The values of theta is the vertical component ay of the acceleration vector greatest in magnitude at 90° and 270°.
Multidimensional stir with constant acceleration can be treated the same way as shown in the former chapter for one- dimensional stir. before we showed that three- dimensional stir is original to three one- dimensional movements, each along an axis vertical to the others.
To develop the applicable equations in each direction, let’s consider the two- dimensional problem of a flyspeck moving in the xy aeroplane with constant acceleration, ignoring the z- element for the moment.
Thinking of circles as parametric equations:
ry=sinθ
rx=cosθ
Note that I have limited θ: 0° <=θ < 360°
Also note that the greatest magnitude of sine and cosine functions is1.
This problem is based only on the y-component, so just consider ry=sinθ.
It hast he greatest magnitude (vertical distance from the center) at90° (and 270°).
Takethe derivative for velocity.
vy=cosθ
It has the greatest magnitudes at 0° and 180°.
Take the derivative for acceleration
ay=-sinθ
It has the greatest magnitudes at 90° and 270°
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Complete question:
At what value(s) of is the vertical component ay of the acceleration vector greatest in magnitude? (Several choices may be correct.) 0° 90° 180° 270°
When a car’s velocity is positive and its acceleration is also positive what is happening to the car’s overall motion?
When a car's velocity is positive and its acceleration is also positive, the car's overall motion is speeding up in a forward direction.
Velocity is the measure of an object's speed in a specific direction, while acceleration is the measure of how quickly an object's velocity changes over time. So, if both the velocity and acceleration are positive, the car's speed is increasing in the forward direction. This means that the car is moving faster and faster in a forward direction.
Likewise, it can be said that the automobile develops an accelerated movement.
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Predict: Suppose a cart with no fans has a starting velocity of 2 m/s. What will be the
velocity of the cart when it reaches the wall?
when it reaches the wall will be 4.5 m/s.
What is meant by ""the rate of doing work is power""?
Answer:
P=W/t
Explanation:
Work is given by the equation W=FxD
- F is force
- D is distance
"the rate of doing work is power" is saying that the rate in time (s) for work is given by Power.
Meaning that Power = Work/time
Think of it like this, a) find the work for a force of 150N over a distance of 10m.
W = (150N)(10m)
W = 1500J
Lets say in the question it also tells you that this work is done for 10 seconds. b)
Given by the equation P=W/t
You would simply plug in these values
P = (1500J)/(10s)
P = 150 W
The units for power is Watts.
In conclusion, the Power is the rate of work done. Also could be thought of as Work per second.
Given by equation P=W/t
The air around a certain chemical reaction becomes warmer as the reaction progresses. How is energy transferred from the system to the surroundings?
A) Molecules in the system absorb energy when they move to the surroundings.
B) Molecules in the system absorb energy when the collide with molecules from the surroundings.
C) Molecules in the system transfer kinetic energy when they collide which molecules in the surroundings.
D) Molecules in the surroundings transfer kinetic energy when they collide with molecules in the system
The correct answer is D) Molecules in the surroundings transfer kinetic energy when they collide with molecules in the system.
What is exothermic chemical reaction?An exothermic chemical reaction is a type of chemical reaction in which heat energy is released into the surrounding environment. During an exothermic reaction, the products of the reaction have less energy than the reactants, and the difference in energy is released as heat. This means that the temperature of the surroundings increases as the reaction proceeds.
Some common examples of exothermic reactions include combustion, oxidation, and neutralization reactions. In contrast, an endothermic chemical reaction is a reaction that absorbs heat from the surroundings as the reaction proceeds, resulting in a decrease in temperature of the surroundings.
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Answer:
C. Molecules in the system transfer kinetic energy when they collide with molecules in the surroundings.
Explanation:
Words that sound the same but have different meanings are called
Words that sound the same but have different meanings are called
synonyms.
homophones.
antonyms.
Option homophones is the correct option.
Words that sound the same but have different meanings are called homophones.
A term that has the same pronunciation as another word but a different meaning is called a homophone. Moreover, a homophone's spelling may vary. The two words can have the same spelling, as in rose and rose, or they can have a distinct spelling, as in rain, reign, and rein.
A homophone is defined as "one of two or more words pronounced alike but different in meaning, derivation, or spelling" by the Merriam-Webster Dictionary. Homophones are described as "words having various meanings which are spoken in the same way but are spelt differently" by the Collins Dictionary.
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Note: The correct question would be as bellow,
Words that sound the same but have different meanings are called
synonyms.
homophones.
antonyms.
you are riding an elevator. an object has been hung from a spring balance attached to the elevator ceiling. the scale reads the weight of the object as w when the elevator is stationary. the elevator then starts moving. the scale then reads the weight of the object as 0.75w. what is the acceleration of the elevator?
According to the question the acceleration of the elevator is 0.25w/t.
What is acceleration?Acceleration is defined as the rate of change of velocity, or the rate at which an object's speed or direction is changing. It is a vector quantity, meaning it has both magnitude and direction. Acceleration can be either positive or negative, depending on the direction of the change in velocity.
The acceleration of the elevator can be calculated by using the following equation:a = (w-0.75w)/t
where 'a' is the acceleration of the elevator, 'w' is the weight of the object when the elevator is stationary, and 't' is the time it takes for the elevator to move.
Since the time it takes for the elevator to move is unknown, we can rearrange the equation to solve for 't':
t = (w-0.75w)/a
By substituting the known values of w and 0.75w into the equation and solving for 'a', we can calculate the acceleration of the elevator:
a = (w-0.75w)/t = (w-(0.75*w))/t = (w(1-0.75))/t = 0.25w/t
Therefore, the acceleration of the elevator is 0.25w/t.
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heat transfer by conduction occurs when: group of answer choices electromagnetic waves travel from one place to another through a vacuum electrons bump into atoms and other electrons large numbers of atoms move from place to place atoms give off heat in the form of electromagnetic waves
Heat transfer by conduction occurs when large numbers of atoms move from place to place.
Conduction is the transfer of heat through a material by the movement of molecules or electrons from a region of higher temperature to a region of lower temperature. In this process, heat energy is transferred from one molecule to another through molecular collisions. This transfer of energy continues until thermal equilibrium is reached, i.e., when the temperature is the same throughout the material.
Electromagnetic waves traveling from one place to another through a vacuum is an example of heat transfer by radiation. Electrons bumping into atoms and other electrons is an example of heat transfer by convection. Atoms giving off heat in the form of electromagnetic waves is an example of heat transfer by radiation.
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5. What is the momentum of a 0.05 kg golf ball moving at 240 m/s?
Answer:
12 kg m/s.
Explanation:
The momentum of an object is equal to its mass times its velocity. In this case, the mass of the golf ball is 0.05 kg and its velocity is 240 m/s, so the momentum of the golf ball is:
0.05 kg * 240 m/s = 12 kg m/s
So, the momentum of the golf ball moving at 240 m/s is 12 kg m/s.
the lowest note on a grand piano has a frequency of 27.5 hz . the entire string is 2.00 m long and has a mass of 400 g . the vibrating section of the string is 1.90 m long
The lowest note on a typical 88-key piano is designated A0. The 0th octave note "A" is identified as such. The first octave's "A" note, which is an octave higher than that, is A1, not A.
What is the lowest note on a grand piano has a frequency?With 88 keys, a full-size piano offers a range of little more than 7 octaves. The third white key from the right end of the piano, which is the highest A note, has a frequency of 3520 hertz.
Discover the relationship between the frequencies of two subsequent notes, or of two adjacent keys on the piano keyboard.
The fundamental harmonic, or lowest note on a grand piano, has a wavelength that is twice the length of the vibrating part of the string, or = 2L, where L = 1.90 m.
The wave's velocity is given by v = f, but it also depends on the tension of the wire, as shown by v = qT, where m/ is the wire's linear mass density ( is the full length of the wire, not the vibrating part).
[tex]T = u(\lambda f)^2= 4 ul^2f^2= \frac{4 ml^2f^2}{l}[/tex]
[tex]= \frac{4.400\times (1.90)^2 (27.5)^2}{2}[/tex]
[tex]= 2185N[/tex]
Therefore, the tension is 2185 N.
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Suppose that two objects attract each other with a gravitational force of 18 units. If the mass of one of the objects was tripled, and if the distance between the objects tripled, then what would be the new gravitational force of attraction between the two objects?
Answer:
6 units
Explanation:
You want the gravitational force between two objects after both the mass of one object and the distance between them triples, if it is initially 18 units.
ForceLet F represent the initial force between the objects. Newton's law of gravitational attraction tells us ...
F = GmM/r²
When one mass is tripled, and the distance between the objects is tripled, the new force is ...
F' = G(3m)M/(3r)² = 3/9(GmM/r²) = F/3
Given the initial force is 18 units, the new force of attraction is ...
F' = (18 units)/3 = 6 units
The new gravitational force of attraction between the objects is 6 units.
If a flea can jump straight up to a height of 0.350 m, what is its initial speed as it leaves the ground?
Answer:
To solve this problem, we can use the fact that the flea's initial kinetic energy is converted entirely into potential energy at the top of the jump. Using conservation of energy, we can set the initial kinetic energy equal to the potential energy at the maximum height:
(1/2)mv^2 = mgh
where m is the mass of the flea, v is its initial velocity, g is the acceleration due to gravity, and h is the maximum height of the jump.
We can solve for v:
v = sqrt(2gh)
where we substitute the given values:
v = sqrt(29.8 m/s^20.350 m) ≈ 2.65 m/s
So the flea's initial speed as it leaves the ground is approximately 2.65 m/s.
Explanation:
three vehicles approach an uncontrolled intersection. car a wants to make a left turn and is across the intersection from car b. car b is ahead of car c and both are in the same lane traveling in the same direction and want to proceed straight through the intersection. the law gives the right-of-way:
Three cars are coming up to an uncontrolled intersection. Across from Car B at the intersection, Car A wants to turn left. According to the legislation, Vehicle B has the right-of-way.
Explain the rules and law of roads?Right-of-Way Rules:
Whenever vehicles, pedestrians, and bikes collide on the road, right-of-way regulations make it clear who should move first. The right-of-way belongs to the car that approaches the intersection first.The driver who has that right-of-way must yield to other cars, bikes, and pedestrians.Intersections:
Any location where one road joins another is considered an intersection. Controlled intersections have signage or lighting for the traffic signals.Any location where one road joins another is considered an intersection. Controlled intersections have signage or lighting for the traffic signals.Automobiles, bicycles, and pedestrians upon it through route (moving forward straight) have always had the right-of-way at T intersections lacking STOP or YIELD signs.Look for pedestrians before making a left turn. Any approaching pedestrian or dangerously close vehicle must be given the right of way.Three cars are coming up to an uncontrolled intersection. Across from Car B at the intersection, Car A wants to turn left.
Thus, according to the legislation, CAR B has the right-of-way.
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The complete question is-
Three vehicles approach an uncontrolled intersection. Car A wants to make a left turn and is across the intersection from Car B. Car B is ahead of Car C and both are in the same lane traveling in the same direction and want to proceed straight through the intersection. The law gives the right-of-way:
To Car A Only.
To Car A and Then Car B.
To Car B and then Car A.
To Car B.
a certain battery charger uses 12 w of power. at 6.0 cents per kilowatt-hour, how much does it cost to charge batteries for a full day?
It would cost approximately 1.7 cents to charge batteries for a full day using this battery charger.
What type of energy is stored in a battery?A battery stores chemical energy. Chemical energy is a form of potential energy that is stored in the chemical bonds between atoms and molecules. In a battery, this energy is stored in the form of chemicals that can be converted into electrical energy when the battery is used.
To calculate the cost of charging batteries for a full day, we first need to determine the amount of energy used by the battery charger in one day.
Since the power of the charger is 12 watts, we can calculate the energy used in one hour as:
12 watts × 1 hour = 12 watt-hours
To get the energy used in one day, we can multiply the energy used in one hour by the number of hours in a day:
12 watt-hours × 24 hours = 288 watt-hours
To convert watt-hours to kilowatt-hours (kWh), we need to divide by 1000:
288 watt-hours / 1000 = 0.288 kilowatt-hours
Finally, we can calculate the cost of using 0.288 kWh of energy at a rate of 6.0 cents per kWh:
0.288 kWh × $0.06/kWh = $0.01728
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A Toy Boat with a force of 40.0 N is required to pull a 10.0-kg wooden toy boat at a constant velocity across a smooth glass surface on Earth. What is the force that would be required to pull the same wooden toy boat across the same glass surface on the planet Jupiter?
The force required in Jupiter is 80 N.
What is the acceleration due to gravity on Jupiter?The strength of the gravitational field on Jupiter is determined by its mass and size, as well as the distance from its surface to the center of the planet. Because Jupiter is much larger and more massive than Earth, its gravitational field is much stronger, which results in a higher acceleration due to gravity.
In this case we need to know the value of the acceleration due to gravity on the Jupiter planet which is 8 m / s 2.
Thus we would need;
mg = 10 Kg * 8 m / s 2. = 80 N
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the two light bulbs are now connected in parallel across the 120- v line. find the current through each bulb.
The current through each bulb is 0.15A.
D)
V = Voltage across each bulb = 120 Volts
i400 = current in 400 ohm resistor = V/R = 120/400 = 0.3 A
i800 = current in 800 ohm resistor = V/R = 120/800 = 0.15 A
E)
P400 = V2/R400 = 1202/400 = 36 Watt
P800 = V2/R800 = 1202/800 = 18 Watt
F)
Ptotal = 36 + 18 = 54 Watt
Current refers to the flow of electric charge through a conducting medium. It is defined as the amount of charge that passes through a given cross-sectional area per unit of time. The SI unit of current is the ampere (A), which is defined as the flow of one coulomb of electric charge per second.
In an electric circuit, the current flows from a higher potential to a lower potential, and the direction of the current is taken as the direction in which positive charges would flow. In DC, the current flows in one direction only, while in AC, the current changes direction periodically. The magnitude of the current depends on the potential difference across the circuit and the resistance of the circuit.
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Complete Question:
Two light bulbs have resistances of 400 Ω and 800 Ω.
D). the two light bulbs are now connected in parallel across the 120- v line. find the current through each bulb.
E). Find the power dissipated in each bulb.
F). Find the total power dissipated in both bulbs.
A car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. What is the cars average acceleration
Answer:
the car's average acceleration is 2.77 m/s^2.
Explanation:
The average acceleration of the car can be calculated using the formula for average acceleration, which is:
a = (v_f - v_i) / t
where:
a is the average acceleration
v_f is the final velocity (70 km/h)
v_i is the initial velocity (0 km/h)
t is the time taken (7 seconds)
First, we need to convert the velocity from km/h to m/s, as the formula requires both velocities to be in the same units. 70 km/h is equivalent to 70 * 1000 / 3600 = 19.44 m/s.
Plugging the values into the formula:
a = (19.44 - 0) / 7
a = 2.77 m/s^2
So the car's average acceleration is 2.77 m/s^2.
a 159 watt motor in a bowling alley lifts an 7 kg bowling ball directly upwards at a constant speed. at what speed does the ball rise?
The speed at which the ball rises is 2.24 m/s.
What is power output?Power output refers to the amount of power that a device, machine, or system produces or generates. It is a measure of the rate at which work is done or energy is transferred, and is usually expressed in units of watts (W) or kilowatts (kW).
We can use the formula for power to find the speed at which the ball rises. The power output of the motor is given by:
Power = Work done / time taken
Since the ball is lifted at a constant speed, the work done by the motor is equal to the gravitational potential energy gained by the ball, which is given by:
Work done = mgh
where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s²), and h is the height through which the ball is lifted. The time taken to lift the ball is equal to the height of the lift divided by the speed of the lift, which is given by:
time taken = h / v
where v is the speed of the lift. Substituting these expressions into the formula for power, we get:
Power = mgh / (h/v)
Power = mgv
Solving for v, we get:
v = Power / (mg)
v = 159 W / (7 kg x 9.8 m/s²)
v = 2.24 m/s
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What interventions prevent respiratory infections?
There are several interventions that can help prevent respiratory infections, including: Vaccinations, Hand hygiene, Quitting smoking
mention few respiratory infections ?
Some examples of respiratory infections include the common cold, influenza (flu), pneumonia, bronchitis, tuberculosis, whooping cough (pertussis), and respiratory syncytial virus (RSV) infection.
Vaccinations: Getting vaccinated against certain viruses, such as the flu and pneumococcus, can help prevent respiratory infections.
Hand hygiene: Washing your hands frequently with soap and water, or using hand sanitizer, can help prevent the spread of respiratory infections.
Avoiding close contact with sick individuals: Limiting contact with individuals who are sick, and avoiding crowds during respiratory infection outbreaks, can help prevent respiratory infections.
Covering your mouth and nose: Covering your mouth and nose with a tissue or your elbow when coughing or sneezing can help prevent the spread of respiratory infections.
Cleaning and disinfecting surfaces: Cleaning and disinfecting frequently touched surfaces, such as doorknobs and countertops, can help prevent the spread of respiratory infections.
Quitting smoking: Smoking can damage the lungs and make individuals more susceptible to respiratory infections, so quitting smoking can help prevent these infections.
Improving indoor air quality: Good indoor air quality can reduce the risk of respiratory infections, so opening windows, using air purifiers, and avoiding exposure to pollutants can help prevent respiratory infections.
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6.What do contemporary psychologists generally believe with respect to the relationship between themind and the brain? How does the modern view relate to Descartes’ position?A.Contemporary psychologists believe that consciousness exists in the brain. This viewcontrasts with Descartes’ dualism.B.Contemporary psychologists believe that consciousness exists in the brain. This viewaccords with Descartes’ dualism.C.Contemporary psychologists believe that consciousness is separate from the brain. Thisview contrasts with Descartes’ dualism.D.Contemporary psychologists do not believe that consciousness exists. This view contrastswith Descartes’ dualism.ANS:ADIF:ModerateREF:4.1 Consciousness Is a Subjective Experience
The correct answer is A.According to modern psychologists, consciousness is a brain phenomenon.
This view contrasts with Descartes’ dualism, which argued that the mind and the body are separate entities and that the mind can exist independently of the body. Thus, according to Descartes, the mind is not necessarily dependent on the brain. However, contemporary psychologists believe that the mind and the brain are closely intertwined and that consciousness is a product of brain activity.Contemporary psychologists use a variety of approaches to explain and understand behavior, including cognitive, evolutionary, social, physiological, and cultural approaches. These approaches often overlap and combine to provide a comprehensive understanding of human behavior.
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if the other charges are fixed in place and charge 2q is allowed to move, what will be the kinetic energy k2q of charge 2q when it is very far from the other charges? express your answer in terms of q , d , and appropriate constants.
K2q = 7.76kg^3/d will be the kinetic energy k2q of charge 2q when it is very far from the other charges.
At the corner of the square, the potential energy of interaction of other charges with the charge 2q is given by U_2q
So
U2q.i = k2qq1 / d+k2qq1 / d+k2qq1 = 7.746kg^3 / d
Also, since v_B also
The initial energy of the system is given by;
E_i = U2qi + k2qi =7.76*kg^2/d
Since U2qf=0, the final energy of the system is obtained by
Ef = U2qf + K2qf =k2qf
From the law of conservation of energy, Ei = Ef
Therefore, K2q = 7.76kg^3/d
Kinetic energy is the electricity an item possesses with the aid of distinctive feature of its movement. it is described because the work required to accelerate an object from relaxation to its present day speed. The faster an object moves, the greater its kinetic energy.Kinetic energy is a fundamental concept in physics, and it has important applications in many fields, including engineering, sports, and transportation.
It is also a crucial concept in understanding the behavior of particles and molecules in chemistry and biology.The formula for calculating kinetic energy is 1/2 * mass * velocity^2, where mass is the mass of the object and velocity is its speed in a given direction. This equation shows that the amount of kinetic energy an object has is proportional to its mass and the square of its velocity.
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Whether a truck comes to a stop by crashing into a haystack or a brick wall, the stopping force is
A) both the same
B) greater with the haystack.
C) greater with the brick wall.
C) Greater with the brick wall. Stopping force is determined by the amount of friction a surface provides.
What is friction ?Friction is a force that acts between two objects when they come into contact with each other. It is an important force that affects our everyday life. Friction can be both beneficial and detrimental. It is beneficial in that it allows us to walk, run, drive, and even write without slipping or sliding. It also helps us to stop when we need to. On the other hand, friction can be detrimental when it causes machines to wear down, resulting in energy being wasted. Friction can also cause heat, noise, and wear on the surfaces of the two objects.
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What are the advantages and disadvantages of an electromagnet?
Answer:
Advantages
1) No power supply needed
2)Cling to vertical surfaces
3)No electrical contact problems
4)Inexpensive
Disadvantage
1)Direct field only
2)Deteriorate with wear
3)Have to be pulled from test surface
4)No control over field strength
the chances of your being involved in an auto collision, during your lifetime, in which someone is injured or killed are close to:
According to the statistic, 3% of drivers with a license are in collisions each year. Not all drivers with licences actually drive. As a result, more than 3% of drivers who are now on the road are involved in accidents.
What are the chances of auto collision?You have a 1 in 366 risk of being involved in an automobile accident for every 1000 kilometers you drive. Every 17.9 years, the average driver will submit an insurance claim for a car accident. According to this, the typical person is involved in three to four auto accidents over their lives.
According to a poll, 77% of drivers had been in one or more collisions. In addition, the typical person can anticipate participating throughout three to four auto accidents in their lifetime.
Therefore, you're likely to experience an automobile accident of some kind at some time in your life.
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How do you find the radius of a planet with gravity?
The formula for gravitational force is F=GMm/r2. The force of gravity will weaken as the Earth's radius (r) increases, which also affects your weight.
Similar to how your weight would grow if the Earth's radius (r) decreased.
The link between the mass, radius, and acceleration brought on by gravity at the surface of several planets is what this problem is about. Because of this knowledge, we will now examine Newton's law of universal gravitation. And we have a formula we can employ in this situation. The acceleration brought on by gravity on a planet's surface is known as g, and it is equal to capital G multiplied by m over r squared, where m is the mass, r is the radius, and capital G is the universal gravitational constant.
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you are standing 1.00 meters away from a sound source. at your position, the sound has an intensity of 75.0 db. how much farther from the sound source must you go for a 15.0 db reduction in intensity?
The sound intensity follows the inverse square law, so a 15.0 dB reduction in intensity corresponds to a distance twice as far from the sound source that is 2.00 meters away from the sound source.
The sound power at a given point diminishes as the separation from the sound source increments, observing the converse square regulation. This intends that assuming the separation from the sound source is multiplied, the sound force will diminish by 6.02 dB, which is a portion of the power. To accomplish a 15.0 dB decrease in force, the separation from the sound source should be expanded by an element of [tex](10^(15.0/10))^(1/2)[/tex] = 5.62, since each variable of 10 relates to a 10 dB change in power. Consequently, the separation from the sound source should be expanded by a component of 5.62, which compares to roughly 2.00 meters, to accomplish a 15.0 dB decrease in power from 75.0 dB to 60.0 dB.
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at the time of processing, the energy of the trapped electrons is released by exposure to a laser in a process called
a layer of phosphor (or active layer). This coating of photostimulable phosphor "traps" electrons while they are exposed to light. It is often composed of crystals of barium fluorohalide, chlorohalide, or bromohalide phosphors from the barium fluorohalide family.
What is the Photostimulable luminescence?Light that can be stimulated by light. the capacity to store x-ray energy for eventual release as light when triggered by a laser. Photostimulation. after being excited by laser light, emitting visible light. Tube with a photomultiplier.
The DenOptix® PSP needs to be exposed to a bright light source for a while in order to completely remove the leftover picture signal. The imaging plate's erasing time might vary from 30 seconds to two minutes depending on the brightness of the light source.
Therefore, at the time of processing, the energy of the trapped electrons is released by exposure to a laser in a process called Photostimulable luminescence.
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Why does the moon appear during the day some of the time and during the night at other times?
Answer:
As the Earth rotates, the Moon rises just as the Sun sets, but just on that one day of the month. In the days before a full Moon, if you look in the eastern sky, you can find the almost full Moon rising before the sun sets. We can see the moon during the day for the same reason we see the moon at night. The surface of the moon is reflecting the sun's light into our eyes
Explanation:
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a motorist traveling at 11m/s encounters a deer in the road 41 m ahead. if the maximum acceleration the vehicle's brakes are capable of is -7m/s^2, what is the macimum reaction time of the motorist that will allow her or him to avoid hitting the deer? answer in units of s
The maximum reaction time of the motorist that will allow her or him to avoid hitting the deer is 1.57s
The maximum reaction time of the motorist will be the time it takes for the vehicle to come to a complete stop. To find this, we can use the equation:
Vf^2=Vi^2+2ad
Where Vf is the final velocity (0 m/s), Vi is the initial velocity (11 m/s), a is the acceleration (-7 m/s^2) and d is the distance (41 m).
We can rearrange this equation to solve for t, the time it takes for the vehicle to come to a complete stop:
t=-(Vi+Vf)/a
Plugging in our values, we get:
t=-(11+0)/(-7)
t= 1.57 s
Therefore, the maximum reaction time of the motorist will be 1.57 seconds in order to avoid hitting the deer.
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8. What is meant by the critical angle of a boundary of two materials? Show how to derive the critical
angle equation.
9. Explain how the concept of total internal reflection can be applied to optical fibres.
10. Give three advantages of using optical fibres for communication.
11. a) An optical fibre has a core and cladding with refractive indices of 1.52 and 1.40 respectively. Find
the critical angle for the boundary.
1. b) What angle of incidence would light need to be at for total internal reflection to happen at this
boundary?
(8) The critical angle of a boundary of two materials is the angle of incidence, measured from the normal to the surface.
The critical angle equation can be derived from Snell's law of refraction, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two materials.
(9) Total internal reflection can be applied to optical fibers by using it to confine light inside the fiber.
(10) Three advantages of using optical fibers for communication are:
Low attenuation, Immunity to electromagnetic interference and Large bandwidth.
(11. a) The critical angle for the boundary is 67 degrees.
(11. b) The angle of incidence is 90 degrees.
What is the critical angle for the boundary?The critical angle for the boundary can be found by using the critical angle equation derived from Snell's law.
Setting the refractive index of the first material (core) to 1.52 and the refractive index of the second material (cladding) to 1.40, we have:
sin(critical angle) = (1.40)/(1.52) = 0.92
The critical angle can be found using the inverse sine function:
critical angle = sin^-1(0.92) = 67.3 degrees
The angle of incidence at which total internal reflection occurs can be found by setting the angle of refraction to 90 degrees in Snell's law:
sin(90) = (1.52)/sin(angle of incidence)
Solving for the angle of incidence:
angle of incidence = sin^-1((1.52)/(1.40)) = 90 degrees.
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Answer:
The critical angle of a boundary of two materials is defined as the angle of incidence at which the angle of refraction becomes 90°, causing total internal reflection to occur. In other words, it is the minimum angle of incidence required for light to be completely reflected back into the material with the higher refractive index.
The concept of total internal reflection can be applied to optical fibres by using them to guide light through a core with a higher refractive index surrounded by a cladding with a lower refractive index. The light is completely reflected at the core-cladding boundary and guided along the fiber, allowing it to be transmitted over long distances without significant loss of signal. This is the basic principle behind optical fiber communication.
The advantages of using optical fibers for communication are:
High bandwidth: Optical fibers have a much larger bandwidth compared to traditional copper wires, allowing for much faster and more efficient communication.
Immunity to Electromagnetic Interference (EMI): Optical fibers are immune to EMI and do not emit electromagnetic radiation, making them more secure and reliable for communication.
Immunity to environmental factors: Optical fibers are less susceptible to environmental factors such as temperature, humidity, and water damage compared to copper wires, leading to fewer signal disruptions and failures.
a) The critical angle for the boundary can be found using the equation:
sin(Θc) = n2/n1
where n1 is the refractive index of the core (1.52) and n2 is the refractive index of the cladding (1.40). Plugging in these values, we find:
sin(Θc) = 1.40/1.52 = 0.921
Taking the inverse sine of both sides, we find the critical angle:
Θc = sin^-1(0.921) = 63.7°
b) For total internal reflection to happen at the boundary, the angle of incidence must be greater than the critical angle. Thus, the angle of incidence required for total internal reflection to occur is:
Θ = Θc = 63.7°
An object slides at constant speed on the frictionless surface. What forces act on the object? What work is done by each force?
There are two main forces acting on an object sliding at a constant speed on a frictionless surface: gravity and the normal force. No force happens in the direction of displacement of the object because the object is sliding at a constant speed.
Gravity is the force that pulls the object downward, while normal force is the force that pushes the object upward to counteract gravity. Since the object is sliding at a constant speed, these two forces are equal and opposite, which means that they cancel each other out. As a result, there is no net force acting on the object, and therefore no work is being done by either force.
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