The period of the vibration is 3.9ms
What is Period of a vibration?The period (T) of a vibration is the time to complete one oscillation or revolution and is measured in seconds. The period of vibration is given as
T= 1/F
For example, if the period of a vibration is 0.1 second (one vibration takes 0.1 second), then the frequency of the vibration is 1/0.1=10 vibrations per second or 10 hertz.
Similarly if the frequency of a vibration is 256hz, the period T= 1/F= 1/256=0.0039s
1second= 1×10³ms
therefore 0.0039s = 0.0039×10³= 3.9ms
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in state-of-the-art vacuum systems, pressures as low as 1.00 10-9 pa are being attained. calculate the number of molecules in a 1.30-m3 vessel at this pressure and a temperature of 31.0°c.
Number of molecules in the vessel are n = 3.15 x [tex]10^{11}[/tex] molecules
What pressure ?A physical formula that states that the ratio of an ideal gas's measurable qualities is P (pressure) V (volume) = n (number of moles) R (the gas constant) T. (temperature in Kelvin). It is developed from a synthesis of the Boyle, Charles, and Avogadro gas laws. referred to as the universal gas law.
According to the given information
P = 1.00 x 10-9 Pa
V = 1.30 [tex]m^{3}[/tex]
Temperature T = 26° C = 299.15 K
Known
Gas constant R = 8.314 J/ moles K
Avogadro's constant N = 6.022 x [tex]10^{23}[/tex]
Solution :
PV = n RT
1.00 x [tex]10^{-9}[/tex] x 1.30 = n x 8.314 x 299.15
n = 5.23 x [tex]10^{-13}[/tex] moles
n = 5.23 x [tex]10^{-13}[/tex] x 6.022 x [tex]10^{23}[/tex]
n = 3.15 x [tex]10^{11}[/tex] molecules
Number of molecules in the vessel are n = 3.15 x [tex]10^{11}[/tex] molecules
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A skateboarder traveling at 13.6 meters per second rolls rona stop at the top of a ramp in 2.5 seconds. What is the skateboarder’s acceleration
Answer:
Below
Explanation:
Acceleration = Δ v / Δ t = -13.6 m/s / 2.5 s = - 5.4 m/s^2
( the negative sign shows this to be a deceleration)
compared with the buoyant force of the atmosphere on a 1 liter helium filled balloon the buoyant force of the atmosphere on a nearby 1 liter solid iron block is the same. how do you explain this
The density of fluid which means air is the same for both cases, but the volume of a 1 kg helium balloon is more than the density of iron, so the buoyant force on helium is the same as the buoyant force on iron.
What is Buoyant Force?
The buoyant force is the upward push that a fluid applies to an object when it is submerged in it. The fluid's pressure on the object is what creates the buoyant force. The net upward force results from the fact that the pressure on the bottom of an item is always greater than the force on the top since pressure rises as depth increases.
What is Density?
Mass of a solid substance per unit volume.
d = M/V, where d is density, M is mass, and V is volume, is the formula for density. Grams per cubic centimetre are a typical unit of measurement for density.
Hence, it can be concluded from this that, the buoyant force on both is the same.
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Ben is measuring the effect that the potential energy of an object has on the height of an object's bounce
Which variable represents the height of an object's bounce?
Independent variable
Confounding variable
Response variable
Explanatory variable
The variable which represents the height of an object's bounce is Option A. Response variable
What is a response variable ?In a study or experiment, the query is focused on the response variable. A variable that explains changes in another variable is an explanatory variable. Anything could have an impact on the response variable.
The variable whose fluctuation depends on other variables is known as a response variable (or dependent variable).
The independent variable, often known as the explanatory variable, and the response variable are frequently connected. In an experiment, the response variable is the thing that changes, frequently as a result of variations in the explanatory factors.
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A 4. 0-kilogram object is accelerated at 3. 0 meters per second^2 north by an unbalanced force. The same unbalanced force acting on a 2. 0-kilogram object will accelerate this object toward the north at.
According to the given statement 6.0 m/s² accelerate this object toward the north at.
What is a acceleration explain?Velocity: the rate at which direction and velocity of a moving item vary over time. When something moves faster or slower, it is considered to be accelerating. Motion on a circle increases even while the speed remains constant because the vector will always be changing.
Briefing:The force is directly related to the rate of change in momentum, according to Newton's second law of motion.
F is the energy, m is the mass, and an is the acceleration, so F = ma.
F = 4 × 3
= 12 Newtons
The same force acts on a 2.0 kg object
F = ma
a = F/ m
= 12 /2
= 6.0 m/s²
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for supersonic flow in a round duct, if the diameter increases what happens to static pressure? group of answer choices
Answer: it explodes
Explanation:
four resistors of 3.40 ohms, 6.54 ohms, 8.32 ohms, and 1.34 ohms are connected in parallel with a 12.0 v battery. find the total resistance, in ohms, of the circuit.
The circuit's overall resistance, measured in ohms, is 9.23A. when a 12.0 v battery is linked in parallel with four resistors that have resistance values of 3.40 ohms, 6.54 ohms, 8.32 ohms, and 1.34 ohms.
How can we determine the circuit's overall resistance?You add up the individual resistances to determine the total overall resistance of several resistors connected in this manner. The formula used for this is as follows: Rtotal = R1 + R2 + R3, and so forth. Example: For these three resistors connected in series, determine the total resistance.
How much resistance is there in total?The sum of each component resistance in a series circuit represents the circuit's overall resistance.
1 / Req = 1 /R1 + 1 / R2 + 1 / R3 + 1 / R4Req = 1.3ohms
Current = V / R
I = 9.23A
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In the photoelectric effect, a stopping potential of 3.2 V is needed for radiation of wavelength 200 nm.
(a)What is the work function (in eV) of the material?
(b) What is the maximum kinetic energy (in eV) of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm?
(a) The work function is 7.5(10)¹⁴ Hz.
(b) The kinetic energy of photoelectron is - 1.898 eV
The photoelectric effect consists of the emission of electrons (electric current) that occurs when light falls on a metal surface under certain conditions.
If the light is a stream of photons and each of them has energy, this energy is able to pull an electron out of the crystalline lattice of the metal and communicate, in addition, a kinetic energy.
This is what Einstein proposed:
Light behaves like a stream of particles called photons with an energy
E = h.ν ----- eq1
So, the energy E of the incident photon must be equal to the sum of the Work function Φ of the metal and the kinetic energy K of the photoelectron:
E = Φ + K ----- eq2
Where Φ is the minimum amount of energy required to induce the photoemission of electrons from the surface of a metal, and its value depends on the surface.
In case, Φ = 5eV
So, applying equation (1) in this problem:
E = hν
Where:
h = 4.136(10)⁻¹⁵ eV is Planck constant
ν is the frequency
Now the frequency has an inverse relation with the wavelength
λ = 400(10)⁻⁹ m
ν = c/λ
Being c = 3(10)⁸ m/s is the speed of light in vacuum.
ν = 7.5(10)¹⁴ Hz.
Substituting,
E = 4.136(10)⁻¹⁵ {7.5(10)⁻¹⁰}
E = 3.1 eV
Now,
3.1 eV = 5 ev + K
K = - 1.898 eV
Since a negative kinetic energy is not physically possible, the only explanation is: the conditions for a photoelectric effect were not met, hence the photoelectric effect cannot occur.
Therefore, the main condition for the occurrence of the photoelectric effect is that the energy incident photon must be greater than the work function and E > Φ
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evidence from distant supernovae (as well as from studies of the cosmic microwave background) seems to suggest that the universe is doing something that goes against what nearly all astronomers expected just a decade ago. what is this phenomenon, which is variously attributed to things called the cosmological constant, dark energy, or quintessence?
The first light to ever be capable of freely circling the entire universe is what is known as the Cosmic Microwave Background (CMB), and it has since been cooled.
What is Cosmic Microwave Background (CMB) radiation?In 1965, the CMB radiation was unintentionally discovered. Two radio astronomers from the United States, Penzias and Wilson, recorded a signal in their radio telescope that was impossible to attribute to a specific source in the sky. Day or night, summer or winter, it appeared to have the same intensity everywhere. They came to the conclusion that the signal had to originate from outside of our galaxy. It almost came from the beginning of the universe.Their discovery was viewed by scientists as strong support for the "Big Bang" theory. According to this theory, the 'shockwave' of that primordial explosion would still be observable as a subdued 'wallpaper' coming from everywhere behind all galaxies, quasars, and galaxy clusters. As of right now, the Big Bang theory is still the only theory that can satisfactorily account for the CMB's existence. This theory proposes that the Universe initially consisted of a very hot and dense phase that expanded and then naturally cooled; the temperature during this period was so high that neutral atoms could not form for several hundreds of thousands of years. Neutrons and charged particles were the primary components of matter. At that time, light and matter were tightly coupled because electrons and light particles interacted closely. The Universe was opaque as a result of the inability of light to propagate.To Learn more About Cosmic Microwave Background refer to:
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fingerprints left on a piece of glass such as a windowpane can show colored spectra like that from a diffraction grating. why?
The skin oils from the finger will deposit on smooth surfaces in the pattern of the closely spaced ridges when the finger contacts them.
What is diffraction ?The Huygens-Fresnel principle, which views each point in a propagating wave front as a collection of unique spherical wavelets, describes the diffraction phenomenon in classical physics. When a wave from a coherent source (such a laser) comes into contact with a slit or aperture that is roughly the same size as its wavelength, the characteristic bending pattern is most noticeable.
There are numerous closely spaced ridges and swirls on the skin of a fingertip. The skin oils from the finger will deposit on smooth surfaces in the pattern of the closely spaced ridges when the finger contacts them. In order to create a crude diffraction grating and create a coloured spectrum of the light travelling through or reflecting from the glass surface, open intervals between the lines of deposited oil can be used as slits.
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how do we know that spheroidal stars (stars in the bulge and halo) are older, on average, than disk stars?
There are no blue spheroidal stars.
What is meant by disk stars ?Population I stars are disc stars. They are therefore relatively young stars with circular orbits in the galactic plane. They are typically rich in metal. As a result of the disk's abundance of gas and dust, vigorous star formation occurs there. The spiral arms of the galaxy are where stars develop.
There is always some matter around the star when it originates, and this material collects into a disc around the rotating star's equator. This substance can also condense into solid or gaseous structures in the form of a disc.
The researchers discovered that the thick disc of the galaxy's stars were, in fact, billions of years older than the stars observed elsewhere.
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Which of the following graphs shows the correct relationship betwveen the pressure and volume of an ideal gas at a given temperature? Note the origin corresponds to P= 0 and V= 0.
The volume and temperature graph is straight line passing through origin .
The origin corresponds to V = 0 and T = 0, the volume of gas is directly proportional to absolute temperature at constant pressure. so the volume and temperature graph is straight line passing through origin.
The cube (x3) of a unit of length represents a unit of volume in its most basic form. The cubic metre is the comparable unit of volume, for instance, if the metre (m) is chosen as the length unit (m3). [12] So, L3 is the unit dimension for volume, a SI-derived unit. [13] Metric prefixes that are strictly powers of ten are used with the metric units of volume. When prefixes are applied to volume units, which are stated as units of length cubed, the cube operators are applied to the unit of length containing the prefix. Converting from cubic centimeter to cubic meter is demonstrated by the following formula: 2.3 cm3 = 2.3 (cm)3 = 2.3 (0.01 m)3 = 0.0000023 m3 (five zeros).
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the coefficient of kinetic frition between an object and the surface upon which it is sliding is 0.10. the mass of the object is 8.0 kg. what is the force of friction
The force of friction is 0.8 N.
Friction is the force that prevents motion when the surface of one object comes into contact with the surface of another.
It also has the same SI unit as other forces have as Newton (N).Frictional force can be calculated by the formula F = μ * Fnμ is the coefficient of friction between the surfaces which are in the contact.
Fn is the normal force acting on the object due to its mass.
Mass of the object = m = 8.0 kg
coefficient of kinetic friction between an object and the surface upon which it is sliding = 0.10
Frictional force = F = 8.0 * 0.10
F = 0.8 N
The force of friction is 0.8 N.
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A star can give off white light. Why is this evidence that a star is a blackbody radiator?.
Answer: This is evidence that a star is a blackbody radiator because white light is made up of many different wavelengths of light.
the mass of the puck is difficult to measure because it sublimates and looses mass over time. can this explain the difference between the spring constants you found in part 1 and part 2? give your answer as a cer.
The spring stiffness is quantified by the spring constant, or k. For various springs and materials, it varies. The stiffer the spring is and the harder it is to stretch, the larger the spring constant.
F = -kx. The term "spring constant" refers to the proportional constant k. It gauges the stiffness of the spring. A spring exerts a force F = -kx in the direction of its equilibrium position when it is stretched or compressed to a length that differs by an amount x from its equilibrium length. A large value of k indicates that more force is needed to stretch it a given distance than would be necessary to stretch a less stiff spring the same distance.
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place), estimate the hydraulic conductivity [m/d] of the unconfined aquifer. the radius of influence around the pumping well is approximately 500 m
It is not possible for me to accurately estimate the hydraulic conductivity of an unconfined aquifer without additional information.
The hydraulic conductivity of an aquifer is a measure of its ability to transmit water, and it depends on various factors such as the porosity and permeability of the aquifer materials, the depth and thickness of the aquifer, the extent of the aquifer's saturation with water, and the hydraulic gradient within the aquifer.
The radius of influence around a pumping well is not necessarily related to the hydraulic conductivity of an aquifer.
In order to estimate the hydraulic conductivity of an unconfined aquifer, a hydrologist would need to conduct detailed field measurements and possibly use modeling techniques to take into account the various factors that affect the aquifer's ability to transmit water.
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what frequency of rotation, in rpm , is required to give an acceleration of 1.4 g to an astronaut's feet, if her feet are 1.1 m from the platform's rotational axis?
The frequency of the rotation having a radius of 1.1 m is 3.53 rpm
The rotational acceleration = 1.4 g
The radius of the rotation = 1.1 m
The frequency of the rotation can be found using the formula,
ω = √(α/r)
where ω is the frequency of the rotation
α is the acceleration of the rotation
r is the radius of the rotation
Let us substitute the known values in the above equation, we get
ω = √ (1.4 x 9.8 / 1.1 )
= √ (13.72 / 1.1)
= √12.47
ω = 3.53
Therefore the frequency of the rotation is 3.53 rpm
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quadrasteer steering systems are being discussed. technician a says at low speeds, the rear wheels turn in the same direction as the front wheels. technician b says at high speeds, the rear wheels turn in the direction opposite to the front wheels. who is correct?
Neither a or b is correct.
What is speed?
An object's velocity (commonly denoted by v) is the rate of change of position over time, or the rate of change of position per unit time. So it's a scalar quantity. The average velocity of an object over a time interval is the distance traveled by the object divided by the duration of the interval. The instantaneous velocity is the limit of the average velocity as the time interval approaches zero. Velocity is not the same as speed.
Velocity is the dimension of distance divided by time. The SI unit for speed is meters per second (m/s), but the most common everyday speed units are kilometers per hour (km/h) or miles per hour (mph) in the US and UK. ). Knots are widely used in air and sea travel.
According to special relativity, the fastest speed at which energy or information can travel is the speed of light in a vacuum c = 299792458 meters/second (approximately 10790000000 km/h or 671000000 mph). Matter can never fully reach the speed of light because it requires infinite energy. In relativity physics, the concept of velocity replaces the classical idea of velocity.
Therefore, Neither a or b is correct
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A star was observed to have a planet orbiting it at a distance of 1.12×108 km. The orbital period of the planet is 329 days. Calculate the mass of the star.
The mass of the star would be 9.97 x 10³⁵ Kg.
What is Star? What is centripetal force?Stars are huge celestial bodies made mostly of hydrogen and helium that produce light and heat from the churning nuclear forges inside their cores. We can write the relation absolute magnitude [M] and apparent magnitude [m] as follows : M = m + 5(log₁₀p + 1). The centripetal force is the force needed to make a body move in circular motion. It is given by : F{C} = mv²/rWe have a star was observed to have a planet orbiting it at a distance of 1.12 × 10⁸ km. The orbital period of the planet is 329 days.
Let the mass of star be [M] and that of planet be [m]. Since, the planet revolves around the star, we can write -
F{Centripetal} = F{Gravitation}
mv²/r = GMm/r²
v² = GM/r
(rω)² = GM/r
r²ω² = GM/r
ω² = GM/r³
(2π/T)² = GM/r³
M = (2π/T)² (r³)/G
M = 46.8 x (r³)/G
M = {46.8 x (1.12)³ x (10⁸)³}/{(6.6) x 10 ⁻¹¹}
M = (65.7/6.6) x (10²⁴/ 10 ⁻¹¹)
M = 9.97 x 10³⁵ Kg
Therefore, the mass of the star would be 9.97 x 10³⁵ Kg.
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a friend of yours is loudly singing a single note at 500 hz while racing toward you at 27.2 m/s on a day when the speed of sound is 343 m/s. what frequency do you hear?
The frequency heard by you is 6305.15 Hz.
Given that,
f₁ = 500 Hz
v₁ = 27.2 m/s
f₂ = ?
v₂ = 343 m/s
If the frequency of a wave is directly proportional to the velocity.
We know that, f = kv
where, f is frequency
k is constant of proportionality
v is velocity
k = f/v
From the above formula, we can write, f₁ /v₁ = f₂ /v₂
We have to find out f₂, f₂ = f₁ *v₂ /v₁
Substituting the values, we have,
f₂ = 500* 343/ 27.2 = 6305.15 Hz
Thus, the frequency heard by you is 6305.15 Hz.
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The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
The absolute value equation is |x - 430| ≤ 20.
What is equation?An equation is a formula that is express the equality of two equation.
b) Solution: 410 ≤ x ≤ 450
Explanation:
1) Call x the variable, actual weight of the soccer ball
2) Recomended weight: 430 g
3) Difference using absolute value is | x - 430|
4) The accepeted variation (difference) is up to 20 g means that the difference has to less than or equal to 20 g ⇒ | x - 430| ≤ 20
5) Solution:
i) start: |x - 430| ≤ 20
ii) as per the definition of absolute value: -20 ≤ x - 430 ≤ 20
iii) addition property of inequalities: add 430 to all the parts:
- 20 + 430 ≤ x - 430 + 430 ≤ 20 + 430
iv) do the operations: 410 ≤ x ≤ 450
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a 0.3175 cm sphere of glucose is placed in a water stream flowing at a rate of 0.15 m/s. the temperature of water is 25 °c. the diffusivity of glucose in water is 0.69 x 10 -5 cm2/s. estimate the mass transfer coefficient.
The mass transfer coefficient, based on the provided statement, is 6.16*10⁻¹² m/s.
What does physics mean when it refers to temperature?Temperature is a unit used to represent hotness or coolness on any of a number of scales, includes Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter (body with a temperature higher) to a colder (body with a temperature lower) (one at a lower temperature).
Briefing:Given,
Diameter of glucose sphere,
D = 0.3175cm
D= 0.003 m
Velocity, V = 0.15m/s
Mass diffusivity, [tex]D_{AB}[/tex] = 0.69*10⁻⁵cm²/s
For flow around sphere
[tex]\text { Sh }=\frac{K_C D}{D_{A B}}=2+0.554 Re^{1 / 2} Sc^{1 / 3}[/tex]
Sh = Sherwood number
D = diameter of sphere
[tex]k_{c}[/tex] = Mass transfer coefficient
[tex]D_{AB}[/tex] = Diffusivity
[tex]R_{e}[/tex] = DVρ/M
Diameter (D) = 0.003m
Velocity (V) = 0.15m/s
ρ = Density of water at 25°C = 996kg/m³
M = Viscosity of water at 25°C at 10⁻³ Pa
[tex]R_{e}[/tex] = 0.003*0.15*996/10⁻³
[tex]R_{e}[/tex] = 448.2
Sc = Schmidt no.
For water at 25°C
Sc = 1.6 (From thermodynamics table)
Kc * 0.003/6.9*10⁻⁸ = 2 + 0.554 ([tex]448^{1/2}[/tex])[tex](1.6^{1/3})[/tex]
4.34*10⁻¹² Kc = 26.76
Kc = 6.16*10⁻¹² m/s
This is the mass transfer coefficient.
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The complete question is-
Determine the mass transfer coefficient, kc, for the transfer from a glucose sphere, 0.3175cm in diameter, which is submerged in a 25°C aqueous stream flowing at a bulk velocity of 0.15m/s. The mass diffusivity of glucose in water at 25°C equals 0.69*10⁻⁵cm²/s.
a). Estimate the mass transfer coefficient, k₁
multiple-concept example 7 explores the approach taken in problems such as this one. the blades of a ceiling fan have a radius of 0.380 mm and are rotating about a fixed axis with an angular velocity of 1.50rad/s 1.50rad/s . when the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of 2.00rad/s2 2.00rad/s2 . after 0.500 ss the blades acquire an angular acceleration of 2.00rad/s2 2.00rad/s2 . after 0.500 ss has clapsed since the switch was resct, what is (a) the total acceleration (in m/s2)m/s2) of a point on the tip of a blade and (b)(b) the angle ϕϕ between the total acceleration a→a→ and the centripetal acceleratio
The angle of total acceleration with centripetal acceleration is 13.14 degree.
What is acceleration?
The rate at which an object's velocity with regard to time changes is referred to as acceleration in mechanics. It is a vector quantity to accelerate. The direction of an object's acceleration is determined by the net force that is acting on it. the quantity of acceleration a body undergoes in accordance with Newton's Second Law. For instance, when a vehicle moves from the a standstill (nil velocity, inside of an inertial frame of reference to the a straight line at increasing speeds, it accelerates inside the direction of travel.
Here ,
radius , r = 0.380 m
angular velocity , w = 1.50 rad/s
angular acceleration ,alpha = 2 rad/s^2
after the time 0.5 s
for the final angular velocity
wf = wi + alpha * t
wf = 1.50 + 2 * 1
wf = 2.5 rad/s
Centripetal Acceleration: wf2 * r
ac = 2.5^2 * 0.380 m/s^2
ac = 2.375 m/s^2
for tangential acceleration
at = alpha * r
at = 1.5 * 0.380
at = 0.57 m/s^2
a) for the total acceleration = sqrt(at^2 + ac^2)
total acceleration = sqrt(2.375^2 + 0.57^2)
total acceleration = 2.44 m/s^2
b)
angle =arctan(at/acceleration)
angle = arctan(0.57/2.44)
angle = 13.14 degree
The angle of total acceleration with centripetal acceleration is 13.14 degree
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4. A meteorite travels at 15 km/s before reaching Earth's
atmosphere. Calculate how far it travels in 12 s. (Distance)
Answer:
180 km
Explanation:
velocity (v) = distance (s) / time (t)
From there we get that the distance is: s=v*t
s = 15 km/s * 12 s
s =180 km
dentical rays of light in air are refracted upon entering three transparent materials: (a) water, where the speed of light is 0.75c ; (b) ethyl alcohol; speed 0.7c ; and (c) crown glass; speed 0.6c .
The transition from less dense air to denser glass or water causes light to slow down.
What happens to a ray of light as it passes through air and enters water?A beam of light (a collection of perpendicular rays) will move straight through the air when it is shone at it. Until they come into contact with an object, light rays typically go in straight paths.A sheet of glass's surface will reflect some light when a light ray strikes it, so this happens. However, because glass is transparent, a large portion of the light will flow through the glass.Light beams are similarly impacted by water. While some light will reflect off the water's surface, the translucent water will let in the majority of the light.The direction of a light ray changes when it travels through glass from the atmosphere. As it travels through the glass' surface, the light ray seems to bend.Similar effects occur when a light beam travels from air into water: the light ray is twisted as it collides with the water's surface.Refraction describes the "bending of a ray of light" when it travels through one substance and then another.When a light beam exits glass or water and enters the atmosphere, it will also bend.To Learn more About slow down refer to:
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at sea level, at a latitude where , a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m. what is the value of g in m/s 2 at a location where the length of such a pendulum is 0.960 m for period 2.00 s?
The value of acceleration due to gravity in at a location where the length of such a pendulum is 0.960 m for period 2.00 s is 9.48 m/s².
What is the period of oscillation of pendulum?
The period of oscillation of a pendulum is the time taken for the pendulum to complete one cycle.
Mathematically, the period of oscillation is given as;
T = 2π √ (L / g)
where;
T is the period of the oscillationL is the length of the pendulumg is acceleration due to gravityAt a constant period, the final equation becomes;
L₁ / g₁ = L₂ / g₂
g₂ = (g₁L₂) / (L₁)
g₂ = (g₁ x 0.96 ) / (0.993)
g₂ = 0.967 g₁
g₂ = 0.967 x 9.8 m/s²
g₂ = 9.48 m/s²
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two inductors of self-inductance l1 and l2 are connected in parallel. the inductors are magnetically shielded from one another so that neither produces flux in the other. show that the self-inductance of the combination is given by 1 l
Voltage is proportional to inductance just as, for resistors, it is proportional to resistance. Now, the (independent) voltages for parallel elements are equal (V₁ = V₂) and the currents (which are generally functions of time) add i(t) = i₁(t) + i₂(t)
This leads to the equation,
i = i₁ + i₂ + i₃ = V [(1/R₁) + (1/R₂) + (1/R₃)] for resistors.
We note that this condition on the currents implies
d₁(t)/dt + d₂(t)/dt = d(it)/dt
Thus, although the inductance equation, ε = -L(di/dt) involves the rate of change of current, as opposed to current itself, the conditions that led to the parallel resistor formula also apply to inductors.
Therefore, 1/L(eq) = 1/L₁ + 1/L₂
Therefore to ensure the independence of the voltage values, it is important that the inductors not be too close together. The requirement is that the field of one inductor not to have significant influence (or "coupling") in the next.
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how far from the lens must the film in a camera be, if the lens has a 35.0-mm focal length and is being used to photograph a flower 75.0 cm away? explicitly show how you follow the steps in the lenses.
The lens should be kept at a distance of 3.67 cm from the film in the camera to be photographed and convex lens should be used.
Focal length = f = 35.0 mm = 3.5 cm
Distance at which flower is kept = p = 75 cm
The type of lens that should be used = convex
Distance at which camera should be kept = q =
= Using the lens formula
= 1/p + 1/q = 1/f
= 1/75 + 1/q = 1/3.5
= 1/q = 1/3.5 - 1/75
= q = 3.67 cm
So, the film should be kept 3.67 cm behind the convex lens.
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an object is 50 cm from a concave mirror with radius of curvature of magnitude 60 cm. what is the transverse magnification produced by the mirror?
An object is 50 cm from a concave mirror with radius of curvature of magnitude 60 cm. The transverse magnification produced by the mirror is 75 cm.
To find the transverse magnification, the given data is,
object distance=p=50cm
Radius of curvature=R=60cm
What is the magnification?Magnification refers to the image's size in relation to the item that produced it.
The ratio of image length to object length, measured in planes perpendicular to the optical axis, is referred to as linear magnification.
For imaging, optical microscopes combine ocular and objective lenses. The sum of the magnifying powers of the individual lenses produces the observation magnifying power.
then f=R/2
f=60/2
f=30cm
Using mirror formula,
1/f=1/p+1/q
1/30=1/50+1/q
1/30–1/50=1/q
(5–3)/150=1/q
2/150=1/q
2q=150
q=75
The transverse magnification produced by the mirror is 75 cm.
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in electronic circuits, when analyzing the effect of l or c on the wave shape of non sinusoidal voltages, what is useful?
It retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude.
What has a sinusoidal wave form?Periodic waveforms known as sine waves can be represented graphically using the sine or cosine trigonometric functions. Electrical circuits that receive "AC" voltages and currents, or sinusoidal waveforms whose polarity alternates on each cycle.The strength of the magnetic field that forms around a wire or conductor while an electric current flows through it is inversely proportional to the current value. The movement of this single wire conductor through the magnetic flux induces a "EMF" (Electromotive Force) inside the conductor if it is moved or rotated within a stationary magnetic field.It retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique.To learn more about sinusoidal wave, refer to
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