The wavelength of light will be 5.17 x10⁻⁷ m
Since we are given the angle of 15.0, and transmission grating having 5000 slits/cm, for a normal incidence
since we know the diffraction of first-order formula is :
d sineθ =nλ ,and the separation os the slits are : d= 1/N
=>d=1/ 5000 = 2x 10^-6 m
Now subsituing the value of d in the main formula of diffraction, where we get the wavelength of :
λ = dsine θ/ n
since here n is 1
λ= 2x 10 *sine 15.0/ 1
λ = 2x 10^-6 *0.2588 = 5.17 x10⁻⁷ m
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he amplitude of a lightly damped harmonic oscillator decreases by 3.0% during each cycle.show answer no attempt what percentage of the mechanical energy of the oscillator is lost in each cycle?
The percentage of mechanical energy of the oscillator lost in each cycle is 5.91%.
The difference between mean or equilibrium position and either extreme is the oscillation's amplitude. The particle oscillates completely back and forth from its mean position.
The mechanical energy is the sum of both elastic potential energy and kinetic energy.
The mechanical energy of any oscillator is given by the formula,
E = 1/2 K*A²
When amplitude A decreases by 3%, then
(E₂ - E₁)/ E₁ = [1/2 K( A₂²/A₁²)]/(1/2 K*A₁²)
⇒ [(A₂²- A₁²)/(A₁²)]
⇒ (97² - 100²)/100²
⇒ 5.91% of the mechanical energy is lost in each cycle
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a beam of white light goes from air into water at an incident angle of 75o. at what angles are the red (660 nm) and violet (410 nm) parts of the light refracted?
Consequently, the refraction angles for red and violet light are 46.5° and 46.0°, respectively.
What is the index for refraction?The difference between the speed of light in a vacuum and that in a medium, denoted by the letters c and c', is known as the index of refraction (n): The propagation vector in the new medium has a different angle with respect to the normal when light travels from one medium to another at an angle as a result of this speed difference. In optics, an optical media's refractive index—a dimensionless number that indicates how well the medium bends light—is used to measure that medium's optical properties. When light enters a substance, its refractive index influences how much of its path is bent.
Why do we use refractive index?A material's refractive index, which is quantified, indicates how much a light path is bent or refracted when it penetrates that material. The critical angle for total internal reflection and the amount of light that is reflected when it reaches the contact are both determined by the index of refraction.
Briefing:For light of a specific color and a specific set of media, the sine of the angle of incidence to the sine of the angle of refraction ratio is constant.
According to Snell's law.
The formula for Snell's law is
n=sini/sinr
I stands for incidence angle.
The refraction angle is r.
The medium's refractive index is n.
For red light,
n=sini/sinr
1.331=〖sin75〗^°/sinr
sinr=〖sin75〗^°/1.331
r=〖sin〗^(-1) (0.7258)
r=46.5°
Consequently, the red light refraction angle is 46.5°.
For violet light,
n=sini/sinr
1.342=〖sin75〗^°/sinr
sinr=〖sin75〗^°/1.342
r=〖sin〗^(-1) (0.7197)
r=46.0°
Consequently, the violet light's angle of refraction is 46.0°.
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Complete question is:a beam of white light goes from air into water at an incident angle of 75o. at what angles are the red (660 nm) and violet (410 nm) parts of the light refracted? Red light in water has an index of refraction equal to 1.331 and that of violet light is 1.342.
Under normal conditions the human heart converts about 12.5J of chemical energy per second into 1.25 W of mechanical power as it pumps blood throughout the body. (a) Determine the number of Calories required to power the heart for one day, given that 1 Calorie equals 4186 J. ________ Cal (b) Metabolizing 1 kg of fat can release about 9000 Calories of energy. What mass of metabolized fat (in kg) would power the heart for one day? _____ kg
(a) The number of Calories required to power the heart for one day is 258 Cal.
(b) The mass of metabolized fat that would power the heart for one day is 0.0287 kg.
What is the number of Calories required to power the heart?
The number of Joules of energy required to power the heart for one day is calculated as follows;
Power = 12.5 J / s
Energy = power x time
time = 1 day = 86400 seconds
Energy pumped by heart in one day = 12.5 J/s x 86400 s = 1,080,000 J
The number of calories contained in 1,080,000 J of chemical energy is calculated as;
1 Calorie = 4186 J
= 1,080,000 J / 4186 J
= 258 Cal
The mass of metabolized fat that would power the heart for one day is calculated as;
9000 Cal = 1 kg
258 Cal = ?
= 258 / 9000
= 0.0287 kg
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A bus and a truck leave a gas station at the same time and are headed to the same destination. If the bus traveled 180 miles in 3 hours, and the truck traveled 210 miles in 7 hours, who is on pace to reach the destination first?.
In the given case, The Bus is on pace to reach the destination first.
Explain in detail.
To find which truck will arrive first, you need to find each vehicle's mph. To get the mph of each vehicle you just need to divide the distance by time.
Bus: 180 (miles) ÷ 3 (hours) = 60 (miles per hour)Truck: 210 (miles) ÷ 7 (hours) = 30(miles per hour)To know more about Speed here
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the sun appears to move across the sky, because the earth spins on its axis. to a person standing on the earth, the sun subtends an angle of sun 9.28 103 rad (see conceptual example 2). how much time (in seconds) does it take for the sun to move a distance equal to its own diameter?
During the day, the Sun appears to move across the sky from Earth and disappears at night. As a result of the Earth's eastward rotation, this has occurred.
Why does the Sun appears to move across the sky because?Our nearest star to us is the Sun. Both light and heat are produced by the Sun. Furthermore, it emits harmful ultraviolet light that can lead to cancer and sunburn. Without the Sun, our planet would be completely dark and frozen, devoid of oceans of liquid water and life. There would also be no daylight.1.4 million kilometers across, or 109 Earths lined up side by side, is the size of this enormous ball of extremely hot gas. It weighs the equivalent of 330 000 Earths at 2 million trillion trillion trillion kilograms. The Sun could accommodate about 1 300 000 Earths!From Earth, the Sun appears to move across the sky during the day and vanish during the night. The reason for this is that the Earth is rotating eastward. The North and South poles serve as the Earth's North and South axes, around which the planet revolves. As a result, the Sun appears to rise in the east in the morning and rise steadily in the sky until it reaches its midday position to us here on the rotating Earth. Later in the afternoon, the Sun appears to descend further into the sky before setting in the west.The Sun is approximately 150 million kilometers away, despite appearing small when seen at sunrise or sunset.Even though sunlight is moving at a speed of about 300 000 km/s, it takes about 8 minutes to reach us from this distance. The Sun sets eight minutes after the actual event, according to this.To Learn more About volume of data refer to:
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2.
A book weighs 6 newtons.
A librarian picks up the book from one shelf and puts it on a shelf 2 metres higher.
(a) Calculate the work done on the book. [Show your working].
(b) The next person to take the book from the shelf accidentally drops it.
The book accelerates at 9.8m/s².
Use this information to calculate the mass of the book. [Show your working].
Answer:
0.612 kilograms.
Explanation:
To solve this problem, we need to use the definition of work as the product of force and displacement.
(a) The work done on the book is the force applied to it multiplied by the distance through which it is moved. In this case, the force applied to the book is its weight, which is 6 newtons. The displacement of the book is 2 meters, because it is moved from one shelf to another shelf that is 2 meters higher. Therefore, the work done on the book is 6 newtons * 2 meters = 12 joules.
(b) The next person to take the book from the shelf accidentally drops it. When an object is dropped, it accelerates due to the force of gravity, which is 9.8 m/s². Since the force of gravity is the same for all objects, we can use the acceleration of the book to calculate its mass. Specifically, we can use the formula F = ma, where F is the force acting on the object (in this case, the force of gravity), m is the mass of the object, and a is its acceleration.
In this case, the force acting on the book is its weight, which is 6 newtons. The acceleration of the book is 9.8 m/s². Therefore, we can solve for the mass of the book using the formula F = ma: 6 newtons = m * 9.8 m/s². This simplifies to m = 6 newtons / 9.8 m/s² = 0.612 kilograms.
In summary, the work done on the book when it is picked up and moved to a higher shelf is 12 joules, and the mass of the book is 0.612 kilograms.
What is the frequency of the wave
Answer:
The frequency of a wave is the number of waves that pass by each second, and is measured in Hertz (Hz).
Explanation:
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Once you set a ball rolling in a frictionless bowling alley, the force needed to keep it rolling is.
No alternative is appropriate once you start a ball moving in such a frictionless bowling alley; the force required to keep it rolling is.
A bowling lane has how much friction?The friction variance along the length of modern bowling alleys is modulated by an oil coating. The coefficient of friction is typically 0.04 in oiled regions and 0.2 in unoiled portions.
What does friction have to do with bowling?
A bowling ball goes more quickly the lower its coefficient of friction. The slower a ball moves down the path, the more friction it has. The form, weight, and surface texture of the ball are only a few of the variables that determine friction. When your ball makes contact with the lane, all of these elements affect friction.
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explain how the following rules check if there is a has color in a map factbase. adjacent(x, y) :- edge(x, y); edge(y, x). has color(s1, s2, color1) :- adjacent(s1, s2), color(s1, color1),color(s2, color1).
Prolog runtime will iteratively apply the rules to all the facts to find the matches and mismatches.
In physics, color is specifically associated with the particular range of wavelengths of electromagnetic radiation visible to the human eye. Such wavelengths of radiation make up a portion of the electromagnetic spectrum known as the visible spectrum. H. Light.
So colors have a physical basis. However, our perception of it is complicated by how the human visual system works. Some people have mutations that alter their ability to process incoming light and distort their perception of color.
Opticks is one of the great works of scientific history, documenting Newton's discoveries in his experiments with light passing through a prism. He identified the colors of his ROYGBIV (red, orange, yellow, green, blue, indigo, and violet) that make up the visible spectrum.
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Determine which the following are defined Whenever they occur denctes multivariable function and denotes vector field both of which are twice continuously differentiable on common domain_ (Select all that apply.) V . (F . Vf) V. (V x Vf) V x (V . F) V x (V x f) V x (V x F) V . (V x F)
Yes, all of the above are defined whenever they occur and denote multivariable functions and vector fields which are twice continuously differentiable on a common domain.
What is vector field?
A vector field is the assignment of the a vector to each point inside a subset of space in the fields of vector calculus and physics. For example, a vector field inside the plane could be visualised as a group of arrows, each attached to the a point in the plane and each with a specific magnitude and direction. Vector fields are frequently used to simulate various physical phenomena, such as the strength and motion of a force as it shifts through one point to the next or the speed and trajectory of a fluid moving through space.
The first expression, V . (F . Vf), denotes a multivariable function which is the dot product of a vector V and the composition of a function F with a vector field Vf.
The second expression, V . (V x Vf), denotes a multivariable function which is the dot product of a vector V and the cross product of a vector V and a vector field Vf.
The third expression, V x (V . F), denotes a vector field which is the cross product of a vector V and the dot product of a vector V and a function F.
The fourth expression, V x (V x f), denotes a vector field which is the cross product of a vector V and the cross product of a vector V and a function f.
The fifth expression, V x (V x F), denotes a vector field which is the cross product of a vector V and the cross product of a vector V and a function F.
The sixth expression, V . (V x F), denotes a multivariable function which is the dot product of a vector V and the cross product of a vector V and a function F.
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in Section 24-2. you learned how Neptune is afferent from Uranus, and how its rings and moons fomed and evolved Based on what you leamed about Uranus select all of the correct statements from the following list Neptune is similar to Uranus as far as sze, mass, composition and interior structure Lke Uranus, Neptune shows very little atmospheric activity Neptune's largestmoon Triton, has a retrograde orbit which suggests that it was captured i Beng much farther from the sun. Nepture has less internal heat than Uranus Triton has a tin atmosphere and may be geologically active Lke Uranus. Neptune's solid core prevented from having a magnetic field Neptune's position was predicted before it was discovered
Neptune and Uranus are similar in terms of size, mass, composition, and internal structure. The largest moon of Neptune, Triton, appears to have been captured because of its retrograde orbit.
Triton has a thin atmosphere and could be experiencing geological activity. Neptune's location was anticipated before it was ever discovered. Neptune is one of just two ice giants in the outer solar system (the other is Uranus). The planet's bulk, which is composed of a hot, dense fluid floating atop a tiny, rocky core, is primarily made up of water, methane, and ammonia (80% or more). Uranus is Neptune's identical twin. Their mass and chemical contents are equivalent. They are composed of an exterior layer of rocks and a mantle that is a mixture of water, ammonia, and methane ices. A physical body's mass is its total amount of matter. Inertia, or the body's resistance to acceleration (change of velocity) when a net force is applied, is also measured by this property. The gravitational pull an object has on other bodies is also influenced by its mass. The kilograms is the fundamental mass unit of SI (kg).
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A wooden loop and a wire loop, both with the same shape and size, are placed next to the north poles of identical magnets. Then, the loops are moved closer to and farther from the magnets in exactly the same way. The emf generated around the wooden loop is zero. O less than the emf generated around the wire loop. equal to the emf generated around the wire loop. O greater than the emf generated around the wire loop.
If the loops are moved closer to and farther from the magnets in exactly the same way then the emf generated around the wooden loop is equal to the emf generated around the wire loop.
Electromotive force (emf) can be described as the electric potential that is produced by either changing the magnetic field or is produced by an electrochemical cell.
The emf generated around the wooden loop is equal to the emf generated around the wire loop because Faraday's law is only concerned about how the flux is changing and is therefore independent of the material involved. The loop material is not involved in the magnetic flux expression, so an emf is generated anyhow as long as it experiences a change in magnetic flux since it moves near the end of the bar magnet, changing the magnetic flux through the loop.
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Which properties describe elements that are nonmetal gases? Select all that apply.
B. Composed of individual atoms or diatomic molecules.
D. Low melting point.
F. Weak attractions between particles (option - B,D and F) are correct.
What characteristics do nonmetals share with metals?They are either solids (carbon, sulfur) or gases (oxygen, nitrogen, hydrogen) under normal conditions. Nonmetals have many other characteristics in common as well.
They are not efficient heat or electricity conductors.
In their solid state, they are very fragile.
They lack ductility and malleability.
They typically have densities lower than metals.
Their melting and boiling points are typically lower than those of metals. Carbon is the lone exception.
High ionization energies characterize them.
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a 873-kg (1930-lb) dragster, starting from rest completes a 403.1-m (0.2519-mile) run in 4.935 s. if the car had a constant acceleration, what would be its acceleration and final velocity? m/s2
The acceleration of the dragster is 33.1 m/s².
The final velocity of the dragster is 163.4 m/s.
What is the acceleration of the dragster?
The acceleration of the dragster is calculated by applying the following kinematic equation.
s = ut + ¹/₂at²
where;
u is the initial velocity of the dragstera is the accelerations is the distance traveledt is the time of motions = 0 + ¹/₂at²
a = ( 2s ) / t²
a = (2 x 403.1) / (4.935²)
a = 33.1 ms/²
The final velocity of the dragster is calculated as follows;
v² = u² + 2as
v² = 0 + 2(33.1)(403.1)
v² = 26,685.22
v = √ (26,685.22)
v = 163.4 m/s
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element c above has a strong emission line around 450 nm. does this emission line represent a lower energy or higher energy transition than the emission line at 627 nm? explain your answer. (2 points)
According to the given photon energy formula and with the two emission lines mentioned, it can be concluded that the emission line at 627 nm represents a lower transition energy than the emission line at 450 nm.
It is given to us that -
Element C has a strong emission line around 450 nm.
There is also another emission line at 627 nm.
We have to find out the emission line that has a lower energy or higher energy transition.
We know that Transition energy is the energy required for electrons in the sample to move from one quantum state to another.
Emission spectra measure energy in the form of light emitted when energy is added to a molecule to excite it, support this electronic transition, and move from the excited quantum state to the ground state or the basic state that they were in initially.
This transition energy depends on the wavelength of the emitted radiation which can be represented as a photon energy formula such as -
E = h c / λ
Therefore, from the given photon energy formula and with the two emission lines mentioned, it can be concluded that the emission line at 627 nm represents a lower transition energy than the emission line at 450 nm.
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. after the helium flash, the sun will settle onto the horizontal branch in the h-r diagram. there it is stably burning helium in its core. assume that the helium burning dominates the luminosity of the star (over the h shell burning), and that the luminosity of the sun on horizontal branch is 50 l . further assume that the core is 10% of the mass of the star. for approximately how long can the sun burn he in its core
The duration that helium will burn in the core of the sun is t = 2.144 × [tex]10^{8}[/tex] years.
What is Helium?
The chemical element helium has the atomic number 2 and the symbol He. It is the first member of the noble gas group in the periodic table and is a colourless, odourless, tasteless, non-toxic, inert, monatomic gas. Of all the elements, it has the lowest melting and boiling points.
What are the Calculations?
Let's take the core as 10% of the mass of the star
core mass = 10% of M
= 0.1 M
= 0.1 × 2×[tex]10^{30}[/tex] kg
The luminosity of the sun on a horizontal branch is 50 L
= 50 × 3.78 × [tex]10^{26}[/tex] joule/sec
Each time 4 hydrogen nuclei fuse into the helium nucleus, 0.7% of the mass of hydrogen is converted into energy.
so, the total mass that can be converted to energy
M = 0.1×0.007×2×[tex]10^{30}[/tex] Joule/sec.
= 1.4 × [tex]10^{27}[/tex]kg
so, energy converted, E = M[tex]c^{2}[/tex]
= 1.4 ×[tex]10^{27}[/tex] × [tex]3 * 10^{8} * 3 * 10^{8}[/tex]
E = 1.26 × [tex]10^{44}[/tex] joule.
So, the duration through which it will burn, t [tex]= \frac{1.26 * 10^{44} joule }{50 * 3.78 * 10^{26} joule/sec}[/tex]
Hence, the duration that Helium will burn in the core of the sun is t = 2.144 × [tex]10^{8}[/tex] years.
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A 40 kg crate is pulled at a constant velocity. The coefficient of kinetic friction is 0.5 and the crate moves 7 m . How much work is done?
A 40 kg crate is pulled at a constant velocity. The coefficient of kinetic friction is 0.5 and the crate moves 7 m . The amount of work done is 140 joule.
What is work done?
When an object is moved over a distance by an external force, at least a portion of that force must be applied in the direction of the displacement.
By multiplying the length of the path by the component of the force acting along the path, work can be calculated if the force is constant. The work W is equal to the force f times the distance d, or W = fd, to mathematically describe this idea.
The work is W = fd cos if the force is applied at an angle of to the displacement. Performing work on a body involves moving it in its entirety from one location to another as well as.
Therefore, A 40 kg crate is pulled at a constant velocity. The coefficient of kinetic friction is 0.5 and the crate moves 7 m . The amount of work done is 140 joule.
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which energies change as the bobsled moves down the slope and hits the spring? select all that apply.
In our bobsleds, the bobsled's potential energy on the ramp was converted into kinetic energy as it descended the ramp, and then thermal energy as friction as it came to a stop.
What does science mean by a potential energy?The term "potential energy" describes the energy that is held within an object due to the object's position, state, and arrangement. It is one of the two essential types of energy; the other is energy. The object's position, status, or configuration changes, releasing the stored energy.
Describe a potential energy example.Due to its position, an object might accumulate energy. If a demolition machine's heavy ball is held in an elevated position, for instance, it can store energy. Potential energy is the name for this kinetic energy that is held in a position. As a result of its location, a drawn bow can also store energy.
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a wheel and axle on a bicycle are designed with an axle radius of 0.125 meters and a wheel radius of 0.5 meters. if a force of 800 newtons is applied to the axle, what is the maximum output force of the bike wheel?
If the axle is subjected to a force = 800 newtons. The bike wheel's maximum output force, f, is 200 N.
What is the definition of force?The definition of force in physics is: The pushing or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
How do you determine force?Newton's second motion law provides the definition of the force formula: An object's force is equal to its mass times its acceleration, or F = m a. You must use SI units for this formula: kilograms for mass and newtons for force.
Briefing:The radii of the axle or wheel are R and r, respectively.
The respective applied forces are F and f.
R = 0.5 m
r = 0.125 m
F = 800 N
maximum output force = R/r = F/f,
0.5/0.125 = 800/f
f = 800*0.125/0.5
f = 200N
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you are helping a friend study the eight planets in order from the sun outward. they also need to know if they are terrestrial or jovian. how can you help them memorize these specifics?
They are terrestrial or Jovian and can have specifics of energy level.
Jovian Planets:-
The gas giants, also known as Jovian planets, are planets devoid of any solid material. Technically speaking, Jovian planets are those that are 10 times as massive as the Earth. Jupiter, Saturn, Uranus, and Neptune are examples of such planets in our solar system. These planets bear a striking resemblance to Jupiter, the largest planet in the solar system, which is why they are known as the Jovian planets.Terrestrial Planets:-
Terrestrial planets, also referred to as rocky planets are those planetary bodies that are primarily made of silicate rocks. These bodies include Mercury, the smallest terrestrial planet, Venus, Earth, and Mars. These planets are referred to as "Earth-like" or "terrestrial" (derived from the Latin word for the Earth, terra) because they resemble the Earth to a significant extent. The four terrestrial planets in our solar system are not the only planets with terrestrial characteristics; scientists have found several other planets in the universe.They are telluric planets.To understand more silicate -
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A coin (5 grams), a small parachute (21 grams), and a hammer (710 grams) are all dropped from a height of 10 meters. The coin and the hammer take about the same amount of time to fall. Which statement describes the time it takes for the parachute to fall?
A. It takes less time to fall because it has the least mass.
B. It takes longer to fall because it experiences greater air resistance.
C. It takes the same amount of time to fall because the effect of gravity is the same.
D. It takes less time to fall because it has the most surface area.
Answer: The anwser is B
Explanation:
I say B because a parrashut will take longer a parichute can hold a man up
It can definetly keep its self up.
The parachute takes longer to fall because it experiences greater air resistance. Hence, option (B) is correct.
What is acceleration due to gravity?The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. M/s2 is its SI unit.
Its vector nature—which includes both magnitude and direction—makes it a quantity. The unit g stands for gravitational acceleration.
At sea level, the standard value of g on earth's surface is 9.8 m/s^2.
Hence, a coin (5 grams), a small parachute (21 grams), and a hammer (710 grams) - all of them remain same acceleration due to gravity. So, the coin and the hammer take about the same amount of time to fall. But the parachute takes longer to fall because it experiences greater air resistance.
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a binary star system has two stars where the low mass star orbits the more massive star at a distance of 3 au. they orbit each other with a period of 2 years. their combined mass in solar units is
Their combined mass in solar units is 9.813.
Distance is the numerical often qualitative size of how some distance aside items or factors are. In physics or regular usage, the distance may check with a physical duration or an estimation primarily based on other criteria.
The space between two factors in physical space is the period of an immediate line among them, that's the shortest feasible course.
It reduces the entire international or part of the arena to a small sheet of paper. At the same time as making a map, cartographers pay attention to properly constitute the distance between two locations.
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n the preceding question, you have calculated the frequency of a molecular vibration. the molecule can absorb light at this frequency. the light happens to be in the infrared (ir) part of the spectrum. it is common to quantify the energy of ir photons using inverse centimeters instead of inverse seconds. to do so, one divides the frequency by the speed of light expressed in cm/sec. what is the energy of the infrared photon corresponding to the frequency from the preceding problem, in cm-1?
The Energy of the Infrared photon is 45.678* [tex]10^{-21}[/tex] J
The parameters are :
Frequency (f) = [tex]6.9 * 10^{13}[/tex] Hz
Energy is given by E = hf
where h is the Planck's constant = h = 6.62* [tex]10^{26}[/tex]
Putting these values in the formula for energy,
We evaluate the energy of the infrared photon as,
E = hf
E = [tex]6.62 *10^{-34} * 6.9 *10^{13}[/tex] = 45.678* [tex]10^{-21}[/tex]
IR emissions from materials are measured using infrared spectroscopy at certain wavelengths. As photons (light particles) are absorbed or released by electrons in molecules as the electrons pass between orbits, or energy levels, the IR spectrum of a material will exhibit distinctive dips and peaks.
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what is the maximum speed of a 330 kg car if the spring is compressed the full amount? express your answer with the appropriate units.
Speed can be calculated using Kinetic energy and Potential energy. Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2.
How to calculate speed using Kinetic energy and Potential energy?
We know
Mass of the car = 300kg
G=9.8
Height = 16m
Thus, potential energy U =mgh and kinetic energy is 1/2mv²
0.5*m*v2 = m*g*h
v = √(2*g*h) = √(2*9.81*16)
v=17.71 m/s
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calculate the moment of inertia of a thin, uniform rod of length l and mass m that rotates about a pivot at distance l/3 from one end.
Mass moment of inertia is a quantity that measures the degree of inertia of a body for rotational motion = ML²/9
A rigid body's moment of inertia, also referred to as its mass moment of inertia, angular mass, second moment of mass, or, more precisely, rotational inertia, is a property that establishes the torque required to achieve a desired angular acceleration about a rotational axis, much like mass establishes the force required to achieve a desired acceleration.
Depending on the axis selected and the distribution of the body's mass, a change in the body's rate of rotation will need a greater torque for bigger moments.
The moment of inertia for a point mass is just the mass times the square of the distance perpendicular to the axis of rotation. This is an extensive (additive) property.
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The cable lifting an elevator is wrapped around a 1.2-m-diameter cylinder that is turned by the elevator's motor. The elevator is moving upward at a speed of 2.5m/s . It then slows to a stop, while the cylinder turns one complete revolution.
How long does it take for the elevator to stop?
Express your answer to two significant figures and include the appropriate units.
It will take 2.8 s for the elevator to stop when it is moving with a speed of 2.5m/s
1)The cable will travel a linear distance equal to the distance covered by the elevator because it is constantly taut and neither slipping nor stretching.
2) Since the cylinder makes one full rotation, the cable's length is equal to the cylinder's circumference.
3) As a result, you must determine the cylinder's circumference, which is determined using the formula C = 2[tex]\pi[/tex] radius.
The radius is half the diameter: 1.2 m / 2 = 0.6 m
Hence, C = 2π × 0.6m = 3.8m
⇒ Distance run by the elevator = 3.8m
4) Now, assuming that the elevator decelerated uniformly from its starting speed of 2.7 m/s to a complete halt (Vf = 0), you use the related formulas:
i) [tex](V_{f})^{2}[/tex]= [tex](V_{o})^{2}[/tex] - 2ad ⇒ 2ad = [tex](V_{o})^{2}[/tex]- [tex](V_{f})^{2}[/tex] ⇒ a = [tex](V_{0})^{2}-(V_{f})^{2}[/tex]/ (2d)
a = [2.7 m/s]² / (2×3.8m) = 0.96 m/s²
ii) [tex]V_{f}[/tex] = [tex]V_{0}[/tex]- at ⇒ t = [2.7 m/s] / (0.96 m/s²) = 2.8 s
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a knight sits on a castle wall during a siege. to while away the time, he notes that boul- ders catapulted from below land on the top of his wall with a vertical velocity of 7.6 m/s. if he is 35 m above the catapult, what is the initial velocity of the boulders? the acceleration of gravity is 9.8 m/s2 . answer in units of m/s.
A knight sits on a castle wall during a siege. to while away the time, he notes that boul- ders catapulted from below land on the top of his wall with a vertical velocity of 7.6 m/s. if he is 35 m above the catapult, what is the initial velocity of the boulders? the acceleration of gravity is 9.8 m/s2 . answer in units of m/s. v = 28.21 m/s
vertical velocity of the boulder = 5.6 m/s
height of catapult = 39 m
initial velocity = ?
acceleration due to gravity = 9.8 m/s²
maximum height attained
v² = u² + 2 as
5.6² = = 2 g h
h = 5.6^2/2*9.8
h = 1.6 m
total height above catapulted
H = 39 + 1.6 = 40.6 m
v = under root 2gh
v = under root 3*9.8*40.6
v = 28.21 m/s
so the intial velocity is equal to v = 28.21 m/s
A siege is a navy blockade of a metropolis, or fortress, with the motive of conquering with the aid of attrition, or a well-organized assault. This derives from Latin: sedere, lit. 'to sit down'. Siege warfare is a shape of regular, low-depth struggle characterised by means of one birthday party conserving a sturdy, static, protective role. consequently, an possibility for negotiation among opponents is common, as proximity and fluctuating benefit can encourage diplomacy. The art of undertaking and resisting sieges is called siege struggle, siegecraft, or poliorcetics.
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one of the most common faults of directors is not establishing a clear in a production. at a performance, we are often impatient to see what is coming next, and the director must see to it that the movement from moment to moment and scene to scene has enough drive.
Now that even the director is finished, it is up to the stage manager to put on a dependable performance that upholds the director's intent for the duration of the production.
This entire procedure typically takes 8 to 12 weeks for most projects, though it could take longer for a brand-new or complicated production. When important individuals are absent, sick, out of town, working on another project, or otherwise unavailable, the PA is frequently brought in to perform a number of roles. The position of production assistant and assistant director are sometimes interchangeable in facilities. A dramaturg is a person who reads new plays, collaborates with playwrights on the creation of new scripts, seeks out underappreciated plays from the past, and conducts extensive research on plays.
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a guitar string that is attached at both ends is 40 cm long and produces a fundamental note of frequency 200 hz when it is plucked. what are the frequencies of the first and second overtones of this string?
The first and second overtones are 400hz and 600hz respectively
What is overtone In a stretched string?When a string vibrates in section, it produces overtones. The lowest frequency produced from a plucked string when the string vibrates in one loop is called fundamental frequency. But when it vibrates in multiple loops it is called overtone. Overtones are also called Harmonics of the fundamental frequency.
The first , second and third overtones in a string is 2fo , 3fo and 4fo , where fo is the fundamental frequency.
Therefore if the fundamental frequency is 200hz, the first overtone is 2×200 = 400hz and the second overtone is 3×200 = 600hz.
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calculate the velocity and kinetic energy with which electrons strike the target of an x-ray tube operated at 50,000 volts. what is the short-wavelength limit of the continuous spectrum emitted and the maximum energy per quantum (in joules) of radiation?
The kinetic energy is 8 × 10⁻¹⁵ J , the velocity equals 1.3 × 10⁸ m/s, and the wavelength is 0.248A°, according to the provided statement.
What wavelength is it?A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent emblems) in the consecutive cycles. This length is typically specified in wireless systems in metres (m), centimeters (cm), or millimeters (mm) (mm)
What is the wavelength measured in?The wavelength in the SI system is measured in meters, commonly abbreviated as m. The multiples or decimals of a metre are also used to measure wavelength. Notably, when wavelengths are a significant feature, hyperbolic factors of 10 are used.
Briefing:Kinetic energy = charge × potential difference
Here , charge on electron = 1.6 × 10⁻¹⁸C
Potential difference = 50,000 volts
So, Kinetic energy = 1.6 × 10⁻¹⁹C × 50,000 volts = 8 × 10⁻¹⁵ J
We know,
Kinetic energy = 1/2mv²
8 × 10⁻¹⁵ = 1/2 × 9.1 × 10⁻³¹ × v² [ ∵ m is the mass of electron , e.g., 9.1 × 10⁻³¹ Kg]
v² = 16/9.1× 10¹⁶
v ≈ 1.3 × 10⁸ m/s
As a result, the target is struck by the striking electron with a speed of 1.3 × 10⁸ m/s
Now, wavelength = λ
hc/λ = kinetic energy
1/λ = 8 × 10⁻¹⁵/6.626 × 10⁻³⁴ × 3 × 10⁸
λ = 6.626 × 3 × 10⁻²⁶/8 × 10⁻¹⁵ = 0.248 × 10⁻¹⁰ m
hence, wavelength is 0.248A°
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