I need help

Answers

Answer:

Nancy Elizabeth Lieberman (nacido el 1 de julio de, 1958), apodado "Señora mágica", ] es un ex profesional jugador de baloncesto y entrenador de la WNBA (WNBA) que es actualmente un organismo de radiodifusión para los New Orleans Pelicans de la Nacional La Asociación de Baloncesto (NBA) y la entrenadora principal de Power , un equipo en el BIG3 que lideró en su Campeonato 0.]bLieerman es considerada como una de las figuras más importantes del baloncesto femenino estadounidense.

Explanation:

An ordinary gold wedding ring is tossed end over end into a running MRI machine with a 4.0 T field. The ring spends 1.6 s in the field, during which it completes 60 full rotations.

If the ring has a resistance of 6.0 Ω and a diameter of 17 mm , what is the average power avg dissipated by the ring?

Answers

The ring spends 1.8 s in the field, during which it completes 60 full ... wedding ring is tossed end over end into a running MRI machine with a 4.0 T field.

The ring spends 1.8 s in the field, during which it completes 60 full wedding ring is tossed end over end into a running MRI machine with a 4.0 T field.

What is the function of MRI machine?

Magnetic resonance imaging is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body.

Moreover, an MRI scanner is a large tube that contains powerful magnets. You lie inside the tube during the scan. An MRI scan can be used to examine almost any part of the body, including the: brain and spinal cord. bones and joints.

Hence, a single scan may take a few seconds or 3 to 8 minutes. You may be asked to hold your breath during short scans. The total scan lasts 15 to 90 minutes, depending on the size of the area being scanned and how many images are needed.

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During the middle of a family picnic, Barry Allen received a message that his friends Bruce and Hal
to be saved. Barry promised his wife Iris that he would be back in exactly 5 minutes. From that that picnic
location, Barry runs at a speed of 600 m/s for 2 minutes at a heading of 35° north of west to save Bruce.
He then changed his heading to 30° west of north, slows down to 400 m/s and runs for 1 minute to save
Hal. (The changes in speed are essentially instantaneous and not part of solving this problem).
(aPray a physical representation of the displacement during Barry's full trip.

Answers

The kinematics of the uniform motion and the addition of vectors allow finding the results are:

The  Barry's initial trajectory is 94.30 10³ m with n angles of θ = 138.8º The return trajectory and speed are v = 785.9 m / s, with an angle of 41.2º to the South of the East

Vectors are quantities that have modulus and direction, so they must be added using vector algebra.

A simple method to perform this addition in the algebraic method which has several parts:

Vectors are decomposed into a coordinate system The components are added The resulting vector is constructed

 Indicate that Barry's velocity is constant, let's find using the uniform motion thatthe distance traveled in ad case

              v = \(\frac{\Delta d}{t}\)

              Δd = v t

Where  v is the average velocity, Δd the displacement and t the time

We look for the first distance traveled at speed v₁ = 600 m / s for a time

          t₁ = 2 min = 120 s

          Δd₁ = v₁ t₁

          Δd₁ = 600 120

          Δd₁ = 72 10³ m

Now we look for the second distance traveled for the velocity v₂ = 400 m/s    

  time t₂ = 1 min = 60 s

          Δd₂ = v₂ t₂

          Δd₂ = 400 60

          Δd₂ = 24 103 m

   

In the attached we can see a diagram of the different Barry trajectories and the coordinate system for the decomposition,

We must be careful all the angles must be measured counterclockwise from the positive side of the axis ax (East)

Let's use trigonometry for each distance

Route 1

          cos (180 -35) = \(\frac{x_1}{\Delta d_1}\)

          sin 145 = \(\frac{y_1}{\Delta d1}\)

          x₁ = Δd₁ cos 125

          y₁ = Δd₁ sin 125

          x₁ = 72 103 are 145 = -58.98 103 m

          y₁ = 72 103 sin 155 = 41.30 10³ m

Route 2

          cos (90+ 30) = \(\frac{x_2}{\Delta d_2}\)

          sin (120) = \(\frac{y_2}{\Delta d_2}\)

          x₂ = Δd₂ cos 120

          y₂ = Δd₂ sin 120

          x₂ = 24 103 cos 120 = -12 10³ m

           y₂ = 24 103 sin 120 = 20,78 10³ m

             

The component of the resultant vector are

              Rₓ = x₁ + x₂

              R_y = y₁ + y₂

              Rx = - (58.98 + 12) 10³ = -70.98 10³ m

              Ry = (41.30 + 20.78) 10³ m = 62.08 10³ m

We construct the resulting vector

Let's use the Pythagoras' Theorem for the module

             R = \(\sqrt{R_x^2 +R_y^2}\)

             R = \(\sqrt{70.98^2 + 62.08^2}\)   10³

             R = 94.30 10³ m

We use trigonometry for the angle

             tan θ ’= \(\frac{R_y}{R_x}\)

             θ '= tan⁻¹ \(\frac{R_y}{R_x}\)

             θ '= tan⁻¹ \(\frac{62.08}{70.98}\)

             θ ’= 41.2º

Since the offset in the x axis is negative and the displacement in the y axis is positive, this vector is in the second quadrant, to be written with respect to the positive side of the x axis in a counterclockwise direction

            θ = 180 - θ'

            θ = 180 -41.2

            θ = 138.8º

Finally, let's calculate the speed for the way back, since the total of the trajectory must be 5 min and on the outward trip I spend 3 min, for the return there is a time of t₃ = 2 min = 120 s.

The average speed of the trip should be

             v = \(\frac{\Delta R}{t_3}\)  

             v = \(\frac{94.30}{120} \ 10^3\)

              v = 785.9 m / s

in the opposite direction, that is, the angle must be

               41.2º to the South of the East

In conclusion, using the kinematics of the uniform motion and the addition of vectors, results are:

To find the initial Barry trajectory is 94.30 10³ m with n angles of  138.8º The return trajectory and speed is v = 785.9 m / s, with an angle of 41.2º to the South of the East

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During the middle of a family picnic, Barry Allen received a message that his friends Bruce and Halto

A student drops an object from rest above a force plate that records information about the force exerted on the object as a function of time during the time interval in which the object is in contact with the force plate. Which of the following measurements should the student take, in addition to the measurements from the force plate, to determine the change in momentum of the object from immediately before the collision to immediately after the collision?

a. The mass of the object.
b. The final speed of the object MOH 5000
c. The distance fallen by the object
d. The student has enough information to make the determination

Answers

Answer:

D

Explanation:

The student has enough information to make the determination

Measurements should the student take, in addition to the measurements from the force plate, to determine the change in momentum of the object from immediately before the collision to immediately after the collision the student has enough information to make the determination. Thus, option D is correct.

What happens during the experiment?

A student drops an object from rest above a force plate that records information about the force exerted on the object as a function of time during the time interval in which the object is in contact with the force plate.

Momentum has the measure of motion of the object. Momentum is given by the product of mass and the velocity of the object. The law of conservation of momentum states that the momentum before the collision is equal to the momentum after the collision. It also states that the total momentum of a system or a body remains constant.

Therefore, Measurements should the student take, in addition to the measurements from the force plate, to determine the change in momentum of the object from immediately before the collision to immediately after the collision the student has enough information to make the determination. Thus, option D is correct.

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A ball is thrown straight up and passes point B (at a height of 56.8 m above its starting point O) in 5.8 s. What was its initial speed? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m/s

Answers

Answer:

38.2 m/s

Explanation:

Given:

Δy = 56.8 m

a = -9.8 m/s²

t = 5.8 s

Find: v₀

Δy = v₀ t + ½ at²

56.8 m = v₀ (5.8 s) + ½ (-9.8 m/s²) (5.8 s)²

v₀ ≈ 38.2 m/s

What type of relationship exists between mass and distance?

Answers

Answer:

Gravitational force

Explanation:

Hope this helps :)

Answer: Gravitational force

Explanation: Gravitational Force is an attractive force that exists between all objects with mass; an object with mass attracts another object with mass; the magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects.

what is the average velocity of a van that moves from 0 to 60 m east and 20 seconds

Answers

Explanation:

I have a lot to say it was very nice to meet my parents are u doing well I dont want too its been so much I love you so I was like u know I am not a man but you are the auditions I have been in a long long long life is a triangle and a chair for me and my parents think about the way I

Caroline, a piano tuner, suspects that a piano's G4 key is out of tune. Normally, she would play the key along with her G4 tuning fork and tune the piano to match, but her G4 tuning fork is missing! Instead, she plays the errant key along with her F4 tuning fork (which has a frequency of 349.2 Hz), displays the resulting waveform on a handheld oscilloscope, and measures a beat frequency of 76.7 Hz. Then, she plays the errant key along with her A4 tuning fork (which has a frequency of 440.0 Hz) and measures a beat frequency of 14.1 Hz.
What frequency is being played by the out-of-tune key ?
a. 363.3 Hz
b. 451.1 Hz
c. 33.9 Hz
d. 272.5 Hz
e. 425.9 Hz

Answers

Answer:

e. 425.9 Hz

Explanation:

The computation of the frequency is being played by the out-of-tune key is shown below;

Given that

Δf1  = x - 349.2 = 76.7.........(1)

Δf2 = 440 - x  = 14.1......(2)

Now solve (1) and (2)

(440 - x) - x + 349.2 = 14.1 - 76.7

789.2 + (-2x) = -62.6

x = 425.9 Hz

Hence, the frequency is being played by the out-of-tune key is 425.9 Hz

Therefore the option e is correct

What is the kinetic energy of a 29 kg dog that is running at a speed of 8.5 m/s (about 17 mi/h)?

Answers

The kinetic energy of of given data is K.E. = 1,047.62 J

Equation:

To calculate kinetic energy using the formula,

K.E. = 1/2 m v²

where,

K.E is kinetic energy

m is mass

v is velocity

So, Putting values,

K.E. = 1/2 x 29 x (8.5m/s)²

K.E. = 1,047.62 J

What is kinetic energy in simple words?

The energy an object has as a consequence of motion is known as kinetic energy. A force must be applied to an object in order to accelerate it. We must put in effort in order to apply a force. After the work is finished, energy is transferred to the object, which then moves at a new, constant speed.

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Which is observed globally: "Earth Day" or "Arbor Day"?

Answers

Answer:

Earth Day is observed globally

Explanation:

Earth day is more globally observed. Arbor day is lowkey rare

ចំនុចរូបធាតុមួយចរពាក់កណ្តាលដំបូងនៃចម្ងាយចររបស់វាដោយល្បឿនប, = 2 m/s ហើយកំណាត់ផ្លូវ
ដែលនៅសល់ វាចរដោយល្បឿន I = 3 m/s ដោយប្រើពាក់កណ្តាលដំបូងនៃរយៈពេលសរុបលើកំណាត់ផ្លូវ
និងពាក់កណ្តាលចុងក្រោយដោយល្បឿន 4 = 5 m/s ។
នេះ:​

Answers

Answer:

Explanation:

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a healthy person has a body temperature of 37 degree celsius. if they jump into an ice bath after sports training their temperature only decreases slowly. how can you explain this when a lump of metal at 37 celsius degree placed in the same ice bath cools down to 0 celsius degree in only a couple of minutes

Answers

The difference in cooling rates between a healthy person and a lump of metal when placed in an ice bath can be attributed to several factors:

1. Heat Capacity: The heat capacity of the human body is much higher than that of a small lump of metal. The human body has a large mass and contains a significant amount of water, which has a high heat capacity. This means that it requires more energy to change the temperature of the body compared to a small metal object. As a result, the body cools down more slowly in the ice bath.

2. Insulation: The human body is well-insulated with layers of skin, fat, and clothing. These layers act as thermal barriers and slow down the transfer of heat between the body and the surroundings. On the other hand, a small metal object does not have any significant insulation, allowing heat to transfer more rapidly to the colder environment.

3. Biological Regulation: The human body has mechanisms to regulate its temperature, such as vasoconstriction (narrowing of blood vessels) and shivering, which help generate heat and maintain core temperature. These regulatory processes help to slow down the cooling process and preserve the body's temperature within a narrow range.

4. Surface Area-to-Volume Ratio: The surface area-to-volume ratio is higher for a small lump of metal compared to a human body. A higher surface area facilitates faster heat transfer. Since the metal object has a relatively larger surface area compared to its volume, it cools down more quickly in the ice bath.

Overall, the combination of the human body's higher heat capacity, insulation, biological regulation, and lower surface area-to-volume ratio compared to a small metal object contributes to the slower cooling rate when immersed in an ice bath.

Calculate the force of your body on the ground. (Use your weight in pounds x 4.45 because 2.2lbs=kg)

Answers

Answer:

2.8ibs=kg check with someone else im not for sure.

Explanation:

if you divide 10 divided by 2 it gives you 5 and then subtract it by 2.2 = 2.8

there goes your answer.

Match the following activities.

1.foot-pound
2.work
3.steam
4.newton meter
5.muscular force
6.force of gravity
7.force of wind






1.amount of force times the distance it moves an object

2. kind of force used to operate engines

3.English unit of measuring work equal to moving one pound one foot

4.metric measurement of work equal to moving one newton
one meter

5. kind of force that pulls things toward the center of the earth

6. force used when walking

7. force used to turn a windmill

Match the following activities.1.foot-pound2.work3.steam4.newton meter5.muscular force6.force of gravity7.force

Answers

Answer:

amount of force times the distance it moves an object: work


kind of force used to operate engines: steam


English unit of measuring work equal to moving one pound one foot: foot-pound


metric measurement of work equal to moving one Newton one meter: Newton-meter


kind of force that pulls things toward the center of the earth: force of gravity


force used when walking: muscular force


force used to turn a windmill: force of wind

Explanation:

I found the answers in quizlet

Answer:

im in the same class so here's your answer

Explanation:

Match the following activities.1.foot-pound2.work3.steam4.newton meter5.muscular force6.force of gravity7.force

Where is the potential energy equal to zero?

Where is the potential energy equal to zero?

Answers

Answer:

im sure your already past this but it's E.

Explanation:

This is because in this case potential energy is linear to height, which means that the higher the more potential energy.

What is sound waves

Answers

Sound waves are a type of mechanical wave that propagate through a medium, typically air but also other materials such as water or solids.

Characteristics of sound waves

Frequency: the frequency of a sound wave refers to the number of cycles or vibrations it completes per second and is measured in Hertz (Hz).

Amplitude: the amplitude of a sound wave refers to the maximum displacement or intensity of the wave from its equilibrium position. It represents the loudness or volume of the sound, with larger amplitudes corresponding to louder sounds and smaller amplitudes corresponding to softer sounds.

Wavelength: the wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase, such as from one peak to the next or one trough to the next. It is inversely related to the frequency of the wave.

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A force F is applied to a cylindrical steel cable of diameter 3.5 mm and length 10.0 m. Determine the value of F if the change in length of the cable is 7.8 mm.
Ysteel = 20 x 10^10 N/m2

Answers

Explanation:

Mathematicians seek and use patterns[8][9] to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements.[10] Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.[11]

Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences.

The value of force (F) if the change in length of the cable is 7.8 mm is 1500.89 N

The value of the force can be determined by using the young modulus equation that shows the relation between the tensile of the steel cable when the force is applied.

\(\mathbf{\gamma = \dfrac{F/A}{\Delta L/L}}\)

\(\mathbf{\gamma = \dfrac{F} {A }\times \dfrac{L}{\Delta L} }\)

Making the force the subject of the formula and replacing the values, we have:

\(\mathbf{F =\dfrac{A \times \gamma \times \Delta L }{L} }\)

\(\mathbf{F =\dfrac{ \pi \times (3.5 \times 10^{-3}) \times ( 20 \times 10^{10} \ N/m^2 ) \times (7.8 \times 10^{-3}) }{4 \times 10} }\)

\(\mathbf{F =1500.89 \ N }\)

Therefore, we can conclude that the value of force (F) if the change in length of the cable is 7.8 mm is 1500.89 N

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An object is moving with constant speed in a
circular path. The object's centripetal
acceleration remains constant in
(1) magnitude, only
(2) direction, only
(3) both magnitude and direction
(4) neither magnitude nor direction

Answers

Answer:

both magnitude and direction

Explanation:

When an object moves in a circular path, its motion is called uniform circular motion. In this motion, the force acting on it is centripetal force and it is moving under centripetal acceleration. This type of force acts towards the centre of the circle.

In this type of motion, the speed remains constant while the velocity keeps on changing. The object's centripetal  acceleration remains constant in magnitude as well as direction.

Hence, the correct option is (3).

If an object is moving with constant speed in the circular path the object's centripetal  acceleration remains constant in both magnitude and direction

The formula for calculating the centripetal acceleration of an object is expressed as:

\(a =\frac{v^2}{r}\)

v is the speed of the objectr is the radius of the circular path

If the speed of the object is constant, the acceleration is of the body is also constant.

Hence if an object is moving with constant speed in the circular path the object's centripetal  acceleration remains constant in both magnitude and direction

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an energy transformation flow diagram is shown what type of energy does X most likely represent​

an energy transformation flow diagram is shown what type of energy does X most likely represent

Answers

X represent the wind energy that converted to electrical energy

The hottest recorded temperature in the history of the United States is 134 °F, which is 57 °C. What would the speed of sound at this temperature?

Answers

Answer:

365 m/s

Explanation:

Mrs Finley

An object slows with an acceleration of – 2.0 m/s2. If the object starts with a velocity of 20 m/s, how long will it take to come to a stop?

Answers

Answer:

acceleration = cange in velocity ÷ change in time.

acceleration = (-15 - -10) ÷ 2

acceleration = -5 ÷ 2

ACCELERATION IS -2.5m/s2

Explanation:

100 POINTS AND BRAINLIST FOR BEST ANSWER!

Please help me i have a 77% in science and i need to bring it up today bc its the end of grades today. If you help me you are seriously the best person in the world, theres 4 questions.

100 POINTS AND BRAINLIST FOR BEST ANSWER!Please help me i have a 77% in science and i need to bring it
100 POINTS AND BRAINLIST FOR BEST ANSWER!Please help me i have a 77% in science and i need to bring it
100 POINTS AND BRAINLIST FOR BEST ANSWER!Please help me i have a 77% in science and i need to bring it
100 POINTS AND BRAINLIST FOR BEST ANSWER!Please help me i have a 77% in science and i need to bring it

Answers

Answer:

Air moves from regions of high pressure to regions of low pressure.

Explanation:

When airs moves horizontally from regions of high pressure to low pressure, it creates wind. If the difference between high and low pressure is greater, then it makes the wind faster.

Best of Luck!

Answer:

C. Air moves from regions of high pressure to regions of low pressure.

Explanation:

The air from the regions of high pressure will hold onto that pressure. So, when it moves into the regions with low pressure it'll turn into wind.  

The greater the pressure, the stronger the wind and vise versa.

Hope this helps!

What is the difference between human caused Climate Change and natural
climate cycles?

Answers

Human caused climate change is climate change caused by human made creations such as cars, trucks, factories, and plastic in oceans these all are causing the ozone layer to deteriorate. And natural climate change cycles is any change occurring to the planet's climate either permanently or lasting for long periods of time.

Two point charges q1 and q2 are located at (2.0, 0.0) cm and (8.0, 0.0) cm,
respectively. A positive point charge q3 is placed somewhere so that the net
electrostatic force acting on it due to q1 and q2 is zero. Find the position of q3 if
q1 = 2.0 μC and q2 = -8.0 μC. Sketch a figure that shows the position of all
three point charges and the forces acting on q3.

Answers

The Sketch  of the figure will bear the parameters of the charge that lies   at (4,0,0)

What is co-ordinate of the charge?

Generally, the equation for is  mathematically given as

1)

Since both of the other points, "q1"<"q2," are on the x-axis, the third one must also be on the x-axis, and it must be close to the charge of lesser magnitude. off q1 by x cm

Now, forces on q3 due to q1

\(\vec{F}_{1}=\frac{k q_{1} q_{3}}{x^{2}} \hat{x}\)

Force on q3 due to q2

\(\vec{F}_{2}=\frac{k q_{2} q_{3}}{(6+x)^{2}}(-\hat{x})\)

\(\quad \vec{F}_{1}+\vec{G}_{2}=0$\)

\(&\frac{k q_{1} q_{3}}{x^{2}}-\frac{k q_{2} q_{3}}{(x+6)^{2}}=0 \\&\frac{2}{x^{2}}=\frac{8}{(x+6)^{2}} \Rightarrow \frac{x+6}{x}=\sqrt{\frac{8}{2}}=2 \\&x+6=2 x \Rightarrow x=6 \mathrm{~cm}\)

In conclusion, the charge lies at (4,0,0)

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The phase velocity of transverse waves in a crystal of atomic separation a is given byy = csin(ka/2) pka/2 1. What is the dispersion relation e(k)? 2. What is the group velocity as a function of k?

Answers

Answer:

a

e(k) =  \frac{2a}{c}  *  sin (\frac{k*a}{2} )

b

G_{v} =  \frac{d e(k ) }{dk }  =  \frac{a^2}{c}  *  cos (\frac{k* a}{2} )

Explanation:

From the question we are told that

    The  velocity  of transverse waves in a crystal of atomic separation is  

                  \(b_y  = c \frac{sin (\frac{k*a}{2} )}{\frac{k*a}{2} }\)

Generally the dispersion relation is mathematically represented as

            \(e(k) =  b_y  *  k\)

=>    \(e(k) = c  \frac{sin(\frac{k*a}{2} ) }{ \frac{k*a}{2} }  *  k\)

=>    \(e(k) =   c *  \frac{sin (\frac{k_a}{2} )}{ \frac{a}{2} }\)

=>    \(e(k) =  \frac{2a}{c}  *  sin (\frac{k*a}{2} )\)

Generally the group velocity is mathematically represented as

          \(G_{v} =  \frac{d e(k ) }{dk }  =  \frac{a^2}{c}  *  cos (\frac{k* a}{2} ) \)

The free-fall acceleration on a large asteroid, in the vacuum of space, is 0.45 m/s2. A spacecraft hovering 600 m above the surface drops a 25 kg payload wrapped in a padded jacket.

Answers

Answer:

It will take approximately 8.88 seconds for the payload to reach the surface of the asteroid.

Explanation:

The payload will fall to the surface of the asteroid at a constant acceleration of 0.45 m/s2 due to the gravitational force acting on it. The velocity of the payload at any time can be calculated using the following equation:

v = at

Where v is the velocity, a is the acceleration, and t is the time elapsed.

To find the time it takes for the payload to reach the surface, we can use the following equation:

d = vt + 0.5at^2

Where d is the distance traveled and t is the time elapsed.

We can rearrange this equation to solve for t:

t = (-v + sqrt(v^2 + 2ad)) / a

Plugging in the values given in the problem, we get:

t = (-0 + sqrt(0^2 + 2 * 0.45 * -600)) / 0.45

t = 8.88 seconds

Therefore, it will take approximately 8.88 seconds for the payload to reach the surface of the asteroid.

A 5 kW, 230 V motor draws a current of 24 A from the supply. Determine the efficiency of this motor.

Answers

The efficiency of motor is 90.58%.To determine the efficiency of the motor, we need to calculate the input power and the output power, and then divide the output power by the input power

The input power can be calculated using the formula:

Input Power = Voltage × Current

Given that the voltage is 230 V and the current is 24 A, we have:

Input Power = 230 V × 24 A

Input Power = 5520 W (or 5.52 kW)

The output power of the motor is given as 5 kW (since it is a 5 kW motor).

Now, we can calculate the efficiency:

Efficiency = (Output Power / Input Power) × 100%

Efficiency = (5 kW / 5.52 kW) × 100%

Efficiency ≈ 90.58%

Therefore, the efficiency of this motor is approximately 90.58%.

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which of the following voltage and phase arrangements requires ground-fault protection of equipment for each service disconnecting means rated at 1,000 amperes or greater

Answers

Explanation:

230.95 states that ground-fault protection of equipment shall be provided for solidly grounded wye electrical services of more than 150 volts to ground, but not exceeding 600 volts phase-to-phase for each service disconnecting means rated 1000 amperes or more.

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