The net force that acts on the cart of wagon is calculated as 3N.
What is net force?
The net force of a body can be calculated by multiplying the mass of the body by its acceleration. That is;
Force (N) = weight (N) × acceleration (m/s²)
According to this question, a weight of 20N accelerated across a level surface at 0.15 m/s². The net force can be calculated as follows:
F = 20 × 0.15
F = 3N
Therefore, the net force that acts on the cart of wagon is calculated as 3N.
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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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an mri technician moves his hand from a region of very low (almost negligible) magnetic field strength into an mri scanner’s 2.00 t field with his fingers pointing in the direction of the field. (a) find the average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field. (b) what current is induced in the ring if its resistance is 0.0100 ω? (c) what average power is dissipated?
The average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field is 3mV.
What is magnetic field?
The magnetic impact on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it while the charge is travelling through a magnetic field.
Given:
[tex]- $B=2 T$[/tex] is the magnetic field strength
[tex]- $d=2.2 \mathrm{~cm}=0.022 \mathrm{~m}$[/tex] is the ring diameter
[tex]- $t=0.25 \mathrm{~s}$[/tex] is the time needed to move the ring
(a) The electromotive force (emf) can be calculated using Faraday's law as:
[tex]$$\epsilon=-\frac{d \phi}{d t}$$[/tex]
We can expand the magnetic flux term here:
[tex]$$\epsilon=-\frac{d}{d t}[B A]$$[/tex]
The magnetic field here is constant so it is the area that is changing:
[tex]$$\epsilon=-B\left(\frac{d A}{d t}\right)$$[/tex]
Since we have no actual functions and just the initial area exposed to the magnetic field (zero) and the final area (entire ring area), we can re-write this as:
[tex]$$\epsilon=-B\left(\frac{0-\pi r^2}{t}\right)$$[/tex]
We substitute and recall that the radius is half the diameter:
[tex]$$\epsilon=-(2 T)\left(\frac{0-\pi\left(\frac{0.022 \mathrm{~m}}{2}\right)^2}{0.25 \mathrm{~s}}\right)$$[/tex]
We thus get:
[tex]$$\epsilon=0.003 \mathrm{~V} \approx 3 \mathrm{mV}$$[/tex]
(b) Wedding rings are usually made of metals like gold or silver, which means they are conducting. This means that the resistance of a wedding ring should be low. So here if we use Ohm's law:
[tex]$\epsilon=I R$[/tex]
We can assume that the current is also small here since the emf is fairly small and the resistance is expected to be small. With a small current, the temperature of the wedding ring shouldn't change much.
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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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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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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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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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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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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 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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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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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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Help me please!!
Label the 3 forms of heat transfer. Conduction,
convection, or radiation.
Answer:
a. radiation
b. convention
c. conduction
Explanation:
. 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 swimmer is floating on his back on the sea surface. if his density is 980 kg/m3 and he has a volume of 0.060 m3, what is the buoyant force that supports him in the sea water of density 1025 kg/m3?
The buoyant force that supports him in the sea water of density is 3931.613N.
On the water's surface, a swimmer is lying on his back. if his volume is 0.060 m, and his density is 980 kg/m³.
When an object floats, a force called buoyancy is responsible for this. It is specifically the external force that an object that is partially or completely submerged in water or any other fluid experiences. A body or object is said to be buoyant when it is placed in or submerged in a fluid.
We can also define buoyancy as the upward force applied by the fluid on a body or object in this way. The pressure on two sides of a body submerged in a static fluid causes the buoyancy phenomenon.
The Buoyant Force is measured in Newtons (N), which is also the unit of Force (F).
F=hpg
h=∛0.060
=0.3914m
F=0.3914 x 1025 x 9.8
F=3931.613N
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A force of 10. Newtons toward the right is exerted on a wooden crate initially moving to the right on a horizontal wooden floor. The crate weighs 25 newtons. Calculate the magnitude of the force of friction between the crate and the floor.
The magnitude of the force of friction between the crate and the floor is calculated to be 5 N.
What is force of friction?Force generated by two surfaces that contact and slide against each other is referred to as frictional force.
Given: A force of 10 N towards right is exerted on a wooden crate initially moving to the right on horizontal wooden floor and weight of crate is 25 N
The magnitude of the force of friction between the crate and the floor is given as ;
F= μ* m * g
= 0.2 * 25
= 5N
The magnitude of the force of friction between the crate and the floor is 5 N.
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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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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)
what is the maximum speed with which a 1200- kg car can round a turn of radius 87.0 m on a flat road if the coefficient of static friction between tires and road is 0.55?
The value of speed will be 21.67 m/s
It is given that,
Mass of the car = m=1200 kg
Radius of the round road = r=87.0 m,
Coefficient of static friction= 0.55
As we know,
The value of friction can be determined by using the relationship:
Friction = mCfg
Where, Cf = centripetal force, which can be calculated by relationship:
centripetal force = mv^2/r
As we know,
The point at which the speed is maximum
Then,
Ff = Fc
So, we can write it as:
[tex]mC_fg = \frac{mv^2}{r}\\v^2=\frac{rmC_fg}{m}\\v={\sqrt{C_fgr}[/tex]
So, the value of speed will be:
[tex]v = \sqrt{0.55 \times 9.81 \times 87)}\\v = 21.6658 \approx 21.67\: m/s[/tex]
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A moon orbits a planet in a nearly circular orbit of radius R, as shown in the figure.
Which of the following free-body diagrams could be used to analyze the forces exerted on the moon when it is at the position indicated in the figure?
The correct diagram is option F where GRAVITY arrow pointed to the right.
Explain how the moon orbits a planet ?A planet's gravitational influence on a moon is felt. The moon is dragged into a slightly extended shape because the near side of the moon experiences a stronger pull than the far side. We have ocean tides because the moon has a similar differential attraction on the Earth.
This specific instance of tidal locking was brought on by the gravitational pull of the Moon and Earth (called synchronous rotation).
The Earth takes 365 1/4 days, or one year, to complete one orbit of the Sun. The Moon revolves around the Earth as it revolves around the Sun. The orbit of the Moon lasts 27 1/2 days.
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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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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]
An object is thrown horizontally off a cliff with an initial velocity of 5. 0 m/s.
The vertical speed is 29.4 m/s.
What is vertical speed?
In aeronautics, the rate of climb is an aircraft's vertical speed, that is the positive or negative rate of altitude change with respect to time. In most ICAO member countries, even in otherwise metric countries, this is usually expressed in feet per minute; elsewhere, it is commonly expressed in meters per second.
The acceleration of gravity is 9.8 m/s². This simply means that when anything falls, its downward speed keeps increasing, and it falls 9.8 m/s faster every second than it fell 1 second earlier.
After 3 seconds of falling, the object is falling at (3 x 9.8 m/s) = 29.4 m/s faster than at the beginning of the 3 seconds. If it had no vertical speed at the beginning of the 3 seconds, then THAT's its speed after 3 seconds . . . . . 29.4 m/s downward.
As far as being thrown horizontally off the cliff . . . that has no effect on its vertical speed. Horizontally, it doesn't matter whether it rolls gently over the edge, or somebody throws it horizontally, or it gets shot horizontally out of a high power rifle. It hits the ground at the same time and at the same speed in every case.
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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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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 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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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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which component of an ideal vapor-compression refrigeration cycle is modeled as having internal reversibilities
The heat exchangers, evaporator and condenser, which are where the most irreversibilities are seen, are the most important parts of the VCR system.
Evaporator: What is it?The evaporator operates in opposition to the condenser; here, refrigerant liquid is transformed into gas while absorbing heat from compartment's air. The pressure of the liquid refrigerant has decreased by the time it reaches the evaporator, losing its heat content thus causing it to become significantly colder than the fan air circulating around it.
what are they Condenser and evaporator: what are they?Condenser coils discharge heat into outdoor air while evaporator coils absorb heat from indoor air. When heated refrigerant vapor cycles into the coil and condenses to liquid, it quickly releases the load of heat energy that has been collected from your home and compacted in it.
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An electromagnetic wave of wavelength 435nm is traveling in vacuum in the − z-direction. The electric field has amplitude 2. 70×10−3v/m and is parallel to the x-axis.
The frequency of wave generated is [tex]6.9 * 10^{14} Hz[/tex].
The electromagnetic wave travels at the speed of light.
Speed of light (c) = [tex]3 * 10^{8} m/s[/tex]
Given wavelength is 435nm = [tex]435 * 10^{-9} m[/tex]
We can find the frequency(f) of the wave by using the relationship between f and c:
Frequency = speed of light/ wavelength
= [tex]3 * 10^{8} / 435 * 10^{-9}[/tex]
= [tex]6.9 * 10^{14} Hz[/tex]
So the frequency of wave generated is [tex]6.9 * 10^{14} Hz[/tex].
Complete question:
An electromagnetic wave of wavelength 435nm is traveling in vacuum in the − z-direction. The electric field has amplitude 2. 70×10−3v/m and is parallel to the x-axis. Find frequency of wave generated.
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a 4.0-mm-diameter hole is below the surface of a 2.0-m-diameter tank of water. what is the rate, in mm/min, at which the water level will initially drop if the water is not replenished?
The rate that the water level would first decrease if it is not refilled is 1.06 mm/min.
Meaning of the water level:water volume (plural water levels) the height at which a water body is measured, particularly when done beyond a datum line. the height of the underground water table. the ship's waterline. a device that uses the water's surface on a trough or in vertical tubes connected by the a pipe to indicate level.
How exact is the level of the water?The accuracy of water levels is theoretically limited only by human vision. The length of the tube and the thickness of the liquid are two significant problems that can impair accuracy.
Briefing:h = height of the water level above the hole = 1 m
dh = diameter of hole = 4 mm = 0.004 m
Ah = Area of cross-section of hole = (0.25)\pi d^{2} (for hole)
dt = diameter of tank = 2 m
At = Area of cross-section of tank = (0.25)\pi d^{2} (for tank)
R = rate at which the water level drop
Rate at which the water level drop is given as
R=[Ah(\sqrt{2gh)]/At
R= [ (0.25)\pi d^{2}(\sqrt{2gh) ] /2^{2}
R=17.7*(10)^-6 m/s
R=0.0177mm/s
R=(0.0177)(60) mm/min.
R=1.06 mm/min.
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