a car backfires as it drives along the highway between two mountains. the echo from one side of mountain is heard 1.5 s after the car backfire was fired. the echo from the other mountain is heard 1.0 s after the first echo. how far apart are the mountains? assume the speed of sound in air is 343 m/s. (use guess method)

Answers

Answer 1

The echo from the other mountain is heard 1.0 s after the first echo. So, the two mountains are approximately 600.25 meters apart.

The time for the sound to travel to the first mountain and back is 1.5 seconds, so we can use that time to calculate the distance traveled.

The distance traveled is equal to the speed of sound multiplied by the time it takes for the sound to travel that distance.

d = v * t

d = 343 m/s * 1.5 s = 514.5 m

This distance is the total distance traveled by the sound to reach the first mountain and back to the listener. Since this is a round trip, the distance to the first mountain is half of this value:

d1 = 514.5 m / 2 = 257.25 m

Next, we can use the time it took for the second echo to arrive (1.0 s) to find the distance to the second mountain:

d2 = 343 m/s * 1.0 s = 343 m

Finally, to find the distance between the two mountains, we simply add the distances to the two mountains:

d = d1 + d2 = 257.25 m + 343 m = 600.25 m

Echo is a technology that allows sound to be reflected and repeated back to its source. It is commonly used in a variety of applications including sonar, radar, and audio systems. In sonar and radar, echo is used to determine the distance, speed, and direction of objects. In audio systems, echo is used to create a sense of space and depth in sound recordings. Echo can also be used to reinforce sound in concert halls and other large spaces.

Echo is created by reflecting sound waves off of a surface, such as a wall or a solid object. The time it takes for the echo to return to its source is called the echo delay time, and it can be used to determine the distance of the reflecting surface. In audio systems, echo can be added artificially by using echo chambers, digital signal processors, or other electronic devices.

Echo can also cause problems in audio systems, particularly in communication systems, where echoes can interfere with the clarity of speech. To reduce unwanted echoes, many audio systems use echo cancellers, which are algorithms that identify and subtract echoes from the audio signal.

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Related Questions

how many extra electrons are on this particular oil drop (given the presently known charge of the electron)? select all that app

Answers

Extra electrons are on this particular oil drop is 4.

qE=mg⇒q×1.68×10^5 =1.08×10^−14 g⇒q=6.40×10 ^−19C

q=ne⇒6.4×10 ^−19 =n×1.6×10 ^−19 ⇒n=4

Definition of Electron

Electrons are part of an atom, which can be defined as the particles that make up the atom, which have a negative charge and surround the positively charged nucleus of the atom.

It is because of the presence of electrons that an elemental atom has a neutral charge.

History of the Electron

Electrons were first discovered after the discovery of the cathode tube which emitted a weak green light.

The scientist who first discovered the electron was J.J. Thompson who also put forward the theory of the atomic model.

Light treasury can occur due to a large enough electric potential that is given to the two wires as part of the cathode tube.

The cathode rays are thought to be J.J. Thompson as a particle because it can rotate the propeller that is between the cathode and anode.

The cathode rays were then referred to as part of the constituent atoms we know today as electrons.

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could a material exist that has a coefficient of zero for thermal expansion? describe the requirements for such a material at an atomic level.

Answers

Yes, it is possible for a material to have a thermal expansion coefficient of zero.

The individual atoms that make up a material must expand and contract in a perfectly symmetrical manner when subjected to thermal energy in order for the material to have a coefficient of zero for thermal expansion. For the atoms to expand and contract by the same amount in response to the same amount of thermal energy, they must have precisely symmetrical bonding connections. In addition, despite the temperature fluctuation, the material's lattice structure must hold steady.

Thermal expansion: The process by which an object enlarges as its temperature rises is known as thermal expansion. It is a typical occurrence that happens in a variety of substances, including liquids, gases, ceramics, metals, and plastics. When a material's temperature rises, the molecules inside it obtain kinetic energy and begin to move farther apart, which leads to thermal expansion. The volume and size of the substance expand as a result of the wider spacing between the molecules.

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a block of wood has a mass of 6.0 g and a volume of 12.0 cm3. what is the density of the block of wood?

Answers

Answer:

The density of the block of wood can be calculated by dividing its mass by its volume.

Density = Mass/Volume

Mass = 6.0 g

Volume = 12.0 cm3 = 0.012 liters

Density = 6.0 g / 0.012 L = 500 kg/m^3

Therefore, the density of the block of wood is 500 kg/m^3.

A device that automatically writes down (records) changes in temp is called?

Answers

A thermograph is a gadget that automatically logs (records) temperature changes.

What is the thermograph used for?

By identifying heat leaks, thermography is able to identify inadequate thermal insulation and boost the effectiveness of heating and cooling systems. Air leaks in windows and doorframes can also be discovered during a building envelope assessment.

What exactly is a thermograph device?

An automatic temperature recorder. The thermometric component is typically either a liquid-filled Bourdon tube or a bimetal strip. The bimetal element in the first scenario is shaped like a helical coil, with one end fixed firmly to the device and the other to recorder pen.

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Josif is a pharmacy technician who is having a professional conversation with another staff member of the hospital. Who might Josif be interacting with? Select all that apply.

Answers

Josif, as a pharmacy technician, might be interacting with the following staff members in a hospital:

Pharmacists: They oversee the work of pharmacy technicians and provide medication-related information and advice to patients and other healthcare professionals.
Nurses: They work closely with pharmacists and pharmacy technicians to ensure that patients receive the correct medications at the right time and dosage.
Doctors: They prescribe medications for patients and may provide information about medication interactions or side effects.
Patients: Pharmacy technicians may need to interact with patients to obtain information about their medication history or to provide information about their medications.
Hospital administrators: Pharmacy technicians may interact with administrators to provide information about the hospital's pharmaceutical needs or to discuss issues related to medication storage and dispensing.
Supply chain personnel: Pharmacy technicians may interact with supply chain personnel to order, receive, and manage medication supplies.
These are just a few examples of the staff members with whom Josif may interact in a hospital. The actual interactions may vary based on the hospital and the specific duties of Josif as a pharmacy technician.

what would be the mass of a truck if it is accelerating at a rate of 5 m/s2 and hits a parked car with a force of 14,000 n?

Answers

The mass of the truck is 2800 kg if it is accelerating at a rate of 5 m/s² and hits a parked car with a force of 14,000 N.

What does second law of Newton state?

The Second Law of Newton states that the acceleration of an object is directly proportional to the net force applied to it, and inversely proportional to its mass.

Where is the concept of second law of Newton used?

The Second Law of Newton is used in many areas of physics and engineering to comprehend and predict the motion of objects under the influence of forces like Aerospace engineering, Robotics, Structural engineering, Mechanics, etc.

We can the mass by using:

F = m × a

where F is for force, m is for mass, and a denotes acceleration.

m = F / a

= 14,000 N / 5 m/s²

= 2800 kg

So the mass of the truck is 2800 kg if it is accelerating at a rate of 5 m/s² and hits a parked car with a force of 14,000 N.

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you want to make sure your incubator is operating at correct temperature of 37* c, so you place a thermometer inside the incubator and check it every hour for five hours. you record readings of 36.9, 37.1, 37 and 37,1. is this an accurate, precise, or both......

Answers

Placing a thermostat within the incubator and checking it every hour after five hours will ensure that it is working at the proper temperature of 37 C.

The incubator is set to 37 degrees; why?

Incubators are essential in clinical laboratories because temperature is a crucial physicochemical component that impacts the bacterial habitat. Temperatures between 35 and 37 degrees Celsius are ideal for human diseases to proliferate.

At 37 degrees, do eggs hatch?

Eggs may hatch if the temperature is between 35 and 40.5°C (84.5 and 104.9°F). The ideal temperature (for hen) was 37.5 °C (99.5 °F), and temperatures above this point result in a reduced hatch and a rise in the number or crippled and malformed chicks. No eggs will survive temperatures over 40.5 °C (104.9 °F).

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In what ways does a 30 meter telescope outperform a 10 meter telescope?

Answers

As said, its pictures are nine times brighter compared to those of a ten meters.

Simple explanation of how a telescope functions?

Through a big aperture, considerably larger than human eyes, telescopes gather the same or more light as they can. We may see items alongside them that are undetectable to the unaided eye because they catch so much light.

What are a telescope's primary purposes?

The two most crucial tasks of a camera are to gather the weak light coming from an astronomy source and to concentrate all of the radiation into a single point or picture. The majority of astronomical objects of interest are quite dim; the more illumination we can gather, the better we can examine such objects.

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a red car has an instantaneous acceleration of 16 m/s2 westwards while a blue car has an instantaneous acceleration of 8 m/s2 westwards. based on this information, what can be correctly stated about their motion?

Answers

The direction of the acceleration of both cars is westwards, which means that their velocity in the westward direction will increase over time.

Based on the information that a red car has an instantaneous acceleration of 16 m/s^2 westwards and

a blue car has an instantaneous acceleration of 8 m/s^2 westwards,

the following statements can be made about their motion:

The red car is accelerating at a faster rate than the blue car in the westward direction.

This means that the red car is increasing its velocity in the westward direction at a faster rate than the blue car.

The westward acceleration of the red car is double that of the blue car. This means that if both cars continue to accelerate at these rates,

the red car's velocity in the westward direction will increase at twice the rate of the blue car's velocity.

Statements are based solely on the acceleration values, and other factors such as initial velocity, distance traveled, or time elapsed could also affect the motion of the cars.

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Why do we find it more difficult to recognize inverted faces than other inverted objects?

Answers

Because The FFA responds to upright faces more than inverted faces, indicating that inverted faces are not perceived in the same way that upright faces are.

Are people better at Recognising upright or inverted faces?

According to the face(UI) effect, perception and recognition are better for upright (U) faces than for inverted ones (I). According to the face/object(UI) effect, inversion inhibits face processing more than nonfacial object processing (e.g., buildings or cars).The fusiform face area (FFA) is a brain region situated in the fusiform gyrus with an unknown function. Some experts suggest that the FFA evolved to aid with face perception. Others believe the FFA can distinguish between any familiar stimuli.

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what is the length of a pendulum whose period on the moon matches the period of a 1.4- m -long pendulum on the earth?

Answers

Length of a pendulum whose period on the Moon matches the period of a 1.4 m pendulum on the Earth is approximately 0.23 m.

What is period of pendulum?

The time taken by the pendulum to finish one full oscillation is called time period of a simple pendulum.

The period of a pendulum is : T = 2π√(l/g), where T is period, l is length of the pendulum, and g is acceleration due to gravity. On the Moon,  acceleration due to gravity is approximately 1/6 of that on the Earth, or g_moon = 1.62 m/s².

Let length of  pendulum on the Moon be l_moon. Period of the pendulum on the Moon is T_moon = 2π√(l_moon/g_moon). Setting T_moon equal to the period of the 1.4 m pendulum on the Earth, T_earth = 2π√(1.4 m / 9.8 m/s²), we can find the length of the pendulum on the Moon:

T_moon = T_earth

2π√(l_moon / 1.62 m/s²) = 2π√(1.4 m / 9.8 m/s²)

Solving for l_moon, we find:

l_moon = (1.4 m) * (1.62 m/s²) / (9.8 m/s²) = 0.23 m

So the length of a pendulum whose period on the Moon matches the period of a 1.4 m pendulum on the Earth is approximately 0.23 m.

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if mary points her boat due north, how far from her intended landing spot will she be when she reaches the opposite shore?

Answers

If Mary points her boat north, the distance Mary will reach the other shore is 70.59 m.

The time required is,

t = 190 m/3.5 m/s

t = 54.3 seconds

Mary's time will also be displaced in the east.

x = (1.3 m/s) (54.3 s)

x = 70.59 m

Your question is incomplete but most probably your full question was:

Mary needs to row her boat across a 190 m-wide river that is flowing to the east at a speed of 1.3 m/s. Mary can row at a speed of 3.5 m/s. part an if Mary points her boat due north, how far from her intended landing spot will she be when she reaches the opposite shore?

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suppose a clay model of a koala bear has a mass of 0.190 kg and slides on ice at a speed of 0.610 m/s. it runs into another clay model, which is initially motionless and has a mass of 0.310 kg. both being soft clay, they naturally stick together. what is their final velocity?

Answers

The final velocity of the two clay models after they stick together is 0.545 m/s.

The final velocity of the two clay models after they stick together can be calculated using the conservation of momentum principle, which states that the total momentum of an isolated system remains constant if no external forces act on it. The initial momentum of the system is the momentum of the first clay model and the final momentum is the momentum of the two clay models combined.

The momentum of each clay model can be calculated using the formula:

p = m * v,

where p is momentum, m is mass, and v is velocity.

The initial momentum of the first clay model:

p1 = m1 * v1 = 0.190 kg * 0.610 m/s = 0.116 kg * m/s

Final momentum of the combined clay models:

p_final = (m1 + m2) * v_final = (0.190 kg + 0.310 kg) * v_final

Equating the initial momentum to the final momentum and solving for v_final:

v_final = p1 / (m1 + m2) = 0.116 kg * m/s / (0.190 kg + 0.310 kg) = 0.545 m/s

So the final velocity of the two clay models after they stick together is 0.545 m/s.

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If a car is moving to the left with constant velocity, one can conclude that? a. there must be no forces applied to the car. b. the net force applied to the car is directed to the left. c. the net force applied to the car is zero. d. there is exactly one force applied to the car.

Answers

When an object moves at a constant speed, it indicates that there is no net force acting on it. This results in a condition of balanced forces since all of the forces operating on the item added together equal zero.

The total force exerted on an item is known as the net force. It is the total force operating on an item in both magnitude and direction. According to Newton's second law, F = ma, the net force determines an object's acceleration, which is proportional to the net force and inversely proportional to the object's mass. An object will maintain its velocity and continue to move in a straight path at a constant speed if there is no net force acting on it. If the net force is not zero, the item will accelerate in that direction. In this scenario, the object's velocity will be altered by the net force, which could result in an increase or decrease in speed

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a small object is released from rest and fall 1.00 x 10^2 feet near the surface of the earth neglect air resistance how long will it take to fall through

Answers

It will take 2.49sec to fall through the 1.00 × 10² feet mentioned.

What occurs if air resistance is disregarded?

When objects are stated to be falling freely, they are only being pulled downward by gravity and do not experience much air resistance. Under these conditions, all objects will fall with the same rate of acceleration, regardless of their mass.

A thing falls freely due to gravity.

The distance traveled when free falling is measured in height.

H= Hο −1/2gt

. were Hο is the initial height g is the acceleration due the gravity t is the time

Accepting the final height equal to zero

Hο =1/2gt²

t = √2Hο /g

= 32.17

2 ⁄

t = √2∗1.00∗10²/32.17

= 2.49 sec

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Question:

A small object is released from rest and falls 1.00 × 102 feet near the surface of the earth. Neglect air resistance.

How long will it take to fall through the 1.00 × 102 feet mentioned?

3.12 s

4.50 s

2.49 s

6.25 s

10.0 s

if the internal wall is now made diathermal and the system is allowed to come to equilibrium, what are the internal energies of each of the individual systems?

Answers

What will be the internal energy of each separate system if the inner wall is now rendered diathermal and the unit is allowed to reach equilibrium

Describe smart energy.

With a focus on the design, analysis, planning, and modeling of smart energy systems, Smart Power is an international, multidisciplinary publication. The magazine wants to be a powerful platform and a reliable source of knowledge on how to reform energy demand and supply systems to be more environmentally friendly.

Energy Journal: What is it?

An international, interdisciplinary journal of electrical and electronic engineering and research is called Energy. The journal aspires to be a premier venue for peer review and a reliable source of data for analyses, reviews, and evaluations of energy-related topics. The journal publishes work in mechanical research. ... Reinhard Haas Benhard Sebastian Zwickl

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the moon completes one orbit around the earth every 27.3 days with respect to the fixed stars. how far (in degrees) does the moon move around the earth in one day? (recall that one full orbit is 360 degrees.)

Answers

The moon moves around the earth by approximately 13.2 degrees per day.

This is because the moon completes one orbit around the earth every 27.3 days , and 360 degrees divided by 27.3 days gives us 13.2 degrees per day.

The Moon moves around Earth in an elliptical orbit, completing a full revolution around the planet every 27.322 days. This motion is caused by the force of gravity between Earth and the Moon, which is constantly pulling the Moon towards the Earth. As the Moon orbits, different parts of its surface are illuminated by the Sun, resulting in the Moon's changing phases that we observe from Earth. Additionally, as the Moon moves, it can pass in front of the Sun from Earth's perspective, causing a solar eclipse, or pass into the Earth's shadow, causing a lunar eclipse.

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why is a specimen smaller than 200 nm not visible with a light microscope? why is a specimen smaller than 200 nm not visible with a light microscope? it is too easy to lose on the stage. the lenses only go to 100 x magnification power. anything smaller than 200 nm cannot interact with visible light. visible light is only good at wavelengths below 390 nm. request answer

Answers

Visible light is insensitive to objects smaller than 200 nm. On stage, defeat is all too often. Only wavelengths below 390 nm are suitable for visible light.

Why can't a light microscope see a specimen that is smaller than 20 nm?

Because visible light, which the microscope uses, has a specific range of wavelengths, A smaller item than the wavelength of the light cannot be imaged by the microscope.

Why is a light microscope only capable of 200 nm of resolution?

It was believed throughout the majority of the 20th century that far-field light microscopy could not resolve things closer than 150–200 nanometers (see Milestone 3). Light diffracts when it travels through various media,

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The overall global circulation of air is caused by ____ equatorial air and _____ polar air

Answers

The overall global circulation of air is caused by rising equatorial air,  and sinking polar air.

What is global circulation of air?

The global circulation of air can be described as the world-wide system of winds by which the necessary transport of heat from tropical to polar latitudes is accomplished.

The pattern of global circulation of air is called atmospheric circulation,  and it is caused because the Sun heats the Earth more at the equator than at the poles. It's also affected by the spin of the Earth.

Thus, the overall global circulation of air is caused by rising equatorial air and sinking polar air.

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Answer:

rising

Explanation:

the abs system prevents the wheels from locking or skidding, no matter how hard the brakes are applied or how slippery the road surface. group of answer choices true false

Answers

It is true that the Anti-Lock Braking System (ABS) helps prevent the wheels from locking or skidding when the brakes are applied, even on slippery road surfaces.

What is friction?

Friction is the force that prevents solid surfaces, fluid layers, and material components from sliding against each other. There are several kinds of friction: Dry friction is the force that opposes the relative lateral motion of two in touch solid surfaces. Friction is the force that prevents one solid item from slipping or rolling over another. Frictional forces, such as the traction required to walk without slipping, are advantageous, but they also create a significant amount of resistance to motion. We can manage automobiles because of friction between the tires and the road: more precisely, because there are three types of friction: rolling friction, beginning friction, and sliding friction.

Here,

ABS maintains tire traction and steerability by swiftly applying and releasing the brakes, which enhances braking performance and assists the driver in maintaining vehicle control.

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if the tape timer creates dots at a rate of 35 hz, what time interval in seconds does 3 successive dots represent? g

Answers

The frequency of dot production in this instance is 28 Hz since the tape timer produces 28 dots per second.

How long would it take for the sun's light to travel from space to Earth's surface—150 seconds?

Light moves at a speed of 186,287 miles per second, or 299,792 kilometers per second. 1 Astronomical Unit, or the time it takes for light to journey from the Sun to Earth, is 499.0 seconds.

A second is how many?

The 3rd (symbol: s) is the time unit used in the International Systems of Units (SI). It has historically been defined as 186400 of a day; this number came from the division of a day into 24 hours, 60 minutes, and then 60 seconds.

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Whenever the net force on an object is zero, its acceleration _____.
(a) and velocity are the same
(b) is zero
(c) may be zero
(d) None of the above.

Answers

A is the correct one

true or false: equipotential surfaces of 50 v, 40 v, 30 v, 20 v and 10 v near a single, positive point charge are equally spaced in the radial direction.

Answers

The statement is true, equipotential surfaces of 50 v, 40 v, 30 v, 20 v and 10 v near a single, positive point charge are equally spaced in the radial direction.

The surface in an electric field where the value of electric potential is the same at all the points on the surface is called equipotential surface. The potential difference between two points in an equipotential surface is zero.

Thus, work done in moving the charge from one point to another in an equipotential surface is zero. since the work is done is zero when the direction of force (electric field) and displacement is normal.

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a car has wheels with a 8 inch radius. if each wheel's rate of turn is 6 revolutions per second, how fast is the car moving in units of inches/sec?

Answers

A automobile has 8 inch-radius wheels. If each wheel rotates at the rate of 6 revolutions per second, the car is moving at a speed of 301.71 inches per second.

What exactly does speed mean?

the definition of speed. a direction or speed at which an object's location changes. The distance traveled relative to the time it took to travel that distance is how fast something is moving. Due to its lack of magnitude and merely having a direction, speed is indeed a scalar number.

Which of these is the first speed rule?

Newton's first law states that a body will continue to move until it is acted on by an external power if it is at rest or moving in a specific direction at a fairly constant pace.

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a block released from rest at position a slides with negligible friction down an inclined track, around a vertical loop, and then along a horizontal portion of the track, as shown above. the block never leaves the track. the gravitational potential energy and the kinetic energy of the block are most nearly equal at which position? (consider the potential energy to be zero at position b.)

Answers

The block's gravitational potential energy and kinetic energy are approximately identical at location C.

The block has maximum potential energy at position A since it has been freed from rest, but no kinetic energy. The block's potential energy is converted to kinetic energy when it slides down the inclined track. The block has transformed all of its potential energy into kinetic energy by the time it reaches position C. At this stage, the block's gravitational potential energy and kinetic energy are approximately equal.

The block then loops around the vertical loop, gaining potential energy once more. It will lose some potential energy as it travels along the horizontal part of the rail, but the gravitational potential energy and kinetic energy of the block will not be equal again until the block reaches position B.

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Explain how static electricity works in at least three complete sentences. Remember to use proper
grammar and mechanics when writing your sentences.

Answers

When two objects are rubbed on their surfaces, one gets negatively charged. This polarization causes, the flow of electrons to the positive pole of another object is called the static electricity.

What is static electricity ?

Static electricity is the flow of electrons that occurs due to the temporary polarization of two bodies. When a conducting surface rub on other surface, they gets electrons by frictional force.

These free flow of electrons make them negatively charged. When this negatively charged body comes in contact with a non conducting surface they latter gets polarized by the electrons of negatively charged body.

The positive charges of the nonconducting surface gets attracted to the negative body and the electrons flow from the negatively charged body to the partially polarized positive body. This is called static electricity.

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khaled has a red toy that is painted with a special kind of paint. when he puts the toy under a desk lamp, it stays red. when he puts the toy under an infrared lamp, it turns blue. why does the infrared light cause the toy to turn blue when the light from the desk lamp does not?

Answers

Because infrared light extracts energy from the paint whereas desk lamp light does not.

What is the best explanation of energy?

Energy's "ability to accomplish labor" refers to its ability to exert a force that moves an item. Despite the vagueness of the phrase, energy actually refers to the force which moves objects. The two types of energy are energy and potential energy.

How energy is made?

Nearly majority of the world's energy is produced by steam turbines using carbon fuels, nuclear energy, biofuels, thermal, etc solar thermal energy. Solar photovoltaics, wind turbines, water turbines, gas turbines, and other important electricity generation technologies.

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Cities can reduce earthquake damage by


atleast 3 examples​

Answers

Cities can reduce earthquake damage by identifying hazards, building safer structures, and providing education on earthquake safety.

What is earthquake?

A abrupt release of energy in the Earth's lithosphere that results in seismic waves causes an earthquake, which is the shaking of the planet's surface.

Earthquakes can range in strength from those that are so small that no one can feel them to those that are powerful enough to throw things and people into the air, destroy vital infrastructure, and devastate entire cities. The number, kind, and size of earthquakes that occur in a region over a specific time period is known as its seismic activity.

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a satellite is placed in an orbit with a radius that is half the radius of the moon's orbit. find its period in units of the period of the moon.

Answers

The period of a satellite in an orbit around the Earth with a radius half that of the moon's orbit is 0.35 TM. Thus, Option A is correct.

Based on the answer, we understand that it takes 0.35 times the amount of time for the satellite to complete one full orbit as it takes for the moon to complete one orbit around the Earth.

To explain, the period of a satellite in orbit around the Earth is directly proportional to the square root of the semi-major axis of its orbit. Since the semi-major axis of the satellite's orbit is half that of the moon's orbit, the square root of this value will also be half the square root of the moon's orbit, resulting in a period that is 0.35 times that of the moon's orbit.

Kepler's third law states that the square of the orbital period of a planet or satellite is proportional to the cube of the semi-major axis of its orbit, so a satellite with a smaller semi-major axis will have a shorter period.

The following options should be provided along with the question:

A. 0.35 TMB. 0.125 TMC. 0.5 TMD. 0.63 TM

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if 5.4 j of work is needed to stretch a spring from 10 cm to 16 cm and another 9 j is needed to stretch it from 16 cm to 22 cm, what is the natural length (in cm) of the spring?

Answers

The required natural length of the spring is 0 cm.

How we get the natural length of the spring?

The work done on a spring is given by the equation W = (1/2)kx^2, where W is the work done, k is the spring constant, and x is the change in length of the spring.

From the information given:

we have two equations:

W1 = (1/2)k(16-10)^2 = 5.4 J

W2 = (1/2)k(22-16)^2 = 9 J

Solving for k, we can find the spring constant:

k = (2W1)/(16-10)^2 = (2 * 5.4) / (16-10)^2 = 2.7 / 36 = (2.7 / 12^2) N/m

Next, we can use the spring constant to find the natural length (the length of the spring when no force is applied) by setting x = 0 in the equation for work:

W = (1/2)kx^2 = (1/2)k * 0^2 = 0 J

So, x = (2W / k)^(1/2) = (2 * 0 / (2.7 / 12^2))^(1/2) = 0 cm

This means that the natural length of the spring is 0 cm. Note that the unit cm is not used in the calculation of the spring constant, and that the spring constant has units of N/m.

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