On the starting blocks, sprinters use their feet to push backward. The blocks respond by pressing forward with a force equal to this with their feet.
What drives the sprinter forward?Vertical forces must be larger than the pull of gravity in order to assist the sprinter in moving forward as gravity is pushing him or her downward. The propulsive force is the force that propelled the runner forward.
Basketball players must jump straight up into the air, but how?An interaction diagram and a free-body diagram should be included in your explanation. The player pushes down on the ground, which pushes up against him in return. As a result of his push being stronger than gravity, the player accelerates upward.
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When forces are not in equilibrium (unbalanced) the object's can be described as __________.
Answer: Unbalanced forces
Explanation: When the forces acting on an object are unbalanced, they do not cancel out one another
a bicyclist starts down a hill with an initial speed of 3.5 m/s. she moves down the hill with a constant acceleration, arriving at the bottom of the hill with a speed of 8.6 m/s. if the hill is 12 m long, what was its acceleration traveling down the hill?
The acceleration traveling down the hill is 2.571 m/s^2.
Given:
initial speed (U)=3.5 m/s
Final velocity(V) =8.6 m/s
Distance covered(s)= 12 m.
Formula : (V)^2=(U)^2+ 2as
(8.6)^2 =(3.5)^2+2*a*12
a=2.571 m/s^2
velocity is the directional velocity of a moving item as an indicator of the price of trade of role observed from a particular frame of reference and measured by a specific time fashionable.
Acceleration in mechanics, acceleration is the rate of alternate of an item's pace with respect to time. Acceleration is a vector amount. The direction of an object's acceleration is given with the aid of the route of the net force performing on that object.
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(a) your pendulum clock which advances 1.0 s for every complete oscillation of the pendulum is running perfectly on earth at a site where the magnitude of the acceleration due to gravity is 9.80 m/s2. you send the clock to a location on the moon where the magnitude of the acceleration due to gravity is 1.65 m/s2. does the clock run fast or slow on the moon?
The clock runs slower on moon than on earth.
As we know that time period of simple pendulum will be
T = 2π√(L/G)
Now we will have,
time period of a clock on the surface of earth will be 1 s where we have acceleration due to gravity is g = 9.8 m/s².
Now if we took the pendulum to the surface of moon where acceleration due to gravity will be 1.65 m/s² then this time period will change
so we will say by above equation;
T(earth)/T(moon) = √(G(moon) / G(earth)
From above equation we get;
T(moon) = √(9.80/1.65) * 1 sec
T(moon) = 2.44 sec
So, time period on moon will be 2.44 sec.
Therefore, clock runs slow on the moon.
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Where are most near infrared telescopes located Why?
The Earth bound infrared telescopes are located on the high mountain tops and in very dry climates to improve visibility.
Infrared telescopes are used to explore the structure of galaxies because it has the ability to use infrared light in detecting celestial bodies present in a galaxy. It makes use of the electromagnetic radiation emitted by these bodies that are detected and resolved by the instrument.
Infrared rays are absorbed by the water vapour in the lower parts of our atmosphere such as near the sea level. Infrared telescoped positioned on high mountains can observe the cosmos at a wavelength near-infrared. In this case, this telescope is positioned on a mountain top where the altitude is high.
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Assume you are driving 20 mph on a straight road. Also, assume that at a speed of 20 miles per hour, it takes 100 feet to stop. If you were to increase your speed to 40 miles per hour, your stopping distance is now [distance].
If the stopping distance for a speed (velocity) 20mph is 100ft, then the stopping distance for a speed (velocity) 40mph is 400ft.
It defines the direction of the movement of the body or the object. The velocity of a moving object can be zero. Speed is a prime indicator of the rapidity of the object. Velocity is the prime indicator of the position as well as the rapidity of the object.
How to calculate the stopping distance when the speed (velocity) is 40mph?
Given from the question
V₁ = 20mph = 29.334ft / s
S = 100ft Now, let's use the equation of motion
v² - u² = 2as
Where
v = final velocity = 0 (because the car is stopped)
u = initial velocity
a = acceleration (negative if slowing down)
s = distance moved
0 - 29.334² = 2 * (-a) * 100
-860.483556 = - 200a
a = 4.302 ft / s²
Now, when velocity is 40mph, equal to 58.6667 ft/s
using the same equation
v² - u² = 2as
0 - 58.6667² = 2 * (-4.302) * s
-3441.78168889 = - 8.604 * s
s = 400feet (rounded)
Therefore, if you were increase your speed to 40 miles per hour, your stopping distance will be 400 feet.
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A star is born when
A . it first starts to fuse hydrogen into helium.
B. it first starts to fuse helium into hydrogen.
C. it gets its first planet.
D. when it goes supernova.
Answer:
a & b
Explanation:
Camille knows that range of motion is very important. She is designing a weekly exercise program and is not sure where flexibility fits in. What
type of exercise will BEST allow her to work on range of motion?
O A.
aerobic
B. balance
C. flexibility
D. strength training
The best activity for her to do to improve her range of motion is flexibility.
What are a few range of motion illustrations?The term the range of motion (ROM) describes the extent to which a joint or muscle may be moved or stretched. Everybody has a distinct experience. For instance, whereas some people can perform a complete split, others cannot because their joints are stiff and their muscles are unable to extend as far.
What restricts motion range?A joint is said to have a restricted range of motion when it cannot move easily and completely in its typical position. A mechanical issue within the joint, swollen tissues around the joint, or pain may restrict motion.
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Jack is testing how sound travels. Damon stood on the opposite side of the room and whispered a sentence to him. Then, jack held a balloon to his own ear as damon whispered the sentence to him again. Jack heard the sentence better the second time. How did the balloon affect the sound of damon's whisper?.
Answer:
Sound travels better through the compact molecules of air inside the balloon than the less compact molecules on the outside.
Explanation:
Need help! Thanks lots!
The final momentum of the ball after collision is 13 kg(m/s) because this is closed isolated system and in this the momentum is conserved .
How is the final momentum calculated ?The given parameters;
initial momentum of the box (P₁)
initial momentum of the ball (P₂)
final momentum of the ball (P₃)
final momentum of ball after collision (P₄)
∴ P₁ = 15 kg(m/s)
∴ P₂ = 3 kg(m/s)
∴ P₃ = 5 kg(m/s)
Apply the principle of conservation of linear momentum to determine the final momentum of the ball after collision;
total momentum before collision = total momentum after collision
∴ P₁ + P₂ = P₃ + P₄
∴ 15 + 3 = 5 + P₄
∴ 18 = 5 + P₄
∴ 18 - 5 = P₄
∴ P₄ = 13
Hence, the final momentum is 13 kg(m/s)
What is the law of conservation of momentum ?The law states that the sum of two bodies' momentums before contact equals the sum of their momentums after impact. Both bodies move at different speeds before colliding, yet in some circumstances, the bodies move at the same speed after colliding.
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What is the kinetic energy of a 1400 kg sports car Travelling down the road with a speed of 30 m s?
The kinetic energy of the sports car is 630 KJ.
The kinetic energy is the energy possessed by the system by virtue of its motion.
Also kinetic energy is equal to the net work done on the object.KE = ΔW
The SI unit of the kinetic energy is joule (J).The formula to calculate the kinetic energy is KE = (1/2)*m*v²Where,
m = mass of the object
v = speed at which the object is moving
Kinetic energy depends on the speed squared of the object. This means that when an object's speed is doubled, its kinetic energy is quadrupled.Mass of the car = 1400 Kg
Velocity of the car = 30 m/sec
KE = (1/2)*1400*(30)²
KE = (1/2)*1400*900
KE = 630000 J
KE = 630 KJ
The kinetic energy of a 1400 kg sports car travelling down the road with a speed of 30 m/s 630 KJ.
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the magnitude of the component of the force that does the work is 43 n. how much work is done on a bookshelf being pulled 5 m at an angle of 37o from the horizontal?
172 joules work is done on a bookshelf being pulled 5 m at an angle of 37o from the horizontal.
Work = Force * times *distance
we will use the component of the force in the direction of the distance
In this problem, let’s say the distance (5.00 m) is horizontal. The horizontal component of the force is Fcosθ
W=(Fcosθ)(D)
or
W = (43.0)(cos37.0)(5.00)
= 172Nm
= 172 Joules
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a cheetah running at a velocity of 18 m/s accelerates 1 m/s2 for 5 sec. what is the final velocity of the cheetah?
The final velocity of the cheetah is 23 m/s.
How is velocity and accleration related?Acceleration, then, is the alteration in that velocity. As you maintain or increase speed, acceleration moves in the same direction as velocity. The direction of velocity is in this. While you are retaining or gaining speed, you are accelerating in this direction. An object is accelerating if its velocity is changing, whether by a fixed amount or a variable quantity. Additionally, an item moving at a constant speed is not accelerating. The rate at which velocity varies is known as acceleration. In other words, accelerating. Increasingly, decreasingly, and in a different direction.
A vectorial quantity with both magnitude (speed) and direction is velocity. I can answer your question by using the example of uniform circular motion. In this example, the speed is constant, but the direction is constantly shifting.
Given u = 18m/s
a = 1 m/s^2
t = 5 sec
v = final velocity
We know that according to equation of motion
v = u + at
v = 18 + 1 x 5 = 18 + 5 = 23 m/s
Th final velocity of cheetah is 23m/s.
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2. a concave lens made out of air is immersed in water (two watch glasses glued to a piece of pipe so that air is inside). will it form a real image that can be focused on a screen? why or why not? justify your answer using a refraction ray diagram.
The lens will form real image that can be focused screen.
As air has less optical density than water, and the shape of air lens is concave, it would act as converging lens when placed in water. And hence it can form a real image that can be focused on a screen.
The behavior of lens can be justified by calculating the focal length. For concave lens R1 is negative and R2 is positive.
Since, focal length is positive and behave as converging lens and forms the real image.
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Brandon is on one side of a river that is 80 m wide and wants to reach a point 250 m downstream on the opposite side as quickly as possible by swimming diagonally across the river and then running the rest of the way. Find the minimum amount of time if brandon can swim at 2 m/s and run at 4 m/s.
The minimum amount of time Brandon needs to reacha point 250m downstream is 97.20 seconds.
Please refer to the picture bellow for better understanding.
From the case, we have some informations such:
river wide = 80 m
river length = 250m
v1 = v swim = 2 m/s
v2 = v run = 4 m/s
Using the velocity formula, we know the relationship between velocity, distance, and time is:
v = s/t
where:
v = velocity
s = distance
t = time
Hence, we could rewrite the velocity formula in terms of time such:
t = s/v ... (i)
Now, let's try to find the time Brandon needs for swimming diagonally.
We assume that Brandon's swimming distance is r with wide 80m and length x m. Hence:
r = [tex]\sqrt{80^{2} +x^{2} }[/tex] ... (ii)
The time Brandong spends swimming is:
t1 = s1/v1
t1 = r/v1
t1 = √(80²+x²) ... (iii)
2
Meanwhile the time Bradon spends for running is:
t2 = (250-x)/4 ... (iv)
We know that the total time would be:
t total = t1 + t2
t total = √(80²+x²) + 250 - x
2 4
To find the minimum time, we will use derivative function of t:
t total' = 0
d (√(80²+x²) + 250 - x ) dx = 0
2 4
x - 1 = 0
2[√(80²+x²)] 4
2x = 1
√(80²+x²)
2x = √(80²+x²)
4x² = 80² + x²
x ≈ 46.2m ... (v)
We will subtitute the value of x to the equations (iii) and (iv):
t1 = √(80²+x²) / 2
t1 = 92.4 / 2
t1 = 46.25s
t2 = (250-x) /4
t2 = 203.8 / 4
t2 = 50.95s
The minimum amount of time for Brandon to reach his targeted point is:
t total = t1 + t2
t total = 46.25 + 50.95
t total = 97.20 s
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In a binary-star system that produces a nova, the white dwarf pulls matter from the companion star. the matter forms an accretion disk that orbits the white dwarf. then a specific sequence of events must take place for a nova event to occur.1. Material accumulates onto the white dwarf's surface, increasing in temperature and density. 2. At a temperature of 10 million K, the accumulated surface hydrogen begins nuclear fusion. 3. Nuclear fusion reactions cause an enormous but temporary increase in luminosity. 4. As nuclear fuel is burned up or blown into space, fusion ceases and the star dims.
As a head-up, it is important to notice that a white dwarf only shine to the stored energy and light, because a white dwarf doesn't have any hydrogen left to perform nuclear fusion.
Now, the process:
First, the white dwarf accumulates all the extracted matter from its companion onto its own surface. This extra matter increases the white dwarf's temperature and density.
After a while, the start reaches about 10 million K, so nuclear fusion can begin. The hydrogen that has been stolen from the other start and accumulated in white dwarf's surface it is used for the fusion, dramatically increasing the star's brightness for a short time, causing what we know as a nova.
As this fuel, it is quickly burnt out or blown into space, the star goes back to its natural white dwarf state. Since the white dwarf nor the companion star are destroyed in this process, it can happen countless of times during their lifespan.
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A gas is enclosed in a cylinder fitted with a light frictionless piston and maintained at atmospheric pressure. When 254 kcal of heat is added to the gas, the volume is observed to increase slowly from 12.0 m^3 to 16.2 m^3.
a. Calculate the work done by the gas.
b. Calculate the change in internal energy of the gas.
The work done by the gas for question A will be 4.2 * 10^5 J.
The change in internal energy of the gas for question B is 6.43 * 10^5 J.
What is work (in gas)?For a gas, it is the product of the pressure P and the volume V during a change of volume. The formula for work done in gas is W (work) = P (pressure) * V (volume)
Now, let's calculate the work done by gas to answer question A.
Work = Pressure * (Volume 2 - Volume 1)
= 1 atm * (16.2 - 12)
= 10^5 Pa * 4.2
= 4.2 * 10^5 J
So the work done by the gas is 4.2 * 10^5 J.
Now, let's find the change in internal energy of the gas.
The heat energy added to the system is
Q = 254kcal
= 254kcal * (4184J / 1 kcal)
= 1.063 * 10^6 J
The change in internal energy of gas is
ΔU = Q (the heat energy added) - W (work done by gas)
= 1.063 * 10^6 J - 4.2*10^5 J
= 6.43 * 10^5 J
Therefore, the change in internal energy of the gas is 6.43 * 10^5 J
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What is the internal energy of a system including the kinetic and potential energy of its particles?
Internal energy of a system is the product of specific heat and temperature included with number of moles. (i=nCT) and kinetic energy is product of Boltzmann constant and temperature.
All systems have a certain amount of energy that can be converted into other energy to do work. The kinetic energy within the molecules and atoms that make up the body and the energy generated by the intermolecular forces between them are collectively called internal energy.In other words, the energy hidden in the system that can appear under different conditions can be called the internal energy of the system.Internal energy is the sum of two energies:
(a) Thermal energy, which is the kinetic energy of molecules in random motion, and
(b) Potential energy of atoms.
Potential atomic energy arises from the atomic forces acting between the atoms of molecules and the intermolecular forces between molecules.Total internal energy, E = kinetic energy (K.E.) + potential energy (P.E.).The state function describes the equilibrium state of the system, as well as the system itself. It is called the state function because the internal energy U is defined by the quantity that determines the state of the system at equilibrium. It is completely determined by the initial and final state of the system. As the temperature of the system increases, the molecules move faster, resulting in an increase in kinetic energy and an increase in internal energy.To learn more about Internal energy -
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If two trucks have the same mass, but truck a is traveling 15 km/h, and truck b is traveling 30 km/h, what statement is true?.
The true statement is truck B will have a greater stopping distance because its speed is greater hence more distance to cover.
Kinetic energyThe equation of kinetic energy is:
½ mv²
So, the higher the speed/velocity of a moving object, the greater the energy it has.
The question was incomplete, there should be several options :
Truck A has greater kinetic energyTruck A will have a greater stopping distanceTruck B has less kinetic energyTruck B will have a greater stopping distanceThe answer is truck B will have a greater stopping distance than truck A, because its speed is greater hence more distance to cover.
Truck B also will have greater kinetic energy because it has more velocity.
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an electromagnetic wave of wavelength 435nm is traveling in vacuum in the − z-direction. the electric field has amplitude 2.70×10−3v/m and is parallel to the x-axis.
Given wavelength λ=435λ=435 nm, we can find the frequency by using the formula f=c/λ f=6.89×1014 Hz
What is an example of an electric field?
The area of space surrounding any electrically charged particle and object where the charge body perceives force is known as the electric field.Examples are:Charges and their arrangements, such as in capacitors and battery cells, produce electric fields.
What are electric field and what does it mean in SI?Volts / metre (V/m) is the electrical field's SI unit.The Newton's per coulomb unit is the same as this one.These units are derivations from Newton, which stands for force, and Coulomb, which stands for charge.
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a magnetic field near the ceiling points down and is increasing. looking up at the ceiling, does the non-coulomb electric field curl clockwise or counter-clockwise?
The Non-coulomb electric field curls will be counterclockwise
Electric field can be defined as force per unit charge.
Non columbic field formula is
Fnc = qEnc
It is created by a change in magnetic field.
when the magnetic field near the ceiling point is increasing, the non coulomb force will curl counterclockwise by applying right hand thumb rule.
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what is mass wasting? what are some of the important variables used to identify and distinguish types of mass wasting (4 points)?
When a slope breaks, there is mass wasting. When a slope is excessively steep and unstable given the materials and environmental factors at play, it fails. The slope angle and the underlying material's strength are the two main criteria that eventually influence slope stability.
Slope failures are categorized according to three factors:
The material that collapsed, its mechanism of failure (how the material moved while failing), and its pace of movements, such as bedrock or loose sediment (how quickly the material moved).
The most crucial feature of a slope collapse is the failure mechanism. The three primary mechanisms of slope failure are as follows:
When anything falls, it travels through the air vertically or almost vertically.
Slide: In slides, the substance slides along a sloping surface as a cohesive mass (with little to no internal motion inside the substance); and
Flow: Inflows, the failing substance moves within, much like a fluid.
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gravitational field of the earth is 11.2 km s the ratio of the escape velocity to the root-mean-square speed of helium, argon, and xenon atoms at 2000 k. does your result help explain the low abundance of the light gas helium in the atmosphere? explain.
The ratio of escape velocity of Helium, Argon and Xenon is 31.5 %, 10.0 % and 5.5 % respectively.
Calculation:-
taking T = 2000 K and R = 8.315 J mol-1 K-1
Molar mass for Helium = 4.0026 x 10?3 kg mol-1
Molar mass for Argon = 39.948 x 10?3 kg mol-1
Molar mass for Xenon = 131.29 x 10?3 kg mol-1
We get the rms speed for the given gases as followed
Helium = 3.53 km s-1
Argon = 1.12 km s-1
Xenon = 0.62 km s-1
The ratio of the escape velocity to the root-mean-square speed of the given gases
The ratio of helium = 31.5 %
The ratio of argon = 10.0 %
The ratio of xenon = 5.5 %
Yes, the fraction (or ratio) of the speed exceeding the escape velocity (31.5%) is larger in helium, which makes low abundancy of the helium in the atmosphere.
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Coherent light with wavelength 400 nm passes through two very narrow slits that are separated by 0.200 mm, and the interference pattern is observed on a screen 4.00 m from the slits. (a) What is the width (in mm) of the central interference maximum? (b) What is the width of the first-order bright fringe?
(a) The width (in mm) of the central interference maximum is [tex]8.0mm[/tex].
(b) The width of the first-order bright fringe is [tex]8.0mm[/tex].
fringe width = w=D/d λ is the wavelength of light
D is the screen distance from the slit
d is a separation between slits
Constructive interference,
⇒dsinθ = n ×λ
⇒sinθ = [tex]\frac{n}{d}[/tex] ×λ
⇒ y = R [tex]\frac{n}{d}[/tex] ×λ ............(1)
here n= 0, ±1 , ........
the width of the central interference maximum,
⇒[tex]y_{max}[/tex] = R λ× [tex]\frac{1}{d}[/tex] = [tex]\frac{4,0m}{0,2mm}[/tex] ×[tex]400nm[/tex]
⇒[tex]y_{max}[/tex] = [tex]8.0mm[/tex]
the width of the first-order bright fringe.
⇒[tex]y_{1}[/tex] - [tex]y_{0}[/tex] = [tex]\frac{R}{d}[/tex]×λ -0 = [tex]\frac{4,0m}{0,2mm}[/tex] ×[tex]400nm[/tex]
⇒[tex]y_{1}[/tex] = [tex]8.0mm[/tex]
In physics, wave assets are coherent if their frequency and waveform are equal. Coherence is an excellent asset of waves that enables stationary (i.e., temporally, or spatially constant) interference. It contains numerous awesome concepts, that are proscribing cases that never pretty arise in fact however permits knowledge of the physics of waves, and has grown to be a very essential idea in quantum physics. more generally, coherence describes all homes of the correlation among physical quantities of a single wave, or between several waves or wave packets.
Interference is the addition, in the mathematical experience, of wave features. A single wave can interfere with itself, but this is nevertheless an addition of two waves (see younger's slits experiment). optimistic or unfavorable interference is restricted cases, and two waves continually intervene, despite the fact that the result of the addition is complex or now not amazing. while interfering, two waves can add collectively to create a wave of more amplitude than either one (optimistic interference) or subtract from each difference to create a wave of lesser amplitude than both (negative interference), relying on their relative section.
Two waves are said to be coherent in the event that they have a consistent relative phase. the amount of coherence can effectively be measured through interference visibility, which looks at the dimensions of the interference fringes relative to the enter waves (as the section offset is numerous); a specific mathematical definition of the diploma of coherence is given with the aid of correlation capabilities.
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a flight attendant pushes a cart down the aisle of a plane in flight. in determining the acceleration of the cart relative to the plane, which factor do you not need to consider?
A flight attendant pushes a cart down the aisle of a plane in flight. in determining the acceleration of the cart relative to the plane, The velocity of the plane, need to consider.
What is speed?The pace at which a distance changes over time is referred to as speed. It has a dimension of time-distance. As a result, the fundamental unit of time and the basic unit of distance are combined to form the SI unit of speed. Thus, the meter per second (m/s) is the SI unit of speed. Let us suppose a flight attendant pushes a cart down the aisle of a plane in flight with a force (F) in Newton respectively. Also acceleration of the cart relative to the plane.
Therefore the only factor will be in consideration that will be velocity because we will be neglecting all other factors such as air resistance, relative plane etc.
Hence option (c) will be the correct answer: The velocity of the plane.
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to save money on making military aircraftinvisible to radar, an inventor decides to coatthem with a nonreflective material having anindex of refraction of 1.20, which is betweenthat of air and the surface of the plane. this, hereasons, should be much cheaper thandesigning stealth bombers. (a) what thicknessshould the coating be to inhibit the reflection of4.00-cm wavelength radar? (b) what isunreasonable about this result? (c) whichassumptions are unreasonable or inconsistent?
index of refraction (n) = 1.20 wavelength = 4 cm
What is wavelength radar?
Radar used to measure wind waves is called wave radar. There are several instruments available that are based on various ideas and methods, and they are all frequently termed.
In situations where it's critical to avoid direct contact with the water surface and structural interference, instruments based on radar remote sensing techniques have grown in popularity. Wave measurements from an offshore platform in deep water are an example of a situation where anchoring a wave buoy would be extremely challenging due to rapid currents. Another intriguing situation is that of a ship in motion, where it is extremely impracticable to have equipment in the sea
According to the question:
using the formula for minimum thickness of coating to inhibit reflection: thickness = λ4 thickness = 4 cm
4×1.20 thickness = 0.833 cm
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wavelength = 4 cm index of refraction (n) = 1.20
What exactly is wavelength radar?
Wave radar is a type of radar that is used to measure wind waves. There are several instruments available that are based on diverse concepts and methodologies, and they are all often referred to.
Instruments based on radar remote sensing techniques have increased in popularity in circumstances where it is vital to avoid direct contact with the water surface and structural interference. Wave measurements taken from an offshore platform in deep water are an example of a circumstance in which mooring a wave buoy would be exceedingly difficult owing to strong currents. Another fascinating circumstance is that of a ship in motion, when having equipment in the sea is exceedingly impractical.
Using the formula for minimal coating thickness to reduce reflection: 4 is the thickness 4 cm thickness
4x1.20 mm thick = 0.833 cm
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With respect to saving energy, what aspect of using two-sided printing was discussed in class as providing the most signifiant benefit?
The benefit of employing two-sided printing that was highlighted in class as being the most important is that it only requires one sheet of paper as opposed to two when printing a two-sided document.
What does two-sided printing mean?Standard 2-sided printing can be used to print on both sides of a sheet. You can choose between manual and automatic printing. When printing by hand, even-numbered pages are printed first. After printing these pages, you may simply reload them to print the odd-numbered pages on the opposite side of the paper.
Therefore, double-sided printing can save your business about half as much money as single-sided printing, according to certain important estimates. Due to the fact that duplex printing uses only half as much paper as one-sided printing, businesses can reduce their material costs.
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What is the image of E for a dilation with center 0 0 and a scale factor of 6?
The image E for dilation will be at center , i.e. same locus.
A scaling factor is a factor that enlarges or shrinks the dilated image compared to the original image. Magnification must be positive. If the scale factor is greater than 1, the stretch is an enlargement. Between 0 and 1, dilation is contraction.
The dilation center (or dilation point) is the point at which the image is stretched.
Given: (0,0) center and scale factor 6
Dilation is to transform an image from its original
size to another size without changing its appearance/shape.
Original image is stretched or compressed. The scaling factor is the amount by which the original image is stretched or shrunk.
For example, if A is the point (1, 2) and the scale factor is 2, the center of elongation is given by
OA= (1x2, 2x 2) = (2, 4)
To find the new point, multiply the origin by the scale factor.
Ox 6 = 0, so the specified point (O, O) remains at (0, 0).
The dilated image does not change because the center does not change.
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why did the big bang not produce a significant proportion of elements heavier than helium?
The big bang could able to produce only the highest heavier element helium due to very low temperature.
Big Bang nucleosynthesis produced only a few nuclei of factors heavier than lithium because of a bottleneck, the absence of a strong nucleus with eight or five nucleons. This deficit of large atoms additionally restricted the quantities of lithium-7 produced for the duration of BBN. In the early universe, it becomes too warm for factors to shape till numerous mins into the expansion. At that point, there have been just a few mins in which factors ought to shape earlier than it has become too cool for in addition nucleosynthesis. Thus the heavier element produced by the big bang explosion is helium
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in a certain cyclotron a proton moves in a circle of radius 0.500 m. the magnitude of the magnetic field is 1.20 t. (a) what is the oscillator frequency? (b) what is the kinetic energy of the proton, in electron-volts?
The frequency of oscillator is 1.83 X 10⁷ Hz and the kinetic energy of the proton is 1.72 X 10⁷ eV.
(a)
Radius of the circle = r = 0.500 m
Magnetic Field = B = 1.20 T
Charge of proton = q = 1.60 X 10⁻¹⁹ C
Mass of proton = m = 1.67 X 10⁻²⁷ Kg
The frequency of oscillator is = f =
= f = 1/t = (qB) / 2πm
= f = ( 1.60 X 10⁻¹⁹ X 1.20 ) / ( 2 X 3.14 X 1.67 X 10⁻²⁷)
= f = 1.83 X 10⁷ Hz
(b)
Radius of the circle = r = 0.500 m
Magnetic Field = B = 1.20 T
Charge of proton = q = 1.60 X 10⁻¹⁹ C
Mass of proton = m = 1.67 X 10⁻²⁷ Kg
The kinetic energy of proton = E =
= E = (r X q x B)² / 2 X m
= E = (0.500 X 1.60 X 10⁻¹⁹ x 1.20)² / 2 X 1.67 X 10⁻²⁷
= E = 1.72 X 10⁷ eV
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A particular species of copepod, a small marine crustacean, emits a flash of light consisting of 1.4×1010 photons at a wavelength of 490 nm. The flash lasts for 2.4 s.What is the power of the flash?
The power of the flash is [tex]2.36 * 10^{-9} W[/tex].
First we calculate the energy of a single photon; i.e.
[tex]E_{1} = hc/\alpha[/tex]
where, h = planck's constant = [tex]6.63 * 10^{-34} Js[/tex]
c = speed of light = [tex]3 * 10^{8} m/s[/tex]
[tex]\alpha[/tex] = wavelength = 490 nm = [tex]4.9 * 10^{-7} m[/tex]
Putting these values in equation, we get
[tex]E_{1} = 4.05 * 10^{-19} J[/tex]
Total energy is given by, E=Pt
where, P = power and t= time
Now number of photons is given by : N = E/[tex]E_{1}[/tex]
⇒ [tex]NE_{1} = E[/tex]
⇒ [tex]NE_{1} /t = P[/tex]
Given, N = [tex]1.4*10^{10}[/tex] and t = 2.4 s
Putting these values in above equation we get P = [tex]2.36 * 10^{-9} W[/tex]
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