If a person goes to the bottom of a very deep mine shaft on a planet of uniform density, then the person's weight is exactly the same as at the surface. Option(A) is true.
The force of gravity is directly proportional to the mass of the planet and inversely proportional to the square of the distance between the person and the center of the planet.
Gravity is a fundamental force that governs the motion of objects in the universe. It is an attractive force between any two objects with mass or energy, and its strength depends on the mass and distance between the objects.
Since the planet has uniform density, the mass beneath the person cancels out, resulting in no change in weight.
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a person in a rocking chair completes 17 cycles in 18 s . What are the periodand frequency of the rocking?
The period of the rocking chair is approximately 1.06 seconds per cycle, and the frequency is approximately 0.94 cycles per second (Hz).
The period is the time it takes to complete one cycle. To find the period, divide the total time by the number of cycles:
Period = Total time / Number of cycles
Period = 18 seconds / 17 cycles
Period ≈ 1.06 seconds per cycle
The frequency is the number of cycles completed in one second. To find the frequency, divide the number of cycles by the total time:
Frequency = Number of cycles / Total time
Frequency = 17 cycles / 18 seconds
Frequency ≈ 0.94 cycles per second (or Hertz, Hz)
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The period of rocking is 1.06 s and frequency of the rocking is 0.94 Hz (cycles per second).
The period (T) of a periodic motion is the time it takes for one complete cycle of the motion. i.e.,
T = (Total time taken) / (Number of cycles)
The frequency (f) of the motion is the number of cycles per unit time or in one second. i.e.,
f = (Number of cycles) / (Total time taken)
Frequency is also considered to be reciprocal of the period.
∴ [tex]f=\frac{1}{T}[/tex]
Now, given
No. of cycles completed = 17
Time taken for 17 cycles = 18 second.
Therefore,
Period, T = (total time) / (number of cycles)
= 18 s / 17
≈ 1.06 s
And,
Frequency, f = (number of cycles) / (total time)
= 17 / 18 s
≈ 0.94 Hz
Or, frequency can also be obtained as,
[tex]f=\frac{1}{T}[/tex]
= 1/1.06
≈ 0.94 Hz.
Therefore, the period of rocking is 1.06 s and frequency of the rocking is 0.94 Hz (cycles per second).
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A square-wave inverter supplies an RL series load with R=25 ohms and L=25mH. The output frequency is 120 Hz. (a) Specify the dc source voltage such that the load current at the fundamental frequency is 2.0 A rms. (b) Determine the THD of the load current (until 9), show all your work. + Vdc
(a) The dc source voltage is 61.2 V.
(b) The THD of the load current is approximately 33.2%.
(a) To calculate the dc source voltage required to produce a load current of 2.0 A rms, we first need to calculate the impedance of the load at the fundamental frequency. The impedance can be calculated as Z = R + jωL, where R is the resistance of the load, L is the inductance of the load, and ω is the angular frequency.
ω = 2πf
ω = 2π x 120 Hz
ω = 753.98 rad/s
Z = 25 + j(753.98 x 0.025)
Z = 25 + j18.85 Ω
The rms value of the load current is given by I = V/Z, where V is the rms value of the voltage supplied by the inverter.
I = 2.0 A rms, Z = 25 + j18.85 Ω
Therefore, V = IZ
V = (2.0 A rms) x (25 + j18.85 Ω)
V = 61.2 + j45.35 V rms
The dc source voltage is the average value of the voltage waveform, which is equal to the rms value multiplied by π/2.
Vdc = (π/2) x 61.2 V rms ≈ 96.2 Vdc
(b) The total harmonic distortion (THD) of the load current is a measure of the distortion of the current waveform from a perfect sinusoid. It is defined as the square root of the sum of the squares of the harmonic components of the current waveform, divided by the rms value of the fundamental component.
THD = √[(I2² + I3² + ... + In²)/I1²] x 100%
where I1 is the rms value of the fundamental component, and I2, I3, ..., In are the rms values of the second, third, ..., nth harmonic components.
For a square-wave inverter, the load current waveform contains only odd harmonic components. The rms value of the nth harmonic component can be calculated as
In = (4Vdc/(nπZ)) x sin(nπ/2)
where n is the harmonic number.
Using this equation, we can calculate the rms values of the first three harmonic components of the load current.
I1 = 2.0 A rms (given)
I3 = (4 x 96.2 Vdc / (3π x 25 Ω)) x sin(3π/2)
I3 ≈ 0.632 A rms
I5 = (4 x 96.2 Vdc / (5π x 25 Ω)) x sin(5π/2)
I5 ≈ 0.254 A rms
The THD can now be calculated as
THD = √[(0.632² + 0.254²)/2.0²] x 100%
THD ≈ 33.2%
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david bowie changed his original name to avoid confusion with which famous dave?
David Bowie changed his original name (David Robert Jones) to avoid confusion with Davy Jones, a member of the popular band The Monkees.
Bowie didn't want to be associated with Davy Jones and sought a distinct identity for his own career in music. Davy Jones was a British singer and actor who gained fame as a member of The Monkees in the 1960s. As David Robert Jones began his own musical journey, he decided to adopt the stage name "David Bowie" to prevent any potential confusion between the two artists. Bowie's new name not only provided him with a unique identity but also allowed him to craft a distinct image and persona that would define his groundbreaking and influential career in music and art.
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A charge q1 = 2 µc is at the origin, and a charge q2 = 10 µc is on the x axis at x = 10 m. find the force on charge q2 . the colulomb constant is 8.98755 × 109 n · m 2 /c 2 . answer in units of n.
The force on charge q2 is approximately 179.751 N.
The force between two point charges can be found using Coulomb's law:
F = (k * q1 * q2) / r^2
Where F is the force between the charges, k is the Coulomb constant (8.98755 × 10^9 N·m^2/C^2), q1 and q2 are the magnitudes of the charges in Coulombs, and r is the distance between the charges in meters.
In this case, q1 = 2 µC and q2 = 10 µC. The distance between the charges is the distance between the origin and the point on the x-axis where q2 is located, which is 10 m.
So, we can calculate the force on q2 as follows:
F = (8.98755 × 10^9 N·m^2/C^2) * (2 µC) * (10 µC) / (10 m)^2
F = (8.98755 × 10^9 * 2 * 10) / 100
F = 1.79751 × 10^9 / 100
F = 1.79751 × 10^7 N
The force on charge q2, we can use Coulomb's Law. Coulomb's Law states that the force (F) between two point charges is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance (r) between them:
F = k * (q1 * q2) / r^2
In this case, q1 = 2 µC, q2 = 10 µC, r = 10 m, and the Coulomb constant (k) is 8.98755 × 10^9 N·m^2/C^2.
The charges to Coulombs: q1 = 2 × 10^-6 C and q2 = 10 × 10^-6 C.
F = (8.98755 × 10^9 N·m^2/C^2) * ((2 × 10^-6 C) * (10 × 10^-6 C)) / (10 m)^2
F = (8.98755 × 10^9 N·m^2/C^2) * (2 × 10^-5 C^2) / (100 m^2)
F = 179.751 N
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consider the following steady, two dimensional velocity field: v = (u, v) = (0.5 1.2 x)i (-2.0 -1.2 y)j is there a stagnation point in this flow field? if so where is it?
Yes, there is a stagnation point in this flow field. The stagnation point is the point where the velocity of the fluid is zero. To find the stagnation point, we need to solve for when u = 0 and v = 0. From the velocity field given, we have:
u = 0.5x
v = -2y - 1.2x
Setting u = 0, we get:
0.5x = 0
Solving for x, we get:
x = 0
Setting v = 0, we get:
-2y - 1.2x = 0
Substituting x = 0, we get:
-2y = 0
Solving for y, we get:
y = 0
Therefore, the stagnation point is at (0,0).
To determine if there is a stagnation point in the given two-dimensional velocity field, v = (u, v) = (0.5 + 1.2x)i + (-2.0 - 1.2y)j, follow these steps:
1. A stagnation point occurs when both the u and v components of the velocity field are zero. So, we need to solve the following system of equations:
0.5 + 1.2x = 0
-2.0 - 1.2y = 0
2. To find the x-coordinate of the stagnation point, rearrange the first equation and solve for x:
3. To find the y-coordinate of the stagnation point, rearrange the second equation and solve for y
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You put a 51.7 gram mass on a spring, set it in motion with a small amplitude, and count 21 cycles. Those 21 cycles took 3.42 seconds What is kHM Answer
The spring constant for a mass of 51.7 grams on a spring that undergoes 21 cycles with a small amplitude in 3.42 seconds is 76.8 N/m.
The value of k for a mass on a spring can be determined using the formula T=2π√(m/k), where T is the period of oscillation, m is the mass, and k is the spring constant. In this problem, we know that the mass is 51.7 grams and that 21 cycles took 3.42 seconds, which means that the period of oscillation is T=3.42/21=0.163 seconds. Since the amplitude is small, we can assume that the motion is simple harmonic, which means that T=2π√(m/k) can be used. Rearranging this formula gives k=m(2π/T)^2, which gives k=51.7(2π/0.163)^2=76.8 N/m.
This value was calculated using the formula k=m(2π/T)^2, where m is the mass and T is the period of oscillation.
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The mass of a density bottle is 20g when empty, 70g when full of water and 55g when full of a second liquid. Calculate the density of the liquid
The density of the liquid is 0.5 g/cm³. to calculate the density, we use the formula: density = mass/volume.
The mass of the liquid can be found by subtracting the mass of the empty density bottle from the mass of the bottle filled with liquid.
For water: mass of liquid = 70g - 20g = 50g.
For the second liquid: mass of liquid = 55g - 20g = 35g.
Since the volume of the density bottle remains the same for both liquids, the density can be calculated as mass of liquid/volume of the bottle.
For water: density = 50g/100cm³ = 0.5 g/cm³.
For the second liquid: density = 35g/100cm³ = 0.35 g/cm³.
Therefore, the density of the liquid is 0.5 g/cm³.
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Consider the de Broglie wavelength of an electron What is the de Broglie wavelength of an electron traveling at a speed of 5.0×106 m/s? Give your answer in pm ト Grade Summary Deductions Potential pm 0% 100% Submissions tan() | π | ( 789 cosO cotanO asin0 acos0 atan acotan0 sinh coshO tanh0 cotanh0 °Degrees -Radians sin Attempts remaining: 999 % per attempt) detailed view 0 END vo DELCLEAR Submit I give up! Hints: for a .0%-deduction. Hints remaining: 0 Feedback: 5%-deduction per feedback.
The de Broglie wavelength of an electron traveling at a speed of 5.0 x 10^6 m/s is approximately 0.145 picometers (pm).
What is the equation for calculating the de Broglie wavelength of an electron, and what is the de Broglie wavelength of an electron traveling at a speed of 5.0 x 10^6 m/s?The de Broglie wavelength of an electron is given by the equation:
λ = h/mv
Where λ is the de Broglie wavelength, h is Planck's constant, m is the mass of the electron, and v is the velocity of the electron.
Substituting the given values, we get:
λ = h/(mv) = (6.626 x 10^-34 J s)/(9.11 x 10^-31 kg x 5.0 x 10^6 m/s)
λ = 0.145 pm (rounded to three significant figures)
Therefore, the de Broglie wavelength of an electron traveling at a speed of 5.0 x 10^6 m/s is approximately 0.145 picometers (pm).
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The waters off the coast of Iceland are filled with pods of killer whales, which migrate there during the summer. Wildlife parks that rely on the killer whales for entertainment hunt the killer whale almost exclusively in the water of Iceland, because strict sanctions forbid them from doing so off the coast of North America, an area also abundant in killer whales. Since Iceland recently gave in to pressure from international groups opposed to the hunting of killer whales, it too will forbid the hunting of killer whales off its coast. Therefore, all wildlife parks will be forced to end their shows featuring killer whales once their current killer whales are unable to perform. " All of the following cast doubt on the conclusion of the argument EXCEPT?
The fact that Iceland recently gave in to pressure from international groups opposed to the hunting of killer whales and will forbid the hunting of killer whales off its coast does not cast doubt on the conclusion of the argument.
It actually supports the conclusion that all wildlife parks will be forced to end their shows featuring killer whales once their current killer whales are unable to perform.
The argument states that wildlife parks rely on hunting killer whales exclusively in the waters of Iceland because they are forbidden to do so off the coast of North America. If Iceland also forbids hunting, the parks will no longer have a source of killer whales, which will ultimately lead to the end of their shows. The conclusion is directly supported by the premise, and there is noccontradictory information provided that would cast doubt on this logical chain of reasoning.
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The dc source supplying an inverter with a bipolar PWM output is 96 V. The load is an RL
series combination with R =32 ohms and L = 24 mH. The output has a fundamental frequency of 60 Hz.
a) Specify the amplitude modulation ratio to provide a 54-V rms fundamental frequency output.
b) If the frequency modulation ratio is 17, determine the total harmonic distortion of the load current.
c) What is the real power absorbed by the load?
a) The amplitude modulation ratio is 0.5625.
b) The total harmonic distortion of the load current is 40.53%.
c) The real power absorbed by the load is 405.36 W.
a) The amplitude modulation ratio (m) can be calculated using the equation m = Erms/Emax, where Erms is the desired rms voltage and Emax is the maximum voltage. Here, Erms is given as 54 V and Emax can be calculated as Emax = √(2) × 96 V = 135.76 V. Substituting these values, we get m = 0.5625.
b) The frequency modulation ratio (f) is given as 17. The total harmonic distortion (THD) can be calculated using the equation THD = √((Vthd² - V1²)/V1²) * 100%, where Vthd is the total harmonic voltage and V1 is the fundamental voltage. Here, V1 is given as 54 V. The total harmonic voltage can be calculated as Vthd = sqrt(sum of squares of all harmonic voltages) = sqrt((V3² + V5² + V7² + ...)/2), where V3, V5, V7, etc., are the harmonic voltages. Substituting the given values, we get Vthd = 43.72 V. Substituting these values, we get THD = 40.53%.
c) The real power absorbed by the load can be calculated using the equation P = V1²/R, where V1 is the fundamental voltage and R is the resistance of the load. Substituting the given values, we get P = 405.36 W.
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Oblem 26. 53 - Enhanced - with Feedback
You have a semicircular disk of glass with an index of
ofraction of n = 156 (Figure 1) You may want to review
Pages 929 - 936)
Part A
Find the incident angle o for which the beam of light in the figure will hit the indicated point on the screen
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The incident angle θ for which the beam of light in the figure will hit the indicated point on the screen is 60 degrees.
In this question, we need to find the incident angle for which the beam of light in the figure will hit the indicated point on the screen. We have a semicircular disk of glass with an index of fraction of n = 156 (Figure 1). We are given that the refractive index of the glass is n = 1.56. Using Snell's law,n1sinθ1=n2sinθ2where, n1= refractive index of the incident medium, n2= refractive index of the refracted medium, θ1= angle of incidence, θ2= angle of refraction. As air is the incident medium, the refractive index of air is 1.n1 = 1 and n2 = 1.56 sin(θ1) = 1.56sin(θ2)
As the angle of incidence (i) and the angle of reflection (r) are equal,i = rso, the angle between the incident ray and the normal, θ1 = 60°
Thus, sin(60) = 1.56sin(θ2)sin(θ2) = 0.63θ2 = 40.94°
As the light is refracted away from the normal, the angle of incidence is greater than the angle of refraction.
Hence, the incident angle of the beam of light is 60°.
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