kepler's third law,
Semi-major cross (r) r³=t² =[tex]T^{\frac{2}{3} }[/tex]
The semi-major axis of short-period comet = [tex](111)\frac{2}{3} ^{}[/tex] = 23.10AU
The semi-major axis of short-period comet = [tex](701)^\frac{2}{3}[/tex] = 78.91AU.
Kepler's third regulation is valid due to the fact the sun is tons more huge than any of the planets and therefore Newton's correction is small. The information Kepler had gotten admission to were now not top-sufficient to reveal this small impact. Kepler posted his first two legal guidelines approximately planetary movement in 1609, having located them via reading the astronomical observations of Tycho Brahe. Kepler's 0.33 law become posted in 1619.
It turns out that the steady in Kepler's 0.33 regulation relies upon on the entire mass of the two our bodies worried. Kepler himself, analyzing the motion of the planets across the sun, always treated the 2-frame device of sun-plus-planet. Kepler's third law: the squares of the orbital intervals of the planets are directly proportional to the cubes of the semi-main axes of their orbits. Kepler's 0.33 regulation implies that the period for a planet to orbit the sun increases rapidly with the radius of its orbit.
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The Short-period comet's using kepler's Third law semi-major axis for 111 years is 23.10AU and for 701 years is 78.91 AU is the short-period comet's semi-major axis.
Cross (r) semi-major [tex]r^3[/tex]=[tex]t^2[/tex]
=> r = [tex]t^\frac{2}{3}[/tex]
so for 111 years is( [tex]111^\frac{2}{3}[/tex]) = 23.10 AU
for 701 years is ([tex]701^\frac{2}{3}[/tex]) = 78.91 AU
According to Kepler's Third Law, the planets' squared orbital periods and cubes of their semi-major axes are directly inversely related. According to Kepler's Third Law, a planet's period of orbiting the Sun grows exponentially with its orbital radius. It turns out that the constant of Kepler's Third Law is a function of the combined masses of the two bodies. When analysing the motion of the planets around the Sun, Kepler himself dealt exclusively with the Sun-plus-planet 2-body system.
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A girl climbs a 12 meter ladder, walks across a 15 meter plank then climbs down another 12 meter ladder as shown in the diagram below. What was the magnitude of the girls displacement
Hence, the magnitude of the displacement for each girl is 400 m. This is equal to the actual length of the path skated by girl.
What is magnitude of the girls displacement?When the motion is in a fixed direction, the displacement's magnitude equals its distance (one direction ). The size of the displacement without respect to direction is what we refer to as the magnitude (i.e., just a number with a unit). For instance, during a lecture, the professor could pace back and forth repeatedly, covering perhaps 150 metres in total, and still only finish up two metres to the right of her starting place. Magnitude is simply "distance or quantity" in the context of physics. In terms of motion, it shows the absolute or relative size, direction, or movement of an object. It is used to describe something's size or scope. Magnitude in physics typically refers to a size or quantity.To learn more about magnitude of displacement refer to:
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An incoming ray of light has a vacuum wavelength of 589 nm.
a) If the light travels from tint glass (n = 1.66) to crown glass (n = 1.52) with an angle of incidence of 23.6 degrees, find the angle of refraction.
b) If the light travels from air to some medium with an angle of incidence of 14.9 degrees and an angle of refraction of 7.53 degrees, find the refractive index of the unknown medium.
c) If the light travels from air to diamond (n = 2.419) at an angle of incidence of 49.1 degrees, find the angle of refraction.
A vacuum of wavelength is an electromagnetic field with a frequency that has no medium to travel through and therefore no wave motion.
What does Electromagnetic field mean?
A physical field produced by electrically charged objects is known as an electromagnetic field. It has an effect on the behavior of charged objects in the field's vicinity. The electromagnetic field is infinite in space and describes electromagnetic interaction. It is one of nature's four fundamental forces.
We are given the following data:
The wavelength of the incoming ray of light is λ=589nm.
(a) We are given the following data:
The refractive index of the tint glass is n1=1.66.
The refractive index of the crown glass is n2=1.52.
The angle of incidence is θi=23.6∘.
The expression for the angle of refraction is using Snell's law is,
n1 sinθi =n2 sinθr
sinθr =
n1 / n2 x sinθi
Substituting the given values in the above expression, we will get
sinθr=1.66/1.52 x sin23.6∘
θr =sin−1
(0.43722)
=25.92∘
≈25.9∘
Thus, the angle of refraction is 25.9∘.
(b) We are given the following data:
The angle of incidence is θi =14.9∘.
The angle of refraction is θr=7.53∘.
The expression for the refractive index of the unknown medium is,
n1 sinθi=n2 sinθr
n2=n1 sinθi / sinθr
We know that the refractive index of air is n1=1.
Substituting the given values in the above expression, we will get
n2=1×sin 14.9∘ / sin7.53∘
=1.962
≈1.96
Thus, the refractive index of the unknown medium is 1.96 .
(c) We are given the following data:
The refractive index of the diamond is n2=2.419.
The angle of incidence is θi=49.1∘.
We know that the refractive index of air is n1=1.
The expression for the angle of refraction using Snell's law is,
n1 sinθi = n2 sinθr
sinθr = n1 / n2 x sinθi
Substituting the given values in the above expression, we will get
sinθr=(1 / 2.419)sin 49.1∘
θr= sin−1 (0.3124)
=18.20 ∘
Thus, the angle of refraction is 18.20∘.
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A gymnast of mass 52.0 kg is jumping on a trampoline. She jumps so that her feet reach a maximum height of 2.46 m above the trampoline and, when she lands, her feet stretch the trampoline 67.0 cm down. How far does the trampoline stretch when she stands on it at rest? Assume that the trampoline is described by Hooke’s law when it is stretched.
A gymnast of mass 52.0 kg is jumping on a trampoline. the trampoline stretches 0.67 m when the gymnast stands on it at rest.
What is the trampoline stretch?Generally, To find the stretch of the trampoline when the gymnast is standing on it at rest, we need to use Hooke's law, which states that the force required to stretch (or compress) a spring is directly proportional to the distance that it is stretched (or compressed).
Mathematically, it is represented as
F = kx,
where
F is the force applied,
x is the distance stretched and k is the spring constant.
As the trampoline stretches by 67 cm when the gymnast lands, we can use the equation
F = kx to find the spring constant k. We know that the force applied is the weight of the gymnast, which is
52 kg x 9.8 m/s^2 = 508 N.
k = F/x '
= 508 N / 0.67 m
= 757 N/m
Now that we know the spring constant, we can use it to find the stretch of the trampoline when the gymnast is standing on it at rest. We can use the equation
F = kx where F = weight of the gymnast and x = stretch of the trampoline when she is standing on it at rest.
x = F/k
= 508 N / 757 N/m
= 0.67 m
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You hold a shiny tablespoon at arm's length and look at the front side of the spoon. (a) Is the image you see of yourself upright or inverted? (b) Is the image enlarged or reduced? (c) Is the image real or virtual?
When holding a shiny tablespoon at arm's length and looking at the front side of the spoon,
a) the image of oneself appears to be inverted
b) the image of oneself appears to be reduced
c) the image of oneself is virtual
This is because the light reflecting off the spoon's surface is being bent, or refracted, by the curved surface of the spoon before it reaches the observer's eye, causing the image to appear upside-down. The image that is seen is also reduced, as the spoon is acting as a small mirror and it is reflecting only a small part of the observer's face, shrinking the size of the image. Finally, the image that is seen is a virtual , as it is not coming from a real object and it is being formed by the reflection of light on the spoon's surface.
Virtual images can't be projected on a screen and can be seen only if you look at the reflecting surface.
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A fully charged capacitor with a voltage of 270 kV is discharged through a resistor.
(a) What is the voltage across the capacitor at the end of four time constants?
(b) At this time, what is the voltage across the resistor?
(I think part a has something to do with V=Vo x e^-4, and part b has something to do with the voltage across a resistor is always zero)
Therefore, V = IR = (3 A)(12 ) = 36 V is the voltage drop across the 12 resistor.
V = IR is the formula, where V is the voltage applied across the conductor, I is the current flowing through it, and R is the resistance the conductor offers to the current flow.
From a starting value of, the discharging current falls until it reaches zero. When the capacitor is entirely discharged, the potential difference across the capacitor plates goes from zero to zero.
T = R C is the formula for the time constant of the discharge. A completely charged capacitor will return to its initial voltage after one period. It is safe to suppose that a capacitor discharges in 5 time constants as a result.
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find the horizontal component of the electric field in n/c, taking east as positive.
Eh = - 209.625
The horizontal component of the electric field is -209.625 n/c.
What is Electric Field?
Electric fields are forces created by the presence of an electric charge. An electric field can be created by either a positive charge or a negative charge. Electric fields exert a force on objects with an electric charge, causing them to move and interact with each other. Electric fields can also be used to transfer energy from one place to another. Electric fields are produced by electric charges, or by time-varying magnetic fields. The electric field is a vector field, meaning it has both a magnitude and a direction associated with it at each point in space. The strength of the electric field is determined by the amount of charge present and the distance from the charge.
What does Magnetic field mean?
A magnetic field is an invisible force field created by an electric current or a magnet. It is an area of influence created by a magnet or electric current that can attract and repel other magnets or electric currents. Magnetic fields are used in a variety of applications, from consumer electronics to medical scanners.Magnetic fields are created by moving electric charges, such as electrons, and can be measured in units of teslas. They are responsible for the force that causes magnets to attract and repel each other, and they also determine the direction of the force.
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a round bar of 10 mm diameter is made of aluminum alloy 7075-t6 (see figure). when the bar is stretched by axial forces p, its diameter decreases by 0.016 mm. find the magnitude of the load p. obtain the material properties from appendix i.
The magnitude of the load is 7037.98 N.
What is the original load supported by the bar?
The original load supported by the bar is calculated by applying the formula for tensile strength of aluminum.
τ = 90 MPa
Original area of the aluminum = πd² / 4
A₀ = ( π x 0.01² / 4 )
A₀ = 7.854 x 10⁻⁵ m²
Original load of the aluminum bar;
P₀ = A₀ x τ
P₀ = 7.854 x 10⁻⁵ x 90 x 10⁶ N/m²
P₀ = 7068.58 N
The final area of the bar;
d' = 10 mm - 0.016 mm = 9.98 mm
A' = ( πd'² / 4 )
A' = ( π x 0.00998² / 4 )
A' = 7.82 x 10⁻⁵ m²
P₀/A₀ = P' / A'
P' = ( P₀ / A₀ )A'
P' = ( 7068.58 x 7.82 x 10⁻⁵ ) / ( 7.854 x 10⁻⁵ )
P' = 7037.98 N
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The electric field 1/5 of the way from a charge q1 to a charge q2 is zero.
How many times larger is q2 than q1 based on the previous statement?
Due to less information provided, The electric field at 1/5 of the way between two charges can be zero if the charges are of equal magnitude, or if the charges are of unequal magnitude but the distance between the two charges is an exact multiple of 5.
What is Electric Field?
A physical quantity associated with an electric charge or a charged particle is known as an electric field. It is a vector field that describes the force exerted by the first particle on another charged particle. The electric potential of the charge, which is often measured in volts, defines the strength and direction of an electric field. A vector field is used to describe an electric field, with the electric field vector E at each point in space proportional to the force acting on a unit positive test charge at that point.
What does Magnatitude means?
Magnatitude is a term used to describe the strength or intensity of something, such as an emotion, a physical force, or an event. It is often used to describe the intensity of an earthquake, hurricane, or other natural disaster. In some cases, the term can also be used to describe the power of a person or group, such as the magnatitude of a leader's influence or the magnatitude of a corporation's reach.
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When the word and appears in category titles and code descriptions in the ICD-10-CM Tabular List of Diseases and Injuries, it is:
When the word and appears in category titles and code descriptions in ICD-10-CM Tabular List of Diseases and Injuries, it is: interpreted as meaning and/or
What is ICD-10-CM?ICD-10-CM is clinical modification of the World Health Organization's ICD-10, that consists of a diagnostic system. ICD-10-CM includes level of detail needed for morbidity classification and diagnostic specificity. It also provides code titles and language that complements accepted clinical practice.
Tabular list in the ICD-10-CM is an alphabetical list of ICD-10-CM terms and their corresponding code or category that helps in deciding which section to refer to in Tabular List and it does not always supply the full code.
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if light did not have a wave nature, would snell's law still be true? explain.
No, Snell's law would not still be true if light did not have a wave nature.
What is Snell law?
Snell's law, also known as Snell–Descartes law or the law of refraction, is a formula used to describe the relationship between the angles of incidence and refraction when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. The law is named after Willebrord Snellius, a Dutch astronomer and mathematician. In the most common form of Snell's law, the ratio of the sines of the angles of incidence and refraction is constant, and is known as the index of refraction for the media.
What is Wave Nature?
Wave nature is a property of particles that can be described by wave equations. This property allows particles to exhibit characteristics of both particles and waves, such as interference and diffraction. Particles that exhibit wave nature include electrons, protons, neutrons, and photons.
Snell's law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities of light in the two media. Since light is a wave, it has a velocity. If light did not have a wave nature, it would not have a velocity, and therefore Snell's law would not be true.
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a 5.00 m long diving board with a mass of 6.6 kg is supported by two pillars. one pillar is at the left end of the diving board, as shown, and the other is 1.50 m away. find the forces exerted by the pillars when a 90.0 kg diver stands at the far end of the board
When a 90.0 kg diver stands at the far end of the board, forces are generated by the pillars -2060N.
In physics, pressure is a force that may change how an object moves. An object having mass can be directed by a force to increase in speed (e.g., from a state of rest). Pressure may also be conceptualised as a push or a pull. A pressure is a vector quantity since it has both value and direction.
The net force exerted on an object is equal to the rate at which its momentum changes over time, according to Newton's second law in its original version. This rule states that, if the mass of the object is constant, the acceleration of an object will be directly proportional to the net pressure acting on the object.
According to second law of motion,
Fnet=ma a=0,
[tex]& F_1+F_2-W_p=0 \\& F_1+F_2=W_p \\& F_1+F_2=90 \times 9.8[/tex]
Angular force for net torque,
[tex]$$\begin{aligned}& F_1 \times 0+F_2 \times d-m g L=0 \\& F_2=\frac{m g L}{F_2 \times 1.5}=90 \times 9.8 \times 5 \\& F_2=\frac{90 \times 9.8 \times 5 \mathrm{~N}}{1.5}\end{aligned}$$[/tex]
=2940N
[tex]& F_1+\frac{m g L}{d}-m g=0 \\& F_1=m g-\frac{m g L}{d} \Rightarrow 90 \times 9.8-\left(\frac{90 \times 9.8 \times 5}{1.5}\right) \\[/tex]
=-2060N
Negative sign indicate downwards direction.
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When a 90.0 kg diver stands at the far end of the board, forces are generated by the pillars -2060N.
According to the second law of motion,
Fnet=ma a=0,
[tex]F_{1}+F_{2} -W_{P} =0\\F_{1}+F_{2} =W_{P}\\F_{1}+F_{2} = 90*9.8[/tex]
Angular force for net torque,
[tex]F_{1}*0+F_{2}*D -mgL = 0\\ F_{2}= \frac{mgL}{ F_{2}*1.5}= 90*9.8*5\\ F_{2}=\frac{90*9.8*5}{1.5} =2940N[/tex]
[tex]F_{1}+F_{2} -W_{P} =0\\F_{1} = 90*9.8-F_{2}\\F_{1} =2060N[/tex]
In physics, pressure is a force that may change how an object moves. An object having mass can be directed by a force to increase in speed (e.g., from a state of rest). Pressure may also be conceptualized as a push or a pull. A pressure is a vector quantity since it has both value and direction.
The net force exerted on an object is equal to the rate at which its momentum changes over time, according to Newton's second law in its original version. This rule states that, if the mass of the object is constant, the acceleration of an object will be directly proportional to the net pressure acting on the object.
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The vapor pressure of solid CO2 (dry ice) is 280 torr at -90. oC and 105 torr at -100. oC. a) What is the value of Go for the reaction CO2(s) CO2(g) at each temperature? b) Use the above values for the standard free energies to determine the standard enthalpies and entropies for the sublimation. Assume both quantities are constant over this temperature range. A dry ice bath is used routinely in the laboratory to keep things cold. It is made by mixing dry ice powder with a solvent to make a slurry. Estimate the temperature of the bath to the nearest degree Celcuis by determining the temperature at which the vapor pressure of CO2 is 1 atm.
a) The standard free energy (ΔG°) for the reaction CO2(s) CO2(g) at -90.0 oC is -28,853 J/mol, and at -100.0 oC is -32,142 J/mol
b) The temperature of a dry ice bath at which the vapor pressure of CO2 is 1 atm is estimated to be around -78 °C.
In part a) of the question, we were asked to determine the standard free energy (ΔG°) for the reaction CO2(s) CO2(g) at -90.0 oC and -100.0 oC.
To do this, we used the Clausius-Clapeyron equation, which relates the change in vapor pressure with temperature to the enthalpy and entropy of sublimation (ΔH° and ΔS°). By rearranging the equation, we were able to calculate the values of ΔH° at -90.0 oC and -100.0 oC to be -28,853 J/mol and -32,142 J/mol respectively.
We then used the same equation to calculate the ΔS° values, which are needed to calculate ΔG° = ΔH° - TΔS°
Now, from Clausius-Clapeyron equation, dP/dT = ΔH°/TΔS°
We can rearrange this equation to solve for ΔH° and ΔS°:
ΔH° = T(dP/dT)ΔS°
At -90.0 oC and 280 torr, ΔH° = -90.0 oC * (105 torr - 280 torr) / (105 torr) = -28,853 J/mol
At -100.0 oC and 105 torr, ΔH° = -100.0 oC * (105 torr - 280 torr) / (105 torr) = -32,142 J/mol
The ΔS° can be calculated using the same equation by substituting the ΔH° values.
In part b) of the question, we were asked to estimate the temperature of a dry ice bath at which the vapor pressure of CO2 is 1 atm. To do this, we used the Clausius-Clapeyron equation again, but this time we used the known value of 1 atm as the vapor pressure and solved for the temperature. P = P₀ * e^(-ΔHₒ/RT) where,
P₀ = 1 atm R = 8.314 J/mol-K, T is the temperature in Kelvin.Solving for T, we get T = ΔHₒ / R * ln(P₀/P)
The temperature to the nearest degree Celsius is about -78 °C.
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the support force on a 10-n book at rest on a table is
A 10N book resting on a table has a 10N support force acting on it. Gravitational force below and normal force upward are the forces at work on the book.
The gravitational force is directly opposed by the direction of this normal force. If there is no net force acting on the book, it remains in equilibrium. Since the book is at rest in the scenario above, the force exerted on it will also be 10 N. Here, the term "supporting force" refers to the normal reaction of the table to the block; in this case, it is equal to its weight. The book is being pulled down by gravity and being pushed back up by the table. These two forces (action-reaction) are equal and in opposition to one another.
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A sock stuck to the inside of the clothes dryer spins around the drum once every 2.0 s at a
distance of 0.50 m from the center of the drum. what is the sock's linear speed?
The sock's linear speed is 1.57 m/s.
What is linear speed?Linear speed is described as the measure of the concrete distance travelled by a moving object or the speed with which an object moves in the linear path is termed linear speed.
The sock spins once every 2.0 seconds, so its period is
T = 2.0 s
Therefore, the angular velocity of the sock is
angular velocity = 2π/ T
angular velocity = 3.14 rad/sec
The linear speed of the sock is given by
v = wr
where
w is the angular velocity
r = 0.50 m is the radius of the circular path of the sock
Substituting the values, we have that
v = wr = 3.14 x 0.50
v = 1.57 m/s.
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If you were caught in freezing weather with only your own body heat as a source, discuss whether you'd be warmer in an Arctic igloo or in a wooden shack.
Answer:
Arctic igloo
Explanation:
An igloo is made up of different components of snow and depending on the type, it will contain air which will help with insulation.
the horizontal motion of a plunger with a shaft is subject to the resistance of the attached disk which moves through the oil bath. if the velocity of the plunger is v0
The plunger's velocity at V0 is v(t) = vo - kx (t)
The direction of a body or object's motion is defined by its velocity. Speed is mainly a scalar quantity. Velocity is fundamentally a vector quantity. It is the pace at which distance changes. It is the displacement's rate of change.
a = -kv
dv/dt = -kv
dv/v = -k dt integrate, lnv(t) = -kt + lnC use v = vo when t = 0 C = vo v(t) = voe-kt
dx/dt equals voe-kt
dx = voe-kt dt integrate,
x(t) = (-vo/k)e-kt + C' usage C' = vo/k
since x(0) = 0 = -vo/k + C'.
x(t) = vo(1 - e-kt)/k
e-kt = 1 - kx(t)/v,
therefore v(t) = vo - kx (t).
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Jaime observes a bird sitting in a tree. Based on Newton's law of gravitation, how would Jaime BEST describe the force of gravity between the bird and Earth? A. The force of gravity acting on the bird is equal to the force acting on Earth. B. The force of gravity acting on Earth is greater than the force acting on the bird because Earth has more mass. C. The force of gravity acting on the bird is greater than the force acting on Earth because Earth has more mass. D. The force of gravity acting on the bird is greater than the force acting on Earth because the tree is supporting the bird.
Answer:
ofooffgggq
i am not
Explanation:
eeffffgggggg
what is the hotrod's final speed, in meters per second, assuming fr = 1000 n?
In an experiment in meters per second, if fr = 1000 then the hotrod's final speed will be 4.47m/s
The final speed of the hotrod, in meters per second, is determined by the formula
Vf = (Mr/fr)√(2gh).
Using the given fr of 1000 n, Mr mass of 15 kg, g of 9.8 m/s² and h height of 5 m,
The final speed of the hotrod can be calculated as
Vf = (15 kg/1000 n)√(2×9.8 m/s²×5 m)
= 4.47 m/s.
The speed of a sound wave depends on the medium it is travelling through.
Therefore, the final speed of the hotrod is 4.47 m/s when fr=1000n
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Please do in degrees. An 14kg block is pulled by a string up a 30* incline by a force of 112N where mu = .15 find the acceleration of the block
The acceleration of the block is 7.8 m/s².
What do you mean by acceleration?The rate at which an object's velocity with respect to time changes is referred to as acceleration. It is a vector quantity to accelerate (in that they have magnitude and direction).
To find the acceleration of the block, we can use the equation:
force = mass X acceleration + friction
Rearranging the equation, we can find the acceleration:
acceleration = (force - friction) / mass
The force of friction can be found using the equation:
friction = friction coefficient X normal force
The normal force is equal to the weight of the object, which can be found using the equation:
weight = mass X gravity
So, friction = friction coefficient X mass X gravity
We know that gravity is 9.8 m/s²
friction = .15 * 14 kg * 9.8 m/s²
Now we can substitute this value for friction and the known values for force and mass into the first equation and solve for acceleration:
acceleration = (112 N - 1.47 N) / 14 kg
acceleration = 7.8 m/s²
So, the acceleration of the block is 7.8 m/s².
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An HVAC engineer is trying to figure out where a system isn't functioning properly. She is looking at the
control sequence. Which is the last event to happen in this sequence?
A. When the room temperature drops below the setpoint, the room thermostat demands heat and closes a switch
to start the burner.
B. When the air temperature within the bonnet reaches the setpoint of the bonnet controller, the blower motor is
energized.
C. Heated air from the furnace is delivered through ductwork to occupied spaces within the building.
D. The generation of heat within the heat exchanger results in a rapid rise in air temperature within the bonnet. The
blower isn't operating yet.
The generation of heat within in the heat exchanger results in a rapid rise in air temperature with in the bonnet. The blower isn't operating yet. is the last event to happen in this sequence.
Who is HVAC engineer?
HVAC (Heating, Ventilation, and Air Conditioning) engineers are responsible for designing and maintaining the systems used to ensure comfortable temperatures and air quality in buildings. They must understand the principles of thermodynamics, fluid dynamics, and heat transfer. They must also be able to read and interpret blueprints, diagrams, and manufacturer specifications. Additionally, they must be knowledgeable of local, state, and federal building codes and regulations. HVAC engineers may also be responsible for overseeing the installation of HVAC systems, monitoring their performance, and troubleshooting any issues that arise.
Option D is the last event to happen because it describes the result of the earlier steps in the control sequence. After the heat is generated in the heat exchanger, the air temperature within the bonnet will rapidly rise and the blower motor won't be operating yet.
Therefore, Option D is the correct answer.
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(5%) Problem 4: Suppose there is an astronaut who is traveling at a significant fraction of the speed of light Randomized Variables d = 4.25 ly v = 0.80227 c Part (a) How long, in years, does it take the astronaut to travel 4.25 ly at 0.8022 7c (as measured by the Earth-bound observer)? sin0 cos0 tan0 cotan0 asin0 acos0 atan0 acotan0 sinh0
cosh0 tanh0 cotanh0
ODegrees ORadians Part (b) How long does it take according to the astronaut in years?
The time it takes for the astronaut to travel 4.25ly at 0.80227c is 5.3yr as measured by the Earth-bound observer and 3.31yrs according to the astronaut.
Given the distance the astronaut would travel (d)= 4.25ly x 1c
The speed at which astronaut is travelling (v) = 0.80227c
The speed of light (c) = 3 x 10^8m/s
(a) The time taken for the astronaut to travel the distance d =Δt
We know that t = distance / velocity = d/v
Hence t = 4.25ly/0.80227c = 4.25 x c/0.80227 x c = 5.29
The time it takes for the astronaut to travel 4.25ly at 0.80227c is 5.3yr
(b) The time as per the astronauts perspective is calculated as from the given equation: γ = 1/√1-(v/c)^2
then γ = 1/√1-(0.8c/c)^2 So, γ = 1/√0.36 = 1.6
The proper time is calculated as: Δγ = Δt/γ = 5.3yr/ 1.6
Δγ = 3.31yr
Thus the time taken by the astronaut to finish the whole journey is 3.3yrs.
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water, initially saturated vapor at 4 bar, fills a closed, rigid container. the water is heated until its pressure is 7bar. for the water, determine the heat transfer, in kj per kg of water. kinetic and potential energy effects can be ignored.
The water, determine the heat transfer, in KJ/Kg. Kinetic energy and potential energy effects can be ignored is 407.5kJ/kg.
From the properties of the saturated water pressure table;
At 4 bar and Saturated vapor
[tex]u_1 =[/tex] 2553.6 kj/kg
[tex]v_1 =[/tex]0.4625m³/kg
Since tank is rigid, volume remains constant therefore,
[tex]v_2 = v_1 =[/tex] 0.4625m³/kg
From the superhead water table
[tex]v_2 = v_1 =[/tex] 0.4625m³/kg And T_2 = 400°C
[tex]u_2 =[/tex]2961.1kJ/kg
Calculate the heat transfer for rigid tank
[tex]Q= u_2 -u_1[/tex]
= 2961.1 - 2553.6
= 407.5kJ/kg
Temperature is a bodily quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Temperature scales want values for definition: the factor chosen as 0 ranges and the magnitudes of the incremental unit of temperature.
Thermometers are calibrated in numerous temperature scales that traditionally have trusted numerous reference points and thermometric materials for definition. The maximum commonplace scales are the Celsius scale with the unit symbol °C (formerly called centigrade), the Fahrenheit scale (°F), and the Kelvin scale (ok), the latter being used predominantly for scientific purposes. The kelvin is one of the seven base units inside the global device of units (SI).
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Complete Question:
Water, initially saturated vapor at 4 bar, fills a closed, rigid container. The water is heated until its temperature is 400 degrees celsius. For the water, determine the heat transfer, in KJ/Kg. Kinetic energy and potential energy effects can be ignored.
The heat transmission from the water is measured in KJ/Kg. It is possible to ignore the effects of kinetic energy and potential energy at 407.5kJ/kg.
Temperature is a physical measure that quantifies how hot or cold something feels. A thermometer is used to determine temperature. The factor selected as 0 ranges and the magnitudes of the incremental unit of temperature are needed for the establishment of temperature scales.
Thermometers are calibrated using a variety of temperature scales, which historically relied on a wide range of reference points and thermometric materials to define them. The most widely used scales are the Kelvin scale (ok), which is mostly used in science, the Fahrenheit scale (°F), and the Celsius scale with the unit sign °C (formerly known as centigrade). One of the seven base units in the worldwide device of units is the kelvin (SI).
Based on the pressure table's characteristics for saturated water;
Saturated vapour at 4 bar
[tex]$$\begin{aligned}& u_1=2553.6 \mathrm{kj} / \mathrm{kg} \\& v_1=0.4625 \mathrm{~m}^3 / \mathrm{kg}\end{aligned}$$[/tex]
Tank's rigidity ensures that volume is constant; as a result,
[tex]$$v_2=v_1=0.4625 \mathrm{~m}^3 / \mathrm{kg}$$[/tex]
Super head water table, from
[tex]& v_2=v_1=0.4625 \mathrm{~m}^3 / \mathrm{kg} \\ { T_2 }=400^{\circ} \mathrm{C} \\& u_2=2961.1 \mathrm{~kJ} / \mathrm{kg}[/tex]
Calculate the rigid tank's heat transfer.
[tex]$$\begin{aligned}Q & =u_2-u_1 \\& =2961.1-2553.6 \\& =407.5 \mathrm{~kJ} / \mathrm{kg}\end{aligned}$$[/tex]
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Note: The complete question would be as bellow,
Water, initially saturated vapor at 4 bar, fills a closed, rigid container. The water is heated until its temperature is 400 degrees celsius. For the water, determine the heat transfer, in KJ/Kg. Kinetic energy and potential energy effects can be ignored.
Suppose we have a circuit with a 7.50-mH inductor in series with a resistor of 3.00 12. What is the current in amps 5.00 milliseconds after the switch is moved to disconnect the battery, if the initial current was 11 A? I = A
The current in amps 5.00 milliseconds after the switch is moved to disconnect the battery, if the initial current was 11 A found to be 1.488A.
What connection exists between the resistor current and the inductor current?Inductors oppose changes in current through them by dropping a voltage directly proportional to the rate of change of current, as opposed to resistors, which merely oppose the flow of current through them (by dropping a voltage directly proportional to the current).
I (t=5ms) = Io exp (- Rt/L)
=> 11 exp (- 3 x 5 / 7.5)
=> 1.488A.
What occurs when an inductor and resistor are connected in parallel?Similar to series circuits, when resistors and inductors are combined in parallel circuits, the overall impedance will have a phase angle between 0° and +90°. The phase angle of the circuit current will be between 0° and -90°.
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What do wind turbines, hydroelectric dams, and ethanol plants have in common?
The spring is often when hydroelectric power is at its highest, when precipitation and snowmelt increase water runoff.
What do hydroelectric and wind energy have in common?Seasonal patterns are observed in both hydroelectric and wind power generation. The spring, when precipitation and snowmelt boost water runoff, is usually when hydroelectric power is at its peak. Across the nation, there are different seasonal patterns for wind generation, but spring and fall often see the highest levels.
Windmills and wind turbines are two often used forms of wind power. Each of these is a type of kinetic energy, which is essentially everything that moves. Despite the fact that both are wind energy technologies, they have a number of significant variances, beginning with their anatomical structures.
Wind turbines of this kind are most frequently found. The majority of them feature two or three long, thin blades that resemble an airplane propeller. In order to face the wind directly, the blades are positioned in this manner.
Therefore, the correct answer is option B. All use generators to produce electrical current
The complete question is:
What do wind turbines, hydroelectric dams, and ethanol plants have in common?
A. All produce electrical current with pollution
B. All use generators to produce electrical current
C. All convert gravitational potential energy to electrical current
D. All convert thermal energy to electrical current
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Which of the following physical properties would you expect for krypton (Kr)? O shiny O hard O conducts electricity O brittle O a gas at room temperature
Correct option is D, Krypton is a gas at room temperature.
Chemical element krypton has the atomic number 36 and the symbol Kr. It is a rare noble gas that is tasteless, colorless, and odorless. It is used in fluorescent lighting frequently together with other rare gases. Krypton is chemically inert, with a few exceptional exceptions.
Other than fluorine gas, nothing else reacts with it. Commercially, krypton is used as the refueling gas for fluorescent lights. Some flash lights used in high-speed photography also make use of it. It has a higher degree of reactivity than the lighter gases in its family and can produce some chemical compounds.
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A sample of 60/27 Co and a sample of 131/53 I both have N0 atoms at t=0. How long will it take until both have the same activity? (Use Appendix F in the textbook for half-life data.)
63 0.708 days is the correct answer .
What is Radioactivity ?
Radioactivity, the property of certain types of matter that spontaneously emit energy and subatomic particles. It is essentially a property of individual atomic nuclei.
Unstable nuclei either decay spontaneously or decay into more stable configurations, but only in some specific ways that emit specific particles or specific forms of electromagnetic energy. Radioactive decay is a property of some naturally occurring elements and artificial isotopes of elements.
The rate at which a radioactive element decays is expressed by its half-life. That is, the time required for half a given amount of isotope to decay.
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Four students run up the stairs in the time shown Which student has the largest power output?
The four students have the same power output. As work done by four of them is same.
What is meant by power and 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. This is known as work in physics.
Work = Force × Distance is the formula for calculating work. The joule (J), sometimes known as the Newton meter (N m), is the SI unit for work. When an object is moved across a distance of 1 m with 1 N of force, one joule is equal to the amount of work that is accomplished.
Power in physics is referred to as the rate of work. In other terms, it calculates the rate at which energy is changed or transported.
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Complete Question -
What does it mean if electric field lines are close together versus farther apart?
A.The electric field is smaller.
B.The strength of the electric field is less.
C.The strength of the electric field is greater.
D.The electric field is larger.
What is the force on a 0.0050 C charge in an electric field of 300 V/m?
A.1.5 N
B.60,000 N
C.300.0050 N
D.1.7 × 10−5 N
What is the strength of an electric field in which a charged particle of 3.0 × 10−9 C is 0.05 m from the test charge?
A. 60 N/C
B. 1.1 × 104 N/C
C. 539 N/C
D. 3.6 × 103 N/C
If electric field lines are close together versus farther apart, the strength of the electric field is greater.
The force on a 0.0050 C charge in an electric field of 300 V/m is 1.5 N.
The strength of an electric field is 1.1 × 10⁴ N/C.
What is field line?A graphic tool for viewing vector fields is a field line. It is made up of a fictitious integral curve that is perpendicular to the field vector over its entire length.
The force on the charge in the electric field is = 300×0.0050 N = 1.5 N.
The strength of an electric field is = (9 ×10⁹×3.0×10⁻⁹)/(0.05)² N/C = 1.1 × 10⁴ N/C.
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Answer:
1. The strength of the electric field is greater.
2. 1.5 N
3. 1.1 × 104 N/C
(for honors ppl)
1. They represent non-contact electrical forces.
2. The strength of the electric field is greater.
3. 1.5 N
4. 1.1 × 104 N/C
5. approximately 1.45 V/m directed away from the positive charge
6. It increases.
a conservative force has the potential energy function u ( x ), shown by the graph above. a particle moving in one dimension under the influence of this force has kinetic energy 1.0 joule when it is at position x1. which of the following is a correct statement about the motion of the particle?
The following is the correct statement about the motion of particle : it cannot move / reach to either x0 or x2. And as this particle is having only one joule of kinetic energy it cannot overcome the required potential energy.
What is conservative force ?Conservative force is the force done in moving a particle from one point to another, such that force is independent of the path taken by particle. It depends on initial and final position of the particle. Gravitational and elastic spring forces are two examples of conservative forces.
Total work done by conservative force is independent of the path resulting in given displacement and is equal to zero when path is a closed loop.
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The particle will oscillate between -1J and -2J in potential energy and will never reach the points x0 and x2.
What is the energy of particle?If two objects collide, the total momentum before and after the collision will be the same if no external force acts on the colliding objects, according to the principle of conservation of momentum.
In x1, potential energy U(x1) = -2J
kinetic energy is V(x1) = 1 J
Total energy = U(x1) + V(x1) = -2J + 1 J = -1 J
Since the force is conserved then the total energy will also remain conserved.
That is, U(x1) = -1J - V(x1)
Since, kinetic energy ≥ 0
U(x1) ≤ -1J
Therefore from the graph we will be able to say that the particle will oscillate between range of potential energy that is -1J to -2J and also it will never reach the point x0 and x2 .
The graph is attached below:
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9. Determine the torque on a 0.35 m long wrench if a force of 960 N is applied at an angle of 70°.
Answer:
Torque = 651.2 N·m
Explanation:
Step 1: Calculate the Moment of Force (Torque)
The moment of force (torque) is calculated using the formula:
Torque = Force x Length x sin (Angle)
Step 2: Substitute the Values
Torque = 960 N x 0.35 m x sin (70°)
Step 3: Calculate the Torque
Torque = 651.2 N·m