Assume that similar quantities of heat are transferred into various masses or mercury and water, resulting in equivalent temperature variations. Mercury's mass is 0.033 times that of water.
What makes Mercury so unique?Of such eight moons of jupiter, Mercury is the smallest and one that is closest to the Sun. Mercury completes three spins of its axis for each of the two circuits it makes around the Sun, so takes around 96 Earth days. This rotation is exclusive to the solar system and is gravitationally locked.
Briefing :According to the statement we have Mass of mercury = M(Hg), and
Mass of Water = M(H₂O)
M(cu) / M(H₂O) , heat transfer and mass are related as we have the formula : Q=mcΔT
according to the formula we have , Q(Hg) = M(Hg) C(Hg)ΔT(Hg)...........(1)
for water , Q(H₂O)= M(H₂O) C(H₂O)ΔT(H₂O)..............................(2)
therefore dividing by specific heat in the temperature = C T from both sides .
we Get : [tex]\frac{ Q(Hg)}{CT} =[/tex][tex]\frac{ M(Hg) C(Hg)ΔT(Hg)}{CT}[/tex] , [tex]\frac{Q(H2O) }{CT} =[/tex] [tex]\frac{C(H2O) Δ TH2O}{CT}[/tex]
∴ Q(Hg)=[tex]\frac{Q(Hg)}{Q(Hg)ΔT(Hg)}[/tex] , Q(H₂O)= [tex]\frac{ Q(H2O)}{C(H2O)ΔTH2O)}[/tex]
by solving we get = Q(Hg)/C(Hg)ΔT(Hg)/Q(H₂O) / C(H₂O)ΔT(H₂O)
= Q(Hg)/C(Hg)ΔT(Hg) × C(H₂O)ΔT(H₂O)/Q(H₂O)
= [tex]\frac{C(H2O)}{C(Hg)}[/tex]= M(Hg)/M(H₂O)
specific heat of water = 4184 J/kg
and specific heat of mercury = 139 J/kg
therefore we get 4184/139 = 0.033 ans or 3:100 in ratio
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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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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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Dancers experience large forces associated with the jumps they make. For example, when a dancer lands after a vertical jump, the force exerted on the head by the neck must exceed the head?s weight by enough to cause the head to slow down and come to rest. The head is about 9. 4% of a typical person?s mass. Video analysis of a 64 kg dancer landing after a vertical jump shows that her head slows down from 4. 2 m/s to rest in a time of 0. 21 s.
Compared with the force her neck exerts on her head during landing, the force that head exerts on her neck is 1845.76 N. Deceleration is same during first half and second half and hence force will also be same.
What is force?In physics, an influence that change the motion of an object is called force.
The head decelerates from 4 m /s to zero in .21 sec ;
Deceleration = (4 - 0) / 0.21
= 19.04 m/s²
If F is the average force, then
F - mg = ma
So Force, F = m ( g + a )
= 64 ( 9.8 + 19.04 )
F = 1845.76 N.
This force will be uniformly acting on head in the upward direction . Therefore deceleration is same during first half and second half and hence force F will also be same.
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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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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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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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why can't the lowest-mass main-sequence stars become giants? giants are huge, so they are massive stars. actually, low-mass stars do become giants. they are not massive enough to fuse helium. they are not hot enough.
Low-mass stars can become giants when they reach the end of their main sequence lifetimes.
What is Low-mass stars?
Low mass stars use the proton-proton chain to fuse hydrogen to helium inside of their cores over the course of billions of years. They typically have a convection zone, and depending on how active it is, we can tell whether the star's activity resembles the sunspot cycle on our Sun. Some tiny stars have convection zones that are incredibly deep. Some of these stars as well rotate quickly, twisting the magnetic fields around them. A flare of radiation, including X rays, may result from the alignment of these field lines. A low mass star uses up its core hydrogen over the course of its lifetime and transforms it into helium. The star gradually grows brighter as the core gradually contracts and heats up. The star's core eventually runs out of hydrogen due to nuclear fusion.
The star will expand significantly and become increasingly luminous as it evolves off the main sequence. This is known as the Red Giant branch, and it occurs as the star runs out of hydrogen fuel and starts to fuse helium in its core. This causes the star to swell in size and increase in luminosity, eventually becoming a Red Giant.
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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.
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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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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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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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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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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ultrasound is used to view the interior of the body, much as x rays are utilized. for sharp imagery, the wavelength of the sound should be around one-fourth (or less) the size of the objects to be viewed. approximately what frequency of sound is needed to produce a clear image of a tumor that is 1.00 mm across if the speed of sound in the tissue is 1550 m/s ?
The frequency of sound needed to produce a clear image of a tumour that is 1.00 mm across is approximately 6.2 MHz (6,200,000 Hz).
What is frequency?
The amount of times this same alternating current (AC) circuits from positive to negative in a second is referred to as frequency. In direct currents, this switching doesn't really take place (DC). Hertz is the unit of frequency (Hz). For instance, a current is said to have a frequency of 60 Hz if it switches from positive to negative 60 times per second. The period of an AC current is the length of time it takes for one cycle to complete, during which the voltage changes from 0 (zero) to positive to negative and back to 0 (zero). The frequency is the reciprocal of the period. In contrast to low frequency, which has fewer waves per second as well as a longer period, high frequency refers to the number of waves produced per second.
This can be calculated using the equation f = v/λ,
which states that the frequency of sound (f) is equal to the speed of sound (v) divided by the wavelength (λ).
The wavelength of sound for this scenario is equal to the size of the object being viewed (1.00 mm), and the speed of sound in the tissue is 1550 m/s. Therefore, plugging these values into the equation, we get f = 1550/0.001 = 6,200,000 Hz, or 6.2 MHz.
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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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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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the uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. the smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. what is the mass of the board?
126 kg is the mass of the board (in kg)
m1=41 kg
m2= 85 kg
r1=3m
mass of the board= m1+m2
mass of the board=41+85
mass of the board=126 kg
In physics, mass is a way to describe inertia, a quality that all matter shares. Essentially, it is a mass of matter's resistance to altering its direction or speed in reaction to the application of a force. The amount of change caused by an applied force decreases as a body's mass increases. The kilogram, the ISU's unit of mass, is equal to 6.62607015 1034 joule seconds using Planck's constant (SI). One joule is created by multiplying one kilogram by one square meter per second. The kilogram is determined by exact measurements of Planck's constant because the second and the meter have already been defined in terms of other physical constants.
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Abigail's toaster produces 50 units of heat and 5 units of light for every 100 units of electricity it uses. What is the efficiency of her toaster?.
The efficiency of her toaster is 45 %
Explain in detail
The efficiency of a system in electronics and electrical engineering is defined as the ratio of useful power output to the total electrical power consumed. For example, if a system uses 50 units of energy to produce a desired task, but also produces 5 units of energy that is wasted, then the efficiency of the system would be calculated as 45 percent. This is because the wasted energy is subtracted from the total energy used for the desired task, resulting in a ratio of 45 percent.Therefore, we can conclude that correct answer is 45%
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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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A satellite that goes around the earth once every 24 hours is called a geosynchronous satellite. If a geosynchronous satellite is in an equatorial orbit, its position appears stationary with respect to a ground station, and it is known as a geostationary satellite.
Find the radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants:
The universal gravitational constant G is 6.67×10−11Nm2/kg2.
The mass of the earth is 5.98×1024kg.
The mass of the satellite is 2.10×102kg.
The radius of the earth is 6.38×106m.
Give the orbital radius in meters to three significant digits.
The radius of the orbit of a geosynchronous satellite that circles the Earth is calculated to be 4.23 x 10^7 m
As the given time period is 24 hours, we first convert it into seconds as follows;
24 x 3600 = 86,400 seconds
The formula for the time period of the satellite can be given as;
T = 2π √r³ ÷ GM
Here r represents the radius, M represents the mass of the Earth and G illustrates the universal gravitational constant.
86,400 = 2 × 3.14 √r³ ÷ (6.67×10^−11) (5.98×10^24)
1.89 × 10^8 = r³ ÷ (6.67×10^−11) (5.98×10^24)
r = 4.23 x 10^7 m
Therefore the radius of the orbit of a geosynchronous satellite is 4.23 x 10^7 m
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you look down at a coin that lies at the bottom of a pool of liquid of depth d and index of refraction n (fig. 34.33). because you view with two eyes, which intercept different rays of light from the coin, you perceive the coin to be where extensions of the intercepted rays cross, at depth da instead of d. assuming that the intercepted rays in fig. 34.33 are close to a vertical axis through the coin, show that da da = d=n.
The water is medium 1, so
n₁ = n(w)
which we simply write as n. The air is medium 2, for which
n₁≈ 1
We refer to points where the light rays strike the water surface as A (on the left side of Figure) and B (on the right side of the picture). The point midway between A and B (the center point in the picture) is C. The penny P is directly below C, and the location of the “apparent” or virtual penny is V.
We note that the angle ∠CVB (the same as angle ∠CVA) is equal to θ₂ and the angle ∠CPB (the same as angle ∠CPA) is equal to θ₁.
The triangles CVB and CPB share a common side, the horizontal distance from C to B (which we refer to as x).
Therefore,
tan θ₂ = x / dₐ
tan θ₁ = x / d
Using the small-angle approximation (so a ratio of tangents is nearly equal to a ratio of
sines) and the law of refraction, we obtain
tan θ₁ / tan θ₂ = sin θ₁ / sin θ₂
⇒ (x / dₐ) / (x / d) ≈ n₁ / n₂
⇒ d / dₐ ≈ n
⇒ dₐ = d / n
Therefore, the above calculations shows that using law of refraction, dₐ = d / n. Hence, proved.
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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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between 1998 and 2018, the proportion of adults who met both the weekly goal of 150 minutes of moderate exercise and the weekly goal of 75 minutes of intense exercise has by percent.
The percentage of adults who reached both the weekly objective of 150 minutes of moderate exercise and the weekly goal of 75 minutes of intensive exercise has increased from 1998 to 2018 by 22.9%.
The activities listed below all meet the criterion of moderate exercise: In 30 minutes, two miles of walking. five kilometers on a bike in thirty minutes. 20 minutes spent swimming laps. 15 minutes to complete 1.5 miles of running. a 30-minute session of water aerobics. 45 minutes were spent playing volleyball. twenty minutes of basketball. Is a moderate exercise.
Basically, anything that requires you to exert intensive exercise, uses numerous muscle groups, and is performed at or close to your maximum heart rate qualifies. So go ahead and create your own unique form of hard workout. Is known as intensive exercise.
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the filament of a light bulb has a resistance of 20.0 ω at 20oc and 160 ω when the light is on. find the temperature of the filament when the light is on. (the temperature coefficient of resistivity is 3.50x10-3 oc-1.)
The temperature of the filament of the bulb when the light is on is equal to 2020° C.
What is temperature of coefficient of resistance?
The change in electrical resistance of a substance with respect to each degree of temperature change is known as the temperature coefficient of resistance sometimes also called as Coefficient of resistivity.
As a result, the process of electron collision within the material determines the electrical resistance of conductors like gold, aluminum, silver, and copper. The process of electron collision speeds up and becomes more rapid as temperature rises. As a result, the resistance will climb as the conductor's temperature rises.
Given in the question,
Initial temperature, T₀ = 20°C
Initial Resistance, R₀ = 20.0 Ω
Final resistance, R = 160 Ω
Coefficient of resistivity, α = 3.50 * 10⁻³ °C⁻¹
and we have to fund the final temperature, T
The change in resistance and temperature is given by the equation:
[tex]R = R_0 [ 1 + \alpha (T - T_0)][/tex]
This equation can also be written as:
[tex]T = \frac{{\frac{R}{R_0}-1} }{\alpha} + T_0[/tex]
On putting the values from the question we get:
[tex]T = \frac{{\frac{160}{20}-1} }{3.5 \times 10^{-3}} + 20[/tex]
T = 2020° C
Hence, the final temperature of the filament is 2020° C.
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Exercise 1:
A small puck of mass m=150g is at rest on a horizontal surface. Ignore the frictional forces.
a) Calculate the magnitude of the normal force.
b) At t=0, we apply on the puck a horizontal and constant force F-0. 30 N.
b. 1) Calculate the acceleration of the puck.
b. 2) Calculate the distance covered by the puck then its speed at t₁-0. 50 s.
| Take
Take g-9. 80m/s²
0N is the magnitude of the normal force. 0.002 m/s is the acceleration of the puck when we apply on the puck a horizontal and constant force F-0. 30 N (Newton).
What is the S.I unit of Force?the S.I unit of force is Newton (N) which is defined as 1N=1Kgm/[tex]s^{2}[/tex].
Data given:
Mass of puck=150g
puck at rest means a (acceleration =0)
Now to find the magnitude of the normal force.
F=ma
F=150*0
F=0N
Hence, 0N is the magnitude of the normal force.
Now, When we apply on the puck a horizontal and constant force F-0. 30 N.
then to find the acceleration of the puck.
a=F/m
a=0.30N/150
a=0.002 m/s
Hence, 0.002 m/s is the acceleration of the puck when we apply on the puck a horizontal and constant force F-0. 30 N.
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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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if his arms are capable of exerting a force of 14001400 n on the rope, what is the maximum speed he can tolerate at the lowest point of his swing?
Given Data
Mass of tarzan: m=80kg
Length of vine:L=4.8m
Maximum force exerted by tarzan on the vine: F=1400N
The expression of the net force along the direction of vein is
F-mg-mv²/L=0
mv²/L=F-mg
v²=L(F-mg)/m
v=√L(F-mg)/m
Substitute the given values in the above expression.
v=√4.8 kg (1400N-80kg×9.8m/80kg
v≈6.08m/s
Thus, the maximum tolerable speed at the lowest point is 6.08m/s
What is centrifugal acceleration?
Where RV is the vertical curve's radius in meters and v is the speed in meters per second, we can calculate the centrifugal acceleration.
I understand that the question you are looking for
If his arms are capable of exerting a force of 1400Non the rope, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg and the vine is 4.8m long.
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the primary coil of a transformer has 260 260 turns and its secondary coil has 520 520 turns. round all answers to two decimal places, as needed. if the ac voltage applied to the primary coil is 150 150 v, what voltage is present in its secondary coil?
3V voltage is present in its secondary coil.
As per the question:
Primary coil turns(Np)=260
Secondary coil turns(Ns)=520
AC voltage to primary coil (Ep)=150V
AC voltage to secondary coil(Es)=?
Es/Ep=Ns/Np
Es=Ns*Ep/Np
Es=520*150/260
Es=300V
Round to two decimal places,
so, Es=3V
What is transformer?The transformer can be defined as a device that steps up or down voltage in the most basic sense. The output voltage is increased in a step-up transformer and dropped in a step-down transformer. For the system to maintain an equal input and output power, the step-up transformer will reduce the output current and the step-down transformer will increase the output current.
What is the principle of transformer?The transformer works on the principle of Faraday's law of electromagnetic induction and mutual induction.
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I understand that the question you are looking for is:
The primary coil of a transformer has 260 turns and its secondary coil has 520 turns. Round all answers to two decimal places, as needed. If the AC voltage applied to the primary coil is 150 v, what voltage is present in its secondary coil?
A spaceship of mass spaceship = 110000.0 kg starts at rest (vi= 0), then accelerates by releasing
exhaust gas of mass gas = 10600.0 kg with a velocity of gas = -100. What is the speed of the spaceship
Answer:
Approximately [tex]9.64\; {\rm m\cdot s^{-1}}[/tex] (assuming that the velocity of the exhaust is [tex](-100)\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
When an object of mass [tex]m[/tex] travels at a velocity of [tex]v[/tex], the momentum [tex]p[/tex] of this object will be [tex]p = m\, v[/tex].
Assume that there is no external force on this spaceship. The total momentum of the ship and the exhaust will be conserved. In other words,
[tex]\begin{aligned}& (\text{Momenum of Spaceship, before}) \\ &+ (\text{Momentum of Exhaust, before}) \\ =\; & (\text{Momenum of Spaceship, after}) \\ &+ (\text{Momentum of Exhaust, after})\end{aligned}[/tex].
Rearrange to find the momentum of the spaceship after releasing the exhaust:
[tex]\begin{aligned} & (\text{Momenum of Spaceship, after}) \\ =\; & (\text{Momenum of Spaceship, before}) \\ &+ (\text{Momentum of Exhaust, before}) \\ &- (\text{Momentum of Exhaust, after})\end{aligned}[/tex].
It is given that the spaceship and the exhaust were initial stationary. Hence, initial momentum will be [tex]0\; {\rm kg \cdot m\cdot s^{-1}}[/tex] for both the ship and the exhaust.
[tex]\begin{aligned} & (\text{Momenum of Spaceship, after}) \\ =\; & (0\; {\rm kg \cdot m\cdot s^{-1}}) \\ &+ (0\; {\rm kg \cdot m\cdot s^{-1}}) \\ &- (\text{Momentum of Exhaust, after})\end{aligned}[/tex].
Since the exhaust is of mass [tex]10600\; {\rm kg}[/tex] and velocity [tex](-100)\; {\rm m\cdot s^{-1}}[/tex], the momentum of the exhaust after release will be:
[tex]\begin{aligned} & (\text{Momenum of Exhaust, after}) \\ =\; & (\text{mass of Exhaust})\, (\text{Velocity of Exhaust, after}) \\ =\; & (10600.0\; {\rm kg})\, ((-100)\;{\rm m \cdot s^{-1}}) \\ =\; & (-1.06000\times 10^{6})\; {\rm kg \cdot m\cdot s^{-1}}\end{aligned}[/tex].
Divide the momentum of the spaceship by mass to find velocity:
[tex]\begin{aligned} & (\text{Velocity of Spaceship, after}) \\ =\; & \frac{(\text{Momentum of Spaceship})}{(\text{mass of Spaceship})} \\ =\; & \frac{((-1.06000\times 10^{6})\; {\rm kg \cdot m\cdot s^{-1}})}{(110000.0\; {\rm kg})} \\ \approx\; & 9.64\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].