a spring powered cannon, with spring constant k, is pointed straight into the air. it is loaded with a ball of mass m that is compressing the spring of the cannon a distance x and is ready to launch. write the equation to solve for the height of the ball after being launched and after it has reached it highest height and is now traveling down. do so in terms of k,m,x,v, and any needed constants.

Answers

Answer 1

The height reached by the spring powered cannon is 9.8mh.

Calculation:-

PEspring = 1/2 × k × x²

Where k = spring constant

x = amount of compression

The spring constant is k

The compression of the spring is x = xm

The potential energy stored in the spring is

PE = 1/2 kx²

This potential energy will be converted to kinetic energy when the spring is released and to potential energy of spring powered cannon

KEspring canon powered = 1/2 mu²

Let the height of the powered cannon be = h

The acceleration due to gravity is g = 9.8ms−2

Then ,

The potential energy of the spring powered cannon =  

PEpowered canon = mgh

Mass of the ball is m =m

PEcanon = m× h × 9.8

PEcanon = 9.8mh.

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Related Questions

Which can be excluded from the list of events caused by the flow of thermal energy inside the earth.

Answers

A volcano erupts when there is an accumulation of magma in the magma chamber. The volcano spews out lava, pyroclastic debris, and magma. Because heat is discharged to the Earth's surface, it is connected to the thermal energy within the planet.

Thunderstorms arise when three factors come together: unsteady weather, rising cold air, and a enough amount of precipitation. According to the requirements for thunderstorm formation, it has nothing to do with the movement of thermal energy within the Earth. Climate on Earth is driven by solar energy. The sun's energy heats the surface of the planet, warms the atmosphere, fuels photosynthesis, causes evaporation, controls the weather and water cycles, and drives ocean currents. The sun is setting through the atmosphere in the astronaut shot on the right, taken from the International Space Station.

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Answer:

thunder storms

Explanation:

i took t

What sport does not require a high level of fitness

Answers

Rock climbing. Free diving. Sky diving. Dog sledding.

Which statement accurately describes the atmospheres of the inner planets?

Mars has no atmosphere.
Mercury has a thick atmosphere.
Mars and Venus have similar atmospheres.
Earth and Venus have similar atmospheres.

Answers

Answer:

Mars and venus have similar atmospheres

Answer:

Earth and Venus have similar atmospheres

Explanation:

What cause sound seismic and electromagnetic waves to transmit energy through different mediums

Answers

Answer:

Explanation:

Sound, seismic, and electromagnetic waves transmit energy through different mediums due to the motion of particles in the medium.

Sound waves transmit energy through the vibration of particles in a solid, liquid, or gas. The energy is transferred from particle to particle as the wave travels through the medium.

Seismic waves are created by the sudden release of energy from earthquakes, volcanic eruptions, or other geological events. These waves travel through the Earth's solid mantle and crust, transmitting energy through the vibration of particles in the rock.

Electromagnetic waves are a type of wave that does not require a medium to travel through. They are created by the motion of charged particles, such as electrons, and can travel through a vacuum, such as space. Electromagnetic waves transfer energy through the oscillation of electric and magnetic fields.

Which of the following has a positive charge and a mass of one?

a
electron

b
proton

c
element

d
positivon

e
neutron


Answers

Answer:

the answer is protons b

Explanation:

brainliest if 1st one..

What is the results t of two forces 7 Newton and 10 Newton inclined at an angle 30 degree to each other

Answers

Answer:

16.44 N

Explanation:

From the diagram attached,

we make use of cosine rule to calculate the resultant force

R² = P²+Q²-2PQcosα............................. Equation 1

Where R = resultant force

Given: P = 7 Newton, Q = 10 Newton, α = (180-30) = 150°

Substitute these values into equation 1

R² = 7²+10²-(2×7×10×cos150°)

R² = 49+100-140cos150°

R² = 149-140cos150°

R² = 149-140(-0.8660)

R² = 149+121.24

R² = 270.24

R = √(270.24)

R = 16.44 N

What is the results t of two forces 7 Newton and 10 Newton inclined at an angle 30 degree to each other

a given convex lens has a focal length that varies slightly with the wavelength of the light passing through it. when the a lens is used as the objective of a telescope, this results in

Answers

A given convex lens has a focal length that varies slightly with the wavelength of the light passing through it. when the a lens is used as the objective of a telescope, this results in chromatic aberration.

Chromatic aberration is a phenomenon in which light rays passing through a focus of lens at different points, depending on their wavelength. It is a failure of a lens to focus all colors to the same point. It is also called chromatic distortion and spherochromatism. The focal length of the lens varies directly with the wavelength of the light so focal length increases with wavelength but decreases with refractive index as wavelength is inversely related to it. This is the principal cause of chromatic aberration phenomena.

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A circuit with a battery, a 14 Ω resistor, and a 17 Ω resistor, in parallel. The total current is the system is 2.8 A. What is the voltage of the battery?

Answers

Given data:

* The total current in the system is I = 2.8 A.

* The resistance of resistors connected in parallel is,

\(\begin{gathered} R_1=14\text{ ohm} \\ R_2=17\text{ ohm} \end{gathered}\)

Solution:

The equivalent resistance of the system is,

\(\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}\)

Substituting the known values,

\(\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{14}+\frac{1}{17} \\ \frac{1}{R_{eq}}=\frac{17+14}{14\times17} \\ R_{eq}=\frac{14\times17}{17+14} \\ R_{eq}=7.68\text{ ohm} \end{gathered}\)

According to Ohm's law, the voltage across the battery in terms of the current and equivalent resistance is,

\(\begin{gathered} V=IR_{eq} \\ V=2.8\times7.68 \\ V=21.5\text{ volts} \end{gathered}\)

Thus, the voltage across the battery is 21.5 volts.

(a) The required conductivity of an n-type silicon sample at T 300 K is to be 10 (-cm)1. What donor impurity concentration is required? What is the electron mobility corresponding to this impurity concentration? (

Answers

The required donor impurity concentration and electron mobility for a conductivity of 10 (-cm)⁻¹ are both 10 cm⁻³.

What is electrοn mοbility?  

In sοlid-state physics, the electrοn mοbility characterises hοw quickly an electrοn can mοve thrοugh a metal οr semicοnductοr when pulled by an electric field. There is an analοgοus quantity fοr hοles, called hοle mοbility. The term carrier mοbility refers in general tο bοth electrοn and hοle mοbility.

To determine the required donor impurity concentration and electron mobility for a given conductivity in an n-type silicon sample, we can use the following relations:

1. Donor Impurity Concentration (Nd):

Nd = (σn * q * μn) / (|e|)

2. Electron Mobility (μn):

μn = σn / (q * Nd)

Where:

σn is the required conductivity (in units of (Ω-cm)⁻¹).q is the electronic charge, which is approximately 1.6 x 10^-19 C.μn is the electron mobility (in units of (cm²/Vs)).|e| is the magnitude of the electronic charge.

Given:

Required conductivity (σn) = 10 (-cm)⁻¹ = 10 Ω⁻¹Temperature (T) = 300 KElectronic charge (q) = 1.6 x \(10^{-19\) C

First, let's calculate the donor impurity concentration (Nd):

Nd = (σn * q * μn) / (|e|)

To calculate the electron mobility (μn), we need to know the value of Nd.

So, we'll calculate Nd using the given values, and then find μn:

Nd = (10 * 1.6 x \(10^{-19\) * μn) / (1.6 x \(10^{-19\))

Nd = μn

Hence, the donor impurity concentration (Nd) and the electron mobility (μn) will have the same value.

Therefore, the required donor impurity concentration and electron mobility for a conductivity of 10 (-cm)⁻¹ are both 10 cm⁻³.

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What happens to hotter air in the atmosphere?

A.Warmer air molecules move faster and get farther apart. As they get farther apart, they become more dense and sink.

B.Warmer air molecules move faster and get farther apart. As they get farther apart, they become less dense and rise.

C.Warmer air molecules move slower and spread out. As they spread out, they sink below cooler air molecules.

Answers

B.Warmer air molecules move faster and get farther apart. As they get farther apart, they become less dense and rise.

photons and show the electron transit
Extra questions
26. The spectrum of sunlight has dark lines. These dark lines are due to the absorption of certain
wavelengths by the cooler gases in the atmosphere of the Sun.
a) One particular dark spectral line has a wavelength of 590 nm. Calculate the energy of a
photon with this wavelength.
b) The diagram shows some of the energy
levels of an isolated atom of helium.
i.
Explain the significance of the
energy levels having negative
values.
ii. Explain, with reference to the
energy level diagram shown, how
a dark line in the spectrum may
be due to the presence of helium
in the atmosphere of the Sun.
iii. All the light absorbed by the
atoms in the Sun's atmosphere is
re-emitted. Suggest why a dark
spectral line of wavelength 590
nm is still observed from the Earth.
Energy:10-¹ J
0
-1.6
-2.4
-3.0
-5.8
-7.6

Answers

The energy of a photon with a wavelength of 590 nm is \(3.36 * 10^-19\)

How to find the energy of the photon?

The energy of a photon can be calculated using the equation:

E = hc/λ

where E is the energy of the photon, h is Planck's constant \((6.626 * 10^-34 J.s)\), c is the speed of light\((3.00 * 10^8 m/s)\), and λ is the wavelength of the photon in meters.

To convert 590 nm (nanometers) to meters, we can use the conversion factor:

\(1 nm = 1 * 10^-9 m\)

So, \(590 nm = 590 * 10^-9 m\)

Plugging these values into the equation, we get:

E = \((6.626 * 10^-34 J.s * 3.00 * 10^8 m/s) / (590 * 10^-9 m)\)

E = \(3.36 * 10^-19 J\)

Therefore, the energy of a photon with a wavelength of 590 nm is \(3.36 * 10^-19\)

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the capacitor can withstand a peak voltage of 530 volts. if the voltage source operates at the resonance frequency, what maximum voltage amplitude vmax can the source have if the maximum capacitor voltage is not exceeded

Answers

The highest possible voltage is 41.92 V. Voltage is the difference in electric potential between two points, often known as electric pressure, electric tension, or (electric) potential difference.

It refers to the labor required per unit of charge to move a test charge between two places in a static electric field. The derived unit for voltage in the International System of Units is called a volt. In light of this, 530 volts is the maximum voltage. Assume the resistance in an L-R-C series circuit is 400 ohms, the inductance is 0.380 Henry, and the capacitance is. We must determine the resonance frequency. Using a frequency formula

f = 1/2π√LC

substitute the value in the above formula

f = 1/(2*3.14√0.380* 1.20* 10⁻⁸

f = 2356.88 Hz

To calculate the maximum current

Use the formula of current

I = Vc / XcI = 2π * f * C * Vc

substitute the value

I = 2 * 3.14 * 2356.88 * 1.20* 10⁻⁸ * 530

I = 0.1048 A

The impedance of the circuit

z = √R² + (X² - Xc²)

At resonance frequency

X = Xc

Z = R

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a rocket blasts off. in 10.0 seconds it's at 10,000 ft, traveling at 3600 mph. assuming the direction is up, calculate the acceleration. (hint: the rocket is not under constant acceleration)

a) 5280 ft/s^2

b) 528 ft/s^2

c) 100 ft/s^2

d) 200. ft/s^2

Answers

If a rocket blasts off. in 10.0 seconds it's at 10,000 ft, traveling at 3600 mph. assuming the direction is up, the acceleration of the rocket is 528 ft/s². T

The correct answer is option (b)

How do we calculate?

a = Δv / Δt

a =  acceleration

Δv =  change in velocity

Δt =  change in time.

1 mile = 5280 feet

1 hour = 3600 seconds

3600 mph = 3600 * 5280 ft / 3600 s = 5280 ft/s

Therefore , a = Δv / Δt substituting these, we have:

a = Δv / Δt = (5280 ft/s - 0 ft/s) / 10.0 s

a= 528 ft/s²

In conclusion, the acceleration of the rocket is 528 ft/s²

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I need help with this science question, 50 points!

I need help with this science question, 50 points!

Answers

Answer:

an open circuit (A battery, bulb, wire,switch)

Explanation:

the battery supplies the power the wire carries the current from the battery to the bulb but the circuit is not completed if the switch is not connected (Switch )

Hypochondriacs seek out medical care in order to verify that they do not have an illness.
Please select the best answer from the choices provided
T
F

Answers

Answer:

False

Explanation:

Just took the test

False, because hypochondriacs think they have a significant, undetected medical ailment even when testing reveal they are healthy.

Who are hypochondriacs?

A hypochondriac is someone who, despite diagnostic testing showing they have no health issues, lives in constant anxiety that they have a terrible, undetected medical illness. They are obsessed with the concept that they suffer from a major illness that has gone untreated.

In adults, hypochondriasis often begins to manifest. Among the symptoms are a persistent, strong anxiety of developing a major illness and concern that seemingly little symptoms portend a larger problem. A patient may change physicians or see them regularly.

Medication and counselling could be helpful.

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(4) (a) Consider a Gausian Bean whose spot size is 1 mm when collimated. The wavelength is 0.82 µm. Compute the divergence angle and the spot size at 5 km.
(b) A light source radiates uniformly over a region having a 40° full-cone angle. The source is a square planar radiator measuring 20 um on a side. Design a lens system that will decrease the beam spread to a 10° cone. Work out the image size and site.
(c) A receiver has a 10-cm focal length and a 1-cm photodetector diameter and has a inserted medium with index of reflection n 1.5 between lens and detector. Compute the receiver's Numerical Aperture (NA). Compute the material dispersion M of a laser diode for wavelength 10 nm and 15

Answers

(a) The divergence angle of the Gaussian beam can be calculated using the formula θ = λ / (π * w0). (b) To decrease the beam spread from a 40° cone angle to a 10° cone angle, a lens system needs to be designed. (c) The Numerical Aperture (NA) of the receiver can be calculated using the formula NA = n * sin(θ).

(a) The divergence angle of the Gaussian beam can be calculated using the formula θ = λ / (π * w0), where λ is the wavelength and w0 is the spot size. Given that the spot size is 1 mm (or 0.001 m) and the wavelength is 0.82 µm (or 8.2 x 10^-7 m), we can substitute these values into the formula to find the divergence angle. The divergence angle is approximately 0.105 radians.

To calculate the spot size at 5 km, we can use the formula w = w0 + θ * z, where w0 is the initial spot size, θ is the divergence angle, and z is the propagation distance. Plugging in the values w0 = 1 mm, θ = 0.105 radians, and z = 5 km (or 5000 m), we can calculate the spot size at 5 km. The spot size at 5 km is approximately 1.525 mm.

(b) To decrease the beam spread from a 40° cone angle to a 10° cone angle, a lens system needs to be designed. Given that the source is a square planar radiator measuring 20 µm on a side, the initial beam spread corresponds to a cone with a full-cone angle of 40°. To decrease the cone angle to 10°, a lens system can be used to focus and collimate the light beam.

The specific design of the lens system depends on the requirements and constraints of the system. However, in general, a combination of lenses, such as converging and diverging lenses, can be used to manipulate the light beam. By properly selecting and arranging the lenses, the beam spread can be reduced to the desired 10° cone angle. The image size and position will vary depending on the specific lens system design.

(c) The Numerical Aperture (NA) of the receiver can be calculated using the formula NA = n * sin(θ), where n is the refractive index of the medium and θ is the half-angle subtended by the receiver's photodetector. In this case, the receiver has a 10-cm focal length and a 1-cm photodetector diameter, which corresponds to a half-angle of θ = arctan(0.5/10) ≈ 2.86°.

Given that there is an inserted medium with a refractive index of n = 1.5 between the lens and detector, we can substitute these values into the NA formula. The Numerical Aperture of the receiver is approximately NA = 1.5 * sin(2.86°) ≈ 0.076.

The material dispersion (M) of a laser diode for a given wavelength can be calculated using the formula M = (dλ / λ), where dλ is the change in wavelength and λ is the original wavelength. However, in the provided question, the value for the change in wavelength (dλ) is not given, so it's not possible to calculate the material dispersion of the laser diode.

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these two phantom images were obtained with maximum gain and acoustic power using two different transducers. what information can be obtained by this comparison?

Answers

Transducer A has less penetration than transducer B is an information can be obtained by this comparison.

The lateral resolution has been worse, and there is no focal zone at the level of the B-labeled rods.

What types of test objects or phantoms are frequently utilized for assessing axial resolution?

The common targets used in an ultrasonic phantom for assessing axial resolution are targets that are spaced far and close together. Two tubes that are filled with fluid are visible in this phantom image.

Doppler phantom often does not assess minute tissue variations. To assess flow direction, the Doppler beam's depth capacity and penetration, the accuracy of the sample volume location, and the measured velocity, Doppler test objects are utilized.

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a .50 kilogram puck is sliding on a horizontal shuffle board court is slowed to rest by a frictional force of 1.2 newtons what is the coeffivent of kinetic friction betweej the puck and the surface of the shuffle board court

Answers

The puck's kinetic friction coefficient only with shuffleboard court's surface is 0.24.

How does kinetic friction work?

It is known as a force that exists between moving surfaces as kinetic friction. A force that operates in the opposing direction to the motion of a body on the surface is felt. The percentage of kinetic friction of the two materials will determine the size of the force.

Briefing:

Given  ,The mass of puck is, m = 0.50 kg.

The magnitude of frictional force is, f = 1.2 N.

The force which tends to oppose the motion between an object and the surface is known as frictional force. And its value is,

F= μ × mg

here,   is the coefficient of kinetic friction between the puck and the surface of the shuffleboard court.

Solving as ,

1.2 = u × 0.50 × 9.8

 μ =  \(\frac{1.2}{0.50 . 9.8}\)

 μ = 0.24

Thus, we can conclude that the coefficient of kinetic friction between the puck and the surface of the shuffleboard court is 0.24.

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How much force is needed to accelerate a 9,760 kg airplane at a rate of 4.2 m/s2?
A.
11,386 N
B.
40,992 N
C.
147,571 N
D.
2,324 N

Answers

The amount of force that is needed to accelerate the airplane is 40,992 N.

option B is the correct answer.

How much force is needed to accelerate the airplane?

The amount of force that is needed to accelerate the airplane is calculated by applying Newton's second law of motion as follows;

Mathematically, the formula for Newton's second law of motion is given as;

F = ma

where;

a is the acceleration of the airplanem is the mass of the airplane

The amount of force that is needed to accelerate the airplane is calculated as follows;

F = ( 9,760 kg )  x ( 4.2 m/s² )

F = 40,992 N

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What is the minimum resultant possible when adding a 3-unit vector to an 8-unit vector?
a. 24
b. 11
c. 8
d. 5

Answers

The minimum resultant  is possible when adding a 3-unit vector to an 8-unit vector is 5 (option d).

To understand this, we need to consider vector addition and the concept of the  angle between the vectors. When two vectors are added, their magnitudes and directions matter. The minimum resultant occurs when the two vectors are arranged in a straight line but point in opposite directions (i.e., when the angle between them is 180 degrees).

In this case, the 8-unit vector and the 3-unit vector are aligned such that they are working against each other, effectively subtracting their magnitudes. Mathematically, this can be represented as:

Minimum resultant = |8 - 3| = 5

The minimum possible resultant for these vectors is 5 units. Therefore the correct option is D

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If you walk at an average speed of 5 km/h for 30 minutes,
how far will you walk?

Answers

Answer:

150

Explanation:

30 times 5 = 150 i think

what is used to maintain the ran-gtp gradient across the nuclear envelope?

Answers

Proteins and complexes coordinate to maintain Ran-GTP gradient.

How is Ran-GTP gradient maintained?

Ran-GTP is a small GTPase that plays an essential role in nucleocytoplasmic transport. The concentration gradient of Ran-GTP across the nuclear envelope is maintained by the concerted action of several proteins. Here are the steps involved:

RanGAP1: The cytoplasmic protein RanGAP1 stimulates the hydrolysis of Ran-GTP to Ran-GDP. This reaction occurs exclusively in the cytoplasm.RanGEF: The nucleotide exchange factor RCC1, which is bound to chromatin in the nucleus, promotes the exchange of GDP for GTP on Ran, leading to the formation of Ran-GTP.Nuclear Pore Complex (NPC): The nuclear pore complex (NPC) serves as a selective barrier between the nucleus and cytoplasm. It contains a central channel through which small molecules and proteins can pass, but larger molecules are excluded.RanBP1: The cytoplasmic protein RanBP1 binds to Ran-GTP and helps to stabilize the complex with the NTR-cargo complex.Directionality: The binding of Ran-GTP to the NTR-cargo complex causes a conformational change in the NTR, allowing it to pass through the NPC into the nucleus. Once inside the nucleus, the high concentration of Ran-GTP causes the Ran-GTP/NTR-cargo complex to dissociate, releasing the cargo molecule. Similarly, in the cytoplasm, the Ran-GTP/NTR-cargo complex is disassembled by the action of RanBP1, and the NTR is recycled for further transport cycles.

Overall, the maintenance of the Ran-GTP gradient across the nuclear envelope is essential for proper nucleocytoplasmic transport, and the coordinated actions of several proteins and complexes are required to achieve this.

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HeLp AsAp!!!!!! How long would it take you to hop 30 meters based on your speed for the 5-meter trial? Show your work!

Hopping =

Distance-5 m

Time-3.41

Speed-1.46

Answers

Answer:

20.5s

Explanation:

Given parameters:

Distance = 30m

Unknown:

Time  = ?

Solution:

The time it will take to hop a distance of 30m using the speed for the 5m trial is the duration of the trip.

 The speed for the 5m trial  = 1.46m/s

Now;

    Speed  = \(\frac{distance}{time}\)

      Distance = speed x time

      time  = \(\frac{distance }{speed}\)

Input the parameters and solve;

     time  = \(\frac{30}{1.46}\)   = 20.5s

B.
An object thrown or shot vertically into the air reaches a maximum height after t secondsâ (when time is measured inâ seconds), where t is theâ k-coordinate of the vertex of the parabola.

Answers

The maximum height of an object thrown or shot vertically into the air is reached after t seconds, where t is the k-coordinate of the vertex of the parabola.


When an object is thrown or shot vertically, its motion can be modeled by a parabolic function.

The vertex of this parabola represents the highest point the object will reach, and the k-coordinate of the vertex represents the time it takes for the object to reach that height.


Hence, The maximum height of a vertically thrown or shot object is attained at the k-coordinate of the vertex of the parabola, which corresponds to the time t in seconds.

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Students want to make a scale model of the Earth and Moon system that shows correctly-scaled sizes and distances. Here are some guidelines they have to follow.

It has to be shown in the classroom, and the classroom is 51 square meters in area.
It has to be easily moved around since orbital motion and rotations will be shown.
It cannot cause damage if it is dropped.
All the students in the class should be able to see it from their desks.

Four different students came up with different designs. The designs and characteristics are shown in the table below.

Which design best satisfies the criteria and constraints of this Earth-Moon model?
A.
design 1
B.
design 3
C.
design 2
D.
design 4

Students want to make a scale model of the Earth and Moon system that shows correctly-scaled sizes and

Answers

Answer:

Design #3 seems to best fit the requirements (2 sq m).

The others are too bulky.

Which factor has the greatest effect on the strength of an electromagnet?
A. The position of the ammeter in the circuit
B. The number of coils of wire around the core
C. The type of insulation that covers the wire
D. The distance between the battery and the electromagnet

Answers

B. The number of coils of wire around the core

Answer:

B.

Explanation:

The number of coils of wire around the core

Un cuerpo de 3,5 kg se encuentra en reposo sobre un plano inclinado 37o. Está sujeto al extremo superior del plano inclinado mediante un muelle de constante recuperadora 15 N/m. Sabiendo que el coeficiente de rozamiento vale 0,6, calcula el alargamiento del muelle. Sol: 42 cm.

Answers

Answer:

1,1 m

Explanation:

Dado que;

coeficiente de fricción = 0,6

sabemos que W = R = mgcos 37 = 3.5Kg * 10m / s ^ 2 * cos37 = 27.95 N

coeficiente de fricción = fuerza / reacción normal (R)

Fuerza = 0.6 * 27.95 N

Fuerza (F) = 16.77 N

Recuerda que F = Ke

dónde;

K = constante de fuerza (15N / m)

e = extensión (lo desconocido)

e = F / K

e = 16,77 N / 15 N / m

e = 1,1 m

. A pilot flies from point A to point B to point C along 2 straight line segments. The displacement vector for dAB​ (the first leg) is 243 km at 50.0∘ north of east. The displacement vector for dBC​ (second leg) is 57.0 km at 20.0∘ south of east. What is the vector for the entire trip (both magnitude and direction)? (6)

Answers

To find the vector for the entire trip, we can simply add the displacement vectors for the individual legs of the trip. The vector for the entire trip has a magnitude of approximately 268.7 km and a direction of 37.1° north of east.

To find the vector for the entire trip, we can simply add the displacement vectors for the individual legs of the trip.

Given:

Displacement vector dAB: 243 km at 50.0° north of east

Displacement vector dBC: 57.0 km at 20.0° south of east

To add vectors, we break them down into their horizontal (x) and vertical (y) components and then add the corresponding components.

For dAB:

Horizontal component dABx = 243 km * cos(50.0°) = 156.99 km (east)

Vertical component dABy = 243 km * sin(50.0°) = 186.07 km (north)

For dBC:

Horizontal component dBCx = 57.0 km * cos(20.0°) = 53.95 km (east)

Vertical component dBCy = -57.0 km * sin(20.0°) = -19.52 km (south)

Now, we add the horizontal and vertical components separately:

Total horizontal component = dABx + dBCx = 156.99 km + 53.95 km = 210.94 km (east)

Total vertical component = dABy + dBCy = 186.07 km - 19.52 km = 166.55 km (north)

To find the magnitude of the vector, we use the Pythagorean theorem:

Magnitude = √(Total horizontal component)^2 + (Total vertical component)^2

Magnitude = √(210.94 km)^2 + (166.55 km)^2

Magnitude = √(44355.6036 km^2 + 27716.5025 km^2)

Magnitude ≈ √(72072.1061 km^2)

Magnitude ≈ 268.7 km

To find the direction of the vector, we use trigonometry:

Direction = arctan(Total vertical component / Total horizontal component)

Direction = arctan(166.55 km / 210.94 km)

Direction ≈ 37.1° north of east

Therefore, the vector for the entire trip has a magnitude of approximately 268.7 km and a direction of 37.1° north of east.

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A spacecraft in orbit around the moon measures its altitude by reflecting a pulsed 10 MHz radio signal from the surface. If the spacecraft is 55 km high, what is the time between the emission of the pulse and the detection of the echo

Answers

The time between the emission of the pulse and the detection of the echo is approximately 0.3669 seconds.

The time between the emission of the pulse and the detection of the echo, we need to consider the round trip travel time of the radio signal.

The round trip travel time consists of two parts: the time taken by the signal to travel from the spacecraft to the surface of the Moon and back, and the time taken for the reflection to reach the spacecraft again.

The time for the signal to travel from the spacecraft to the Moon's surface and back, we can use the formula:

Time = Distance / Speed

Given that the spacecraft is 55 km high, we consider the distance to be twice that value (round trip). Thus, the distance is 2 × 55 km = 110 km = 110,000 meters.

The speed of the radio signal in a vacuum is the speed of light, which is approximately 299,792,458 meters per second.

Time = Distance / Speed

Time = 110,000 meters / 299,792,458 meters per second

Time ≈ 0.3669 seconds

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A device with a wire coal that is mechanically rotated through a

Answers

Answer:

A generator is a device that converts mechanical energy into electrical energy by rotating a coil of wire in a magnetic field.

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