90 J work must Denise do to drag her basket of laundry of mass 8.0 kg a distance of 6.0 m along a floor if the force she exerts is a constant 30.0 N at an angle of [tex]60^0[/tex] with the horizontal.
It is given that,
Mass of the basket = 8.0 Kg.
Distance from where it needs to be dragged = 6.0 m
Constant force = 30.0 N = F
Value of angle = [tex]\theta[/tex]= [tex]60^\circ[/tex]
As we know, the value of work done can be determined by using the formula:
[tex]w=\mathrm{Fscos}(\theta)[/tex]
So, putting the value of F, s and value of angle in above formula:
We will get, the value of work done as:
[tex]\mathrm{w}=30 \times 6 \times \cos (60) \\& =180 \times \frac{1}{2} \\& =90 \text { joule }[/tex]
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Why do astronomers suspect that a supernova explosion occurred near the nebula that gave birth to the solar system?.
Astronomers suspect that a supernova explosion occurred near the nebula that gave birth to the solar system because it generated telltale patterns of unstable, short-lived radioactive isotopes.
Did a supernova cause the solar system to form?Our solar system may have formed when a cataclysmic supernova explosion's shockwave collided with a gas cloud.Samples of early meteorites still contain traces of the material ejected from the ancient blast.The supernova explosion that gave birth to our sun may have also contributed to the rotation of our solar system, enabling the construction of the planets, including Earth, according to scientists researching this process.The shock wave from a supernova may have had enough energy to crush the dust cloud before it, according to earlier research. And investigators have looked for signs of that explosion: Radioactive isotopes that are unstable and short-lived form distinctive patterns after supernovae.The identification of these anomalies' telltale signs in prehistoric rocks would support the theory that a supernova sparked the formation of the solar system.What Is a Supernova?The largest explosion that humans have ever witnessed is a supernova. Each blast is the extremely bright, super-powerful explosion of a star.Can learn more about supernova from https://brainly.com/question/24811835
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the clock on the big ben tower in london reads 12 noon. if you travel away from the clock at a very high speed and view it with a telescope, you would see group of answer choices run faster than a clock in your vehicle. run slower than a clock in your vehicle. be frozen at 12 noon.
"The clock on the big ben tower in London reads 12 noon. If you travel away from the clock at a very high speed and view it with a telescope, you would see it run slower than a clock in your vehicle" (Option A) This phenomenon is known as Time Dilation.
What is time dilation?
Time dilation is defined in physics and relativity as the difference in elapsed time as measured by two clocks. It is either owing to a difference in relative velocity or a difference in gravitational potential between their places.
When left undefined, "time dilation" generally refers to the impact of velocity.
Time dilation is the "slowing down" of a clock as determined by an observer in relative motion with regard to that clock under the theory of special relativity.
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[NOTE: THIS IS AN INCOMPLETE QUESTIO. THE COMPLETE QUESTION IS:
Suppose you look at the huge clock on the Big Ben Tower in London and it reads 12 noon. If you could travel away from the clock at the speed of light and view it with a telescope, it would:
a) run slower than usual
b) run faster than usual
c) be frozen at 12 noon]
50 g of sugar is dissolved in 500 g of water. What is the percent by mass of salt?
HINT: find the total mass of the solution first.
The percentage by mass of the salt, given it was dissolved in 500 g of water is 9.09%
How do I determine the percentage of the salt?we'll begin by obtaining the mass of the solution. This is shown below:
Mass of salt = 50 gramsMass of water = 500 gramsMass of solution =?Mass of solution = Mass of salt + Mass of water
Mass of solution = 50 + 500
Mass of solution = 550 grams
Finally, we shall determine the percentage of the salt. Details below:
Mass of salt = 50 gramsMass of solution = 550 gramsPercentage of salt =?Percentage = (mass of solute / mass of solution) × 100
Percentage of salt = (50 / 550) × 100
Percentage of salt = 9.09%
Thus, the percentage of the salt is 9.09%
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. how does the energy of photons change as they travel from the core to the surface of the sun? explain the methods of energy transfer that occur and why they change as the photons travel from the core.
As the photons travel from the center to the surface, their energy decreases; they cool to a temperature of about 6000 K, which is similar to the sunlight we observe.
Conduction is quite ineffective in this situation, but convection does contribute—it begins at the outer core. The outer core provides energy to the inner convection cells, which then interact with the outer convection cells.
However, radiation is the main cause. It takes a photon a long time to reach the surface because after it emits, hits something, and is excited by that something, the photon is then released once more in an arbitrary direction.
What does radiation signify from a physics perspective?
Radiation is the name for energy that comes from a source and travels through space at the speed of light.
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a particle of charge q and mass m is moving with a velocity v along the x-axis in a magnetic field b which is along the z-axis. how much time will it take for the particle to return to its original location
The time required for the particle to return to its original location is (2πm/Bq) s.
We have to see the direction of magnetic force works on a particle. Using right-hand rule
Point your pointer finger according to the direction particle is moving. To the x-axis.Point your middle finger in the direction of the magnetic field. To the z-axisYour thumb points to the direction of the magnetic force pushing on the particle. To -y-axis.The magnetic force will deflect the direction of the particles so that the particles will move in a circle. The magnetic force becomes the centripetal force because it always points to the center of the circle.
Fc = Fm
[tex]m \frac{v^2}{R} \:=\: Bqv[/tex]
mv² = BqvR
mv = BqR
[tex]R \:=\: \frac{mv}{Bq}[/tex]
R = mv ÷ Bq
If the particle return to its original location, it means the particle travel one full circle. According to uniform motion
t = d ÷ v
t = perimeter of the circle ÷ v
t = 2πR ÷ v
t = (2πmv ÷ Bq) ÷ v
t = (2πm ÷ Bq) s
t = [tex]\frac{2 \pi m}{Bq}[/tex]
t = (2πm/Bq) s
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unpolarized sunlight with intensity 1000 w m2 is incident on two polarizers, whose transmission axes make an angle of 30◦ . calculate the intensity of the transmitted light from the second polarizer. select one of
The intensity of the transmitted light from the second polarizer is 375 W/m².
Let the two polarized sunlight be P₁ and P₂
Given,
Angle between P₁ and P₂ = 30⁰
Intensity of the unpolarized sunlight = 1000 W/m²
Now,
Angle between P₁ and P₂ = 90⁰ - 30⁰ = 60⁰
The intensity of light transmitted by P₁ is
I₁ = I₀/2 = 1000/2 = 500 W/m²
According to Malus law the intensity of light transmitted by P₂ is
I₂ = I₁ cos²30⁰ = 500[(√3)/2]² = 375 W/m²
Therefore, The intensity of the transmitted light from the second polarizer is 375 W/m².
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two of the three atoms in a molecule of water (h2o) are hydrogen. why are earth’s oceans not fusing hydrogen into helium, transforming our planet into a star?
The earth’s oceans is not fusing hydrogen into helium, transforming our planet into a star because Protons (hydrogen nuclei) carry positive electric charge and thus repel each other.
The earth as a planet?The third planet from the sun, Earth is the only place in the known universe confirmed to host life and has a radius of 3,959 miles, Earth is the fifth largest planet in our solar system, and it is the only one known for sure to have liquid water on its surface.
In order for two protons to come close enough to each other that the nuclear force that has short range can bind them, they must be moving at very high speeds.
This is only possible at temperatures in the solar core, but it is very hard to achieve these temperatures on Earth, thus the reason why fusion power has been so difficult to develop.
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you are watching an object that is moving in shm. when the object is displaced 0.600 m to the right of its equilibrium position, it has a velocity of 2.20m/s to the right and an acceleration of 8.40m/s2 to the left. for related problem-solving tips and strategies, you may want to view a video tutor solution of velocity, acceleration, and energy in shm.
The object can move as farther as 0.2m.
Using the Sine Equation,
= x(t) = Asin(ωt)
=Here, t=0, x=0,
Given that,
Distance = x(t) = 0.60 = A sin(ωt)
Velocity = v(t) = 2.20 m/s = Aωcos(ωt)
Acceleration = a(t) = 8.40 m/s² = -Aω²sin(ωt)
Using wave equation,
= x(t) / a(t) = A sin(ωt) / -Aω²sin(ωt)
= ω² = 14 rad²/s²
= ω = 3.74 rad/s
The amplitude of the motion =
= x(t) / v(t) = A sin(ωt) / Aωcos(ωt)
= A = 0.2 m
Therefore, the amplitude of the motion is 0.2 m
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if the objects are brought into thermal contact, is the temperature change of object 1 greater than, less than, or equal to the temperature change of object 2?
If the two objects are brought into thermal contact, object B gives up more heat and changes its temperature more than object A. The heat released by one object is absorbed by the other, and the temperature change of each is the same because the specific heats are the same.
What happens when objects at different temperatures come into contact ?When two objects with different temperatures come into contact with one another, energy moves from the hotter (higher temperature) object to the cooler (lower temperature) object until both objects reach the same temperature.
The thermal energy of the object increases as the average kinetic energy of its constituent particles rises. Therefore, as an object's temperature rises, so does its thermal energy.
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the interaction between two waves that meet is called a. reflection. b. refraction. c. diffraction. d. interference. please select the best answer from the choices provided a b c d
The interaction between two waves that meet is called interference.
Interference is a phenomenon of wave interactions. When two waves meet at a point, they cancel each other out.
There are two types of interference, constructive and destructive.When the crests or troughs of two interfering waves meet, their amplitudes add up. This principle is known as constructive interference. When the opposite happens and it's called destructive interference. When the crest and trough of two interfering waves meet, one amplitude is subtracted from the other.Wave interference is a phenomenon that occurs when two waves meet while traveling through the same medium.Interference of waves causes the medium to take on a shape that results from the net effect of two individual waves on the particles of the medium.Answer d. interference is the correct answer
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while looking at her image in a cosmetic mirror, dina motes that her face is highly magnified when she is close to the mirror, but as she backs away from the mirror, her image first becomes blurry, then disappears when she is about 30 cm from the mirror, and then inverts when she is beyond 30 cm. based on these observations, what can she conclude about the properties of the mirror?
R=60cm We determine that Dina's upright picture is produced as she steps back from the mirror, which is spherical with a concave f=30 cm. Thus, the mirror is spherical but concave and the image of the object is
What are some instances of concave?A form with an inward curvature is said to be concave. Concave shapes include those like the sideview window of a car, which curls inward. When a shape curves outward, it is said to be convex. One excellent example of a convex form is the outward-curving (American) football.
What form is concave?One that veers inward at a single point is said to have a concave shape. A polygon with a sharp inside angle or a curved form with an inwardly curving part can both fit the bill. When a line connects two points inside a shape and leaves the shape at an angle, the shape is said to be concave.
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in an electric motor, a commutator a. is made out of dozens of wire loops wrapped around a ferromagnetic core. b. repeatedly reverses the flow of current through the armature. c. is a magnet. d. is directly connected to the current source. please select the best answer from the choices provided a b c d
Commutators are used in DC machinery, such as universal motors and DC generators. A motor's windings get an electric current from a commutator. By reversing the direction of the current in the spinning windings every half turn, a constant rotational torque is generated.
According to this option b) is correct.
Describe a DC machine.
An electro-mechanical energy conversion system is known as a DC machine. There are two different kinds of DC machines: a DC motor and a DC generator. A DC motor transforms D.C. electrical power into mechanical power (ωT), whereas a DC generator converts mechanical power (T) into DC electrical power (EI).
What does a DC machine do?
An electrical device called a DC generator's principal job is to turn mechanical energy into electricity. Based on the electromagnetic induction theory of Faraday's Laws, an emf will be produced when the conductor cuts the magnetic flux.
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a ceiling fan at rest is turned on and reaches a speed of 12.5 rad/sec in 2.4 sec. how many revolutions does it rotate during this time?
5.20rad/sec revolutions does it rotate during this time.
What is average velocity?Average velocity is a sign of a vector. Average velocity is defined as the difference between a change in position or displacement (x) and the intervals of time (t) during which it occurs. The average velocity may be positive or negative depending on how the displacement is dispersed.
According to the equation v = s/t, velocity (v) is a vector quantity that measures displacement (or change in position, s), over change in time (t).
velocity = number of revolutions / time
12.5 rad/sec = number of revolutions/time
number of revolutions = 12.5/ 2.4
number of revolutions = 5.20rad/sec.
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the cosmic microwave background tells us a lot about our universe, including what shape it is, geometrically! what shape do we believe the universe is, and based on which property of the cmb?
We believe that the shape of the universe is geometrically flat based on critical density of the CMB.
New measurements of the cosmic microwave background by the Atacama Cosmology Telescope find that the universe is flat, with a density matching the critical density. There is no evidence of deviation from flatness. According to ACT scientists, the interpretation that the deviation seen by Planck is a statistical fluctuation.”
The CMB is useful to scientists because it helps us learn how the early universe was formed. It is at a uniform temperature with only small fluctuations visible with precise telescopes. By studying these fluctuations, cosmologists can learn about the origin of galaxies and large-scale structures of galaxies and they can measure the basic parameters of the Big Bang theory.
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An object of an unknown mass is attached to an ideal spring with force constant 120 N/m and is found to vibrate with a frequency of 6.00 Hz.
Find:
(a) the period
(b) the angular frequency
(c) the mass of this object.
An object of an unknown mass is attached to an ideal spring with force constant 120 N/m and is found to vibrate with a frequency of 6.00 Hz: =0.0845 kg.
(a) Time period, T = 1/f = 1/6.0 = 0.167 s
(b) Angular frequency, ω = 2πf = 6.28x6 =37.7 rad/s
(c) For the mass, use the formula. ω2 =k/m
So, mass, m =k/ ω2
= 120/37.68x37.68
=0.0845 kg.
In physics, a force is a power that may change the movement of an object. A force can purpose an object with mass to trade its velocity, i.e., to accelerate. pressure can also be defined intuitively as a push or a pull. A force has both significance and path, making it a vector amount.
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if the power delivered were 59.32 kw, evaluate the outer surface temperature, in k, and the rate of entropy production, in kw/k, for the gearbox as the system, keeping input power, h, and a from example 2.4 the same.
In the case of the gearbox as the system, the outer surface temperature is 297 K, and the rate of entropy formation is 2.3*10-3kW.A surface's temperature is its ambient temperature.
More specifically, it can be talking about: Surface temperature, the temperature of the air at the earth's Surface temperature. A state of disorder, randomness, or uncertainty are frequently associated with the scientific notion of entropy, which is also a quantifiable physical attribute. Since work is produced by ordered molecular motion, entropy also serves as a proxy for a system's molecular disorder or unpredictability.
Q = ha(Ta-Tb) (Ta-Tb)
Q = (0.171)((1.0)(347k) (347k)
Q = 2.3*10^-3kW
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certain stars, like betelgeuse, have a lower surface temperature than the sun and yet are more luminous. how do these stars produce so much more energy than the sun?
Some stars, like Betelgeuse, are more bright and produce a lot more energy than the Sun despite having a lower surface temperature. This is as a result of their expansion into massive stars. Because of their considerably larger size (each portion of the star's surface is cool, but there are so many bits that, collectively, the stars send out more energy), they generate more total energy.
The mass of a star is always drawn toward its core by gravity. There is a mechanism that can prevent a star from collapsing due to gravity, and there is a "balance" between them at different times in a star's life.
When a star is in equilibrium, the gamma rays produced by fusion in the center of the star fight against the inward gravitational collapse. In general, balances are reached when a "fuel" (element) hot enough to fuse is present in the core, as is the case during the main-sequence stage when hydrogen fusion takes place and during helium core fusion following the helium flash
Astronomers who desire to study the evolution of stars can benefit greatly from stellar clusters. It is plausible to believe that each star in a cluster emerged from the same cloud of gas and dust at roughly the same time. The only first distinction between the stars is hence their mass (and not their composition or the time that they began). Additionally, by monitoring where a cluster of stars' stars are now departing the main sequence, we can infer the age of the cluster because high-mass stars evolve considerably more swiftly than low-mass stars do.
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Three identical train cars, coupled together, are rolling east at speed . A fourth car traveling east at catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?
There are two collisions occurring in this question, finally after two collisions the now the five-car train is moving [tex]V_{0}[/tex] velocity, by the conservation of momentum principle.
What is Conservation of Momentum?
According to the Principle of Conservation of Momentum, when two objects meet, their total momentum is the same before and after the collision (provided that no external forces - for example, friction - act on the system). This is incredibly helpful since it means you can predict what will happen following a collision before it occurs.
What are the Calculations?
First collision (between three-car trains and a fourth car moving with 2[tex]V_{0}[/tex] in the same direction)
We will apply conservation of momentum to calculate the velocity of the train after the first collision
M1V1 + M2V2 = (M1 + M2)V 3M([tex]V_{0}[/tex]) + M2[tex]V_{o}[/tex] = (3 M + M)V .(5M)V. V (4M.V) V = [tex]\frac{5}{4} Vo[/tex]
Now the mass of the four-car train is 4M and is moving with a velocity of [tex]\frac{5}{4} Vo[/tex]
Second collision (between four-car trains and fifth car at rest)
Again we will apply conservation of momentum to calculate the velocity of the train after the second collision
M1V1 + M2V2 = (M1 + M2)V (4M × [tex]\frac{5}{4} V_{o}[/tex]) + (M × 0) = (4 M + M)V (5M)[tex]V_{o}[/tex] = (5M)V. V = [tex]V_{o}[/tex]
Finally, after two collisions the now the five-car train is moving [tex]V_{0}[/tex] velocity.
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The frequency which, under the sampling theorem, must be exceeded by the sampling frequency is called the Nyquist rate. Determine the Nyquist rate corresponding to each of the following signals:a) x(t) = 1 + cos(2,000πt) + sin(4,000πt)b) x(t)= sin(4000 π t) / π tc) x(t)= 2 [sin(4000 π t) / πt]2
Nyquist rate = 2*(maximum signal frequency)
Sampling rate must exceed Nyquist rate in order to be able to fully reconstruct the signal.
a) x(t) = 1 + cos (2000πt) + sin(4000πt)
Frequency for each term:-
Term 1 is DC -> w₁ = 0
Term 2 -> w₂ = 2000π
Term 3 -> w₃ = 4000π
Maximum signal frequency (wm) = 4000π
Another way of saying this is that X(jw) = 0 for |w| > 4000π
Acc to Sampling theorem ws > 2wm, ws>8000π
So, the Nyquist rate is 8000π
b) x(t) = sin(4000πt) / πt
Using Fourier Transport table, we have X(jw) = 1 for |w| < 4000π
.0 for |w| > 4000π
Therefore, maximum signal frequency (wm) = 4000π
Acc to the sampling theorem ws > 2wm, ws > 8000π
c) x(t) = {sin(4000πt) / πt}²
We can rewrite the above function as x(t) = x₁(t) x₁(t), where,
x₁(t) = sin(4000πt) / πt
Using the convolution property X(jw) = (1/2π)X₁(jw) * X₁(jw)
We know that convolving a signal with itself will double the maximum frequency therefore:
Therefore, maximum signal frequency (wm) = 8000π
Acc to the sampling theorem ws > 2wm, ws > 16000π
Therefore, the frequency to determine the Nyquist rate is 16000π.
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what happens to the gravitational force between two objects if the distance between them triples? (1 point)
Gravitational force between two objects if the distance between them triples reduces by 9.
What is gravitational force ?
The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation. The force constantly tries to pull different masses towards each rather than pushing them apart from each other we tend to refer to this force of attraction as gravity.
Gravitational force [tex]F[/tex] = [tex]G\frac{m_{1} m_{2} }{r^{2} }[/tex]
where m1 = mass of object 1
m2 = mass of object 2
G gravitational constant
r = distance between the two object
If the distance between the two object is triples i.e. r = 3r
Then Gravitational force [tex]F^{'} = \frac{F}{(3r)^{2} }[/tex] =
[tex]F^{'} = \frac{F}{9r}[/tex]
Thus gravitational force between the object will reduce by a factor of 9.
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What would be the final speed of a 40g car released from an initial height of 25cm?
What would be the final speed of a 600g car released from an initial height of 115cm?
Answer:
Below
Explanation:
Potential Energy of the cars is turned into Kinetic Energy (ignoring friction)
mgh = 1/2 mv^2 divide both sides by 'm'
gh = 1/2 v^2 solve for v
v = sqrt (2gh) Note that the mass of the cars is irrelevent
For the first car : 25 cm = .25 m
v = sqrt (2 * 9.81* .25) = 2.2 m/s
Similarly , for car 2 v = 4.8 m/s (115 cm = 1.15 m)
why did einstein introduce the cosmological constant into the equations of his general theory of relativity when describing the universe?
Because Einstein could neither see or accept the cosmos expanding or contracting, he added a component to his equations that prevented the universe from changing.
Why is there so much stuff in the cosmos?Even the existence of matter in the cosmos is unknown to us. The early cosmos should have created an equal amount of mass and positron, which would subsequently destroy one another, according to modern physics theories.
Do we already know the universe's secrets?Yet modern physicists will be the first to recognize they are not in possession of all the solutions. Dr. Daniel Whiteson, a physicist at the University of California and a co-author of the new book, claims that "there are fundamental facts about the world that we're ignorant of."
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Because Einstein could neither see or accept the cosmos expanding or contracting, he added a component to his equations that prevented the universe from changing.
Why is there so much stuff in the cosmos?Even the existence of matter in the cosmos is unknown to us. The early cosmos should have created an equal amount of mass and positron, which would subsequently destroy one another, according to modern physics theories.
Do we already know the universe's secrets?Yet modern physicists will be the first to recognize they are not in possession of all the solutions. Dr. Daniel Whiteson, a physicist at the University of California and a co-author of the new book, claims that "there are fundamental facts about the world that we're ignorant of."
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a 12 kg runaway grocery cart runs into a spring, attached to a wall, with spring constant 290 n/m and compresses it by 80 cm . part a what was the speed of the cart just before it hit the spring? neglect any friction.
The initial speed of the cart is 1.3m/s.
The velocity of an object is the rate of change of its position with respect to a given time interval.
Given
Mass m of the cart = 12kg
Spring constant =290 N/m.
The compressed length of the spring = 10 cm.
The initial kinetic energy of the cart is given below.
K.E. = 1/2 m v2
v = initial velocity of the cart.
When the cart hits the spring, it is compressed by the cart. When the cart stops, due to the maximum compression, the kinetic energy of the cart will be zero. Hence its kinetic energy will be converted into elastic potential energy of the spring. This is given as,
U = 1/2 kx²
k = spring constant
x = compressed length of the spring.
This elastic potential energy of the spring will be equal to the initial kinetic energy of the cart.
U = 1/2 * 290*(0.80)² = 0.64.
U = 64J.
Elastic potential energy of the spring will be equal to the initial kinetic energy of the cart.
64 = (1/2) * 80 * v²
128 = 80 * v²
v² = 128/ 80
v² = 1.6
v = 1.26 ≅ 1.3
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1. we assumed that no mechanical energy is transferred to thermal energy, but saw that at least a little mechanical energy is lost. Can this explain the difference between the spring constants you found in part 1 and part 2? Please explain ?2. The mass of the puck is difficult to measure because it sublimates and looses mass over time. Can this explain the difference between the spring constants you found in part 1 and part 2.
No mechanical energy is transferred to thermal energy, but saw that at least a little mechanical energy is lost as heat.
1. Due to the vertical oscillation of the pluck connected with the spring, the spring is getting compressed and elongated. There are inter atomic bonds of the material with which the spring is made of. When the spring is getting compressed or elongated atoms connected with inter atomic bonds also gets compressed for elongated. This causes some of the bonds to break.
We know each bond is having some internal energy stored in it. So when the bond breaks that internal energy is emits in the form of thermal energy. Hence we see that some of the energy of oscillation is getting used in breaking the bond. This mechanical energy is getting lost. So with each period of oscillation the energy associated with the oscillating spring mass system decays with time.
Hence the amplitude of oscillation also decrease with time. Since by applying a certain amount of force to the pluck we are getting little small displacement compared to the actual displacement hence the corresponding spring constant will also be different compared to the actual one.
2. We know the spring constant is here define as the the ratio of applied force with the displacement of the mass. Here the force is the resultant of the weight of the mass and the the buoyancy force on the mass by the liquid. But when we sublimate the mass inside the liquid it loses mass with time. Hence the force on the spring also decays with time. Hence the the displacement of the mass also decays with time. Which implies the spring constant also changes.
Thermal power refers back to the energy contained inside a device this is liable for its temperature. warmness is the go with the flow of thermal electricity. an entire branch of physics, thermodynamics, offers with how heat is transferred among specific systems and how paintings is accomplished within the method (see the 1ˢᵗ law of thermodynamics).
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a majorette in a parade is performing some acrobatic twirlings of her baton. assume that the baton is a uniform rod of mass 0.120 kgkg and length 80.0 cmcm . figure1 of 1 part a initially, the baton is spinning about an axis through its center at angular velocity 3.00 rad/srad/s . (figure 1)what is the magnitude of its angular momentum about a point where the axis of rotation intersects the center of the baton? express your answer in kilogram meters squared per second.
The magnitude of its angular momentum about a point where the axis of rotation intersects the center of the baton is 1.92*10^-2 kg*m^2/s and angular momentum of rod 7.68*10^-2 kg*m^2/s.
The axis of rotation intersects the center of the baton is 1.92*10^-2 kg*m^2/s
A)
Moment of inertia of rod = 1/12*m*L^2
= 1/12*0.12*0.8^2 = 0.0064
Angular momentum = I*ω
= 0.0064*3
= 0.0192 = 1.92*10^-2 kg*m^2/s
B)
Moment of inertia of rod = 1/3*m*L^2
= 1/3*0.12*0.8^2 = 0.0256
Angular momentum = 0.0256*3 =
00768 = 7.68*10^-2 kg*m^2/s
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if the distance between two charges is doubled, what will happen to the force between the charges? (4 points)
The force between them is reduced to 1/4 when the distance between the two charges is doubled. The force between them is inversely proportional to the distance.
What is coulomb's law?
Charged bodies experience a force of attraction or repulsion on approach.
From Coulomb's Law, it is possible to predict what the electrostatic force of attraction or repulsion between two particles will be according to their electric charge and the distance between them.
From Coulomb's Law, the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them:
[tex]F=k\frac{Qq}{d^{2}}[/tex]
where:
F is the electrical force of attraction or repulsion. It is measured in Newtons (N).
Q and q are the values of the two-point charges. They are measured in Coulombs (C).
d is the value of the distance that separates them. It is measured in meters (m).
K is a constant of proportionality called Coulomb's law constant. It depends on the medium in which the charges are located.
Thus, force is reduced to 1/4.
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two people hear a tornado siren, but one listener is 71.1 times farther away from the source of the sound than the other. what is the intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener? relative intensity:
-37.03 dB is the intensity level of the sound for the more distant listener relative to that for the nearer listener.
What is intensity level?
The intensity level of a sound, in decibels, is described as 10 times the logarithm to the base 10 of the ratio of the intensity of this sound to a reference intensity.
By using the inverse square law,
As one listener is 71.1 times farther away from the source of the sound than the other.
Then Increasing the distance by 71.1 times reduces the intensity by
(71.1)^2 = 5055.21
The intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is:
= 10log(ratio of intensities)
= 10log(1/5055.21)
= 10log(0.00019782)
=10 × -3.7028
= -37.03 dB (The negative sign represents the sound is less intense for the farther listener)
So, the intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is -37.03 dB.
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assuming that the wave’s frequency ω remains constant, create a plot of the wavelength λ as a function of the current speed u. as u increases, what do you expect to happen to i) the wave’s length? ii) the wave’s amplitude? iii) the wave’s steepness? (5p)
A wave is a propagating dynamic disturbance of one or more quantities. Waves can be periodic, in which these quantities repeatedly oscillate around their equilibrium values at specific frequencies.
Whether vibrations or waves, they can all be characterized by four characteristics: Amplitude, Wavelength, Frequency, Velocity.
u = ωλ
Where, u = velocity of the wave
ω = frequency of wave
λ = wavelength of wave
For the first case:
If the wave’s frequency ω remains constant, then the velocity of wave will be proportional to wavelength:
u ∝ λ
So, if the velocity increases then there will be an increase in wavelength.
For the second case:
The amplitude of the wave is completely independent of the speed of propagation u and depends only on the amount of energy in the wave.
So, there will be no change of amplitude.
For the third case:
Wave steepness is the ratio of wave height(H) to wave length(λ).
Wave steepness = H/λ
This indicates that wave steepness is inversely proportional to wavelength.
Wave steepness ∝ 1/λ
But we know,
u ∝ λ
Then,
Wave steepness ∝ 1/λ ∝ 1/u
So, according to above application wave steepness in inversely proportional to velocity. This means that steepness will decrease with increasing velocity.
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a child on a swing set swings back and forth with a period of 3.3 s and an amplitude of 25°. what is the maximum speed of the child as she swings?
A child on a swing set swings back and forth with a period of 3.3 s and an amplitude of 25° the maximum speed of the child as she swings is approximately 0.829 m/s.
To find the maximum speed of the child as she swings, we can use the formula for the velocity of an object in simple harmonic motion:
v = Aωcos(ωt)
where A is the amplitude of the motion, ω is the angular frequency (ω = 2π/T, where T is the period of the motion), and t is the time.
Given:
- T = 3.3 s (period of the motion)
- A = 25° (amplitude of the motion)
To use the formula, we need to convert the amplitude from degrees to radians:
- A = 25° * (π/180)
= 0.4363 radians
Now we can calculate the angular frequency:
- ω = 2π/T
= 2π/3.3
= 1.90 rad/s
At the maximum displacement (when the child is at the bottom of the swing), the velocity is at its maximum.
At this point, cos(ωt) = 1, so we can simplify the formula to:
v = Aω
Substituting the values, we get:
- v = 0.4363 radians * 1.90 rad/s = 0.829 m/s
Thus, the maximum speed of the child as she swings is approximately 0.829 m/s.
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the plates of a parallel plate capacitor are separated by 0.1mm of bakelite dielectric. if the bakelite has a dielectric constant of 4.9 and the plates have an area of 0.0049 m2 , what is the capacitance in nf?
if the plates of a parallel plate capacitor are separated by 0.1mm of bakelite dielectric, and the bakelite has a dielectric constant of 4.9 and the plates area 0.0049m^2, the capacitance is 2.126nF
What is capacitance?
It is the ability of a component or circuit to collect and store energy in the form of an electrical charge. Capacitors are energy-storing devices available in many sizes and shapes.
How to calculate the capacitance in nF?The formula of capacitance of the capacitors is with dielectric constant as follows :
C = Kε₀A / D
where
C = Capacitance
k = dielectric constant
ε₀ = permittivity free space
d = distance between the plate
A = area between the plate
we are using this formula because it said parallel plate capacitor.
from the question given as follows :
k = 4.9 (dielectric constant)
d = 0.1mm = 1 * 10^-8 m^2
A = 0.0049m^2
ε₀ = 8.854 * 10^-12 F/m (from literature, permittivity of the free space)
C = 4.9 * 8.854*10^-12 * 0.0049 / 1 * 10^-8
C = 0.000021258454
C = 2,125.845 * 10^-12 F
C = 2.125845 * 10^-9 F
C = 2.126nF (rounded)
Therefore, the capacitance is 2.126nF for the plates.
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