The speed of the travelling wave is found to be 20m/s.
The relationship between the frequency of the wave, the wavelength of the wave and the speed of the wave is given by
V = fy
Where,
V is the speed of the travelling wave,
F is the frequency of the travelling wave,
y is the wavelength of the travelling wave.
The frequency of the travelling wave is given to be 10Hz and the wavelength of the travelling wave is 2m.
Now, putting all the values,
V = 10(2)
V = 20m/s
So, the speed of the travelling wave is 20m/s.
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What is the image of a dilation?
Image of dilation is a type of transformation that changes the size of a shape or geometric figure, but keeps the relative proportions and shape the same.
Morphology is known as a broad range of image processing operations that process images based on their shape. It is also known as a tool used to extract image components that help represent and explain the shape of a region.The basic morphological operations are: H. Used to extend element A with structuring element B.Dilation adds pixels to the bounds of the object.Output pixel value is the maximum value of all pixels in the neighborhood. A pixel is set to 1 if any adjacent pixel has a value of 1. The grayscale structuring elements are also functions of the same form, so-called structure functions.To learn about Morphology -
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How do you calculate potential energy stored?
Potential energy stored in spring is calculated by multiplying force with displacement.
Elastic potential energy is considered as the potential energy stored in spring when it is stretched or deformed. It is calculated as force multiplied by displacement. This energy is the energy stored in the spring by virtue of its position. It is the work done to stretch the spring.
When spring is stretched, it is displaced. It comes to its equilibrium position after the removal of the force. So, it exerts an equal and opposite force When it is stretched. Work is done by this force that is stored in the form of potential energy.
Since potential energy = force × displacement
and, force = spring constant × displacement
So, potential energy = spring constant × [tex](displacement)^{2}[/tex]
P.E. = k ×[tex]x^{2}[/tex]
Where,
k = spring constant
x = displacement caused due to stretching
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which color stars have the highest surface temperature? group of answer choices blue red orange yellow
The majority of the energy emitted by stars with temperatures above 30,000 K is in the form of short wavelengths, which is why they appear blue. That is revealed by the blue.
Given that blue light has a higher frequency than red, it denotes a greater level of energy. As stars are dynamic beings that can have a variety of photospheric energies depending on their mass and stage of life, there are undoubtedly some limitations to this. The basic rule, in my opinion, is that blue light has a larger energy level (is hotter) than red light. The red giant Betelgeuse has a lower surface temperature but a higher core temperature than the Sun because the heat produced by fusion in the core is distributed across a larger area. Because the temperature in the center depends more on mass, over a much larger surface.
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a merry-go-round has a mass of 1440kg and a radius of 7.50m. how much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 7.00s? assume it is a solid cylinder.
Work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 7.00s is 12,640 Joules
The following equation is used to calculate the net work necessary to accelerate a merry-go-round from resting to a rotational speeds with one rotation every 7.00 secs:
Work is calculated as (mass x radius x angular acceleration) / 2.
In which: 1440 kg in mass
R = 7.50 meters
Angle acceleration is equal to 2/7.00s times 0.89 rad/s2.
Hence, this mathematical methodology is used to compute the net work needed:
Work is equal to (1440 kg x 7.50m2 x 0.89 rad/s2) / (2 x 7.50m x 1440 kg x 1 revolution/7.00s) / 2 = 5,524,000 J or 5.52 MJ.
Acceleration was its term for the variation in velocity. Generally speaking, and sometimes not, acceleration denotes a shift in speed. Regardless of whether an object is moving in a circle, its velocity route is still changing, therefore it keeps gaining speed.
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a 0.4m rod of some material elongates 0.1 mm on heating from 30 to 118. determine the value of the linear coefficent of thermal expansion
The value of the linear coefficient of thermal expansion is : α= 2.841 * 10⁻⁶ (ºC)⁻¹
Li = 0.4m
ΔL = 0.1 mm = 0.0001m
T1 = 30ºC
T2 = 118ºC
ΔT = 88ºC
α =ΔL/(Li*ΔT)
α =0.0001m /(0.4m * 88ºC)
α = 2.841 * 10⁻⁶ (ºC)⁻¹
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the wheels on a bicycle have a 10 inch radius. if the bike must travel exactly 2000 inches , how many revolutions are required? assume that no sliding or slipping occurs between the wheel and the road.
The wheels on a bicycle have a 10 inch radius. If the bike must travel exactly 2000 inches, the number of revolutions the wheel would make will be 31.85 revolutions.
The perimeter of the circle is called the circumference of circle.
Given, radius of the wheel = 10 inches
Diameter of the wheel = 20 inches
Length required to cover = 2000 inches
For one revolution, distance equal to the circumference moved.
1 rev = π D
1 rev = π * 20
1 rev = 62.8 inches
Number of revolutions to travel 2000 inches is 2000/62.8 = 31.85 rev
Thus, the number of revolutions required are 31.85 rev.
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on the moon, the acceleration due to gravity is -1.6 meters per second per second. a stone is dropped from a cliff on the moon and hits the surface of the moon 28 seconds later. how far did it fall? (round your answer to one decimal place.)
a) - 627.7 m
b) - 44.8 m/s
a) we use the formula,
d = gt²/2
when we substitute the values,
d = -1.6 X 28²/2
= -1.6 X 784/2
= - 627.2m
distance travelled by the stone was - 627.2m
b) calculate the impact,
v = gt
substitute,
v = (-1.6) X 28
v = - 44.8 m/s
The negative sign here indicates that the object is going down.
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describe how the universe changed in going from the early universe to the universe some time later.
They moved away from each other in going from the early universe to the universe some time later.
As time goes on, the Universe not only forms elements, atoms, and clumps and clusters together that lead to stars and galaxies, but expands and cools the entire time. The Universe continues to expand even today, growing at a rate of 6.5 light-years in all directions per year as time goes on.
Starting from extremely high density and temperature, space expanded, the universe cooled, and the simplest elements formed. Gravity gradually drew matter together to form the first stars and the first galaxies.
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the masses of the two moons are determined to be 2m for moon a and m for moon b. it is observed that the distance between moon b and the planet is two times that of the distance between moon a and the planet. how does force exerted from the planet on moon a compare to the force exe
Eight times more gravitational pull is exerted by the planet on Moon A than Moon B due to gravitational attraction.
All material objects in the universe are subject to gravity, commonly known as gravitation. The force of gravity tends to pull any two objects or particles with nonzero mass toward one another. From subatomic particles to galaxy clusters, gravity affects all sizes of objects. Additionally, it works over all distances, no matter how tiny or large.
One of the most researched physics phenomena is gravitation. With his renowned Law of Universal Gravitation, Isaac Newton described its behaviour. According to Newton's theory, the gravitational force between any two spherical objects of uniform density is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
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given the ideas presented here about how galaxies form, would you expect to find a giant elliptical galaxy in the local group? why or why not? is there in fact a giant elliptical in the local group?
Because of the size and variety of galaxies in the Local group, I would anticipate finding large elliptical galaxies there. There isn't a huge elliptical galaxy right now, but that could change when other galaxies develop and give rise to one.
A galaxy type known as an elliptical galaxies has an appearance that is smooth and almost featureless, and it has a roughly ellipsoidal form. These galaxies, along with spiral and lenticular galaxies, are one of the four primary kinds of galaxy that Edwin Hubble described in his 1936 book The Realm of the Nebulae and Hubble sequence. Elliptical (E) galaxies, lenticular (S0) galaxies with their large-scale disks, and ES galaxies with their intermediate-scale disks are all parts of the "early-type" galaxy population.
Most elliptical galaxies are made up of older, low-mass stars with scarce interstellar space and little star formation, and they frequently have a dense globular cluster population surrounding them. According to estimates, the Virgo Supercluster contains between 10% and 15% elliptical galaxies.
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how could we counteract the impact of fast fashion (select all that apply, there are one to four possible correct answers)?
Buy quality and consume less
Repurpose our clothes
Buy Second Hand Swap, & Rent Clothing
Change our attitudes toward fast fashion
Shop and drop for charity
Choose organic cotton
Rent or borrow clothes
Watch your washing
Even the greenest garment uses resources for production and transport to your home, creating some environmental impact.More and more fashion brands take into account the environmental and social impact of their production.Don’t throw your clothes in the normal bins! Most of them consist of synthetic, non-biodegradable fiber and will just pile up in the landfill.
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if i want to find a sizeable collection of population ii stars in the milky way galaxy, where would be a good place to look?
Population II stars can be detected to be present in the halos of different spiral galaxies and in the huge globular clusters of the milky way galaxy.
It is known to us that -
There are populations I and II stars and stellar collections
These stars can be differentiated on the basis of their age from creation time, chemical constitution, and their location in the galaxy systems
Since, we want to identify the place where a sizeable collection of population II stars can be found in the milky way galaxy, let us first learn a bit about the population II stars.
Population II stars constitute of the oldest identified stars and clusters. These stars were created nearly 1,000,000,000 - 15,000,000,000 years ago.
These population II stars can be detected to be present in the halos of different spiral galaxies and in the huge globular clusters of the milky way galaxy.
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a car approaches a stationary police car at 30 m/s. the frequency of the siren (relative to the police car) is 500 hz. what is the frequency (in hz) heard by an observer in the moving car as he approaches the police car? (assume the velocity of sound in air is 343 m/s.) a. 544 b. 226 c. 448 d. 550 e. 483
The frequency (in Hz) heard by an observer in the moving car as he approaches the stationary police car (assuming the velocity of sound in air is 343 m/s) is 544 Hz. So, the answer is A.
What is velocity?It is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.
Assuming the velocity of sound in air is 343 m/s, what is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car?
Velocity of car Vc = 30 m/s
Velocity of sound V = 343 m/s
frequency of siren f = 500 Hz
So, the frequency that heard by the observer when the police car approaches is :
f1 = f * (V + Vc) / V
where
f = frequency of siren (relative to the police car)
V = velocity of the car
Vc = velocity of sound in air
f1 = frequency heard by the observer
= 500 * (343 + 30) / 343
= 543.73Hz
= 544 Hz (rounded)
Therefore, the frequency that heard by the observer when the police car approaches him is 544Hz, and the answer is A.
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In a mechanical wave, the restoring force is the force that actually causes the oscillation. In which direction does a restoring force act?
For oscillation in mechanical wave, restoring force acts in a direction opposite to direction of displacement.
In physics, an object is said to be in equilibrium if there is no net force acting on the object. This can happen when the magnitude and direction of the forces acting on the object are perfectly balanced or simply because there are no forces acting on the object.Not all forces try to restore the object back to equilibrium, but forces that do so are called restoring forces.A restoring force is a force acting against the displacement in order to try and bring the system back to equilibrium.The restoring force is a function that depends on the position of an object or system. This type of force is responsible for generating oscillations and is necessary for an object to be in moving in simple harmonic motion. The restoring force is what causes the change in acceleration of an object in simple harmonic motion. A displacement from the equilibrium position results in the system storing potential energy.To know more about forces visit:
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Radio waves travel at a speed of 1.7x10^8 m/s through ice. A radio wave pulse sent into antarctic ice reflects off earth at the bottom and returns to the surface in 32.9x10^-6 s. how deep is the ice?
The depth of the ice was found to be 26.55 x 10 ^ 12 m.
What exactly are radio waves?
A transmitter emits nonparticulate radiation, which is sensed by a receiver. An antenna allows a transmitter to transfer energy into house and a receiver to pick up energy from space. Transmitters and receivers are typically designed to operate on a limited range of frequencies.
The ice depth is then 26.55 x 1012 m.
Let's call the radio wave's speed 'v.'
Let the frequency of the radio wave be represented as 'f'.
Let's call the radio wave's distance's.'
Let's call the radio wave's time period 't.'
Distance formula:
v=s/t
v=s/1/t
The inverse of time period is frequency. As a result, 1/t in the preceding formula can be substituted by f.
v=sxf
filling in the blanks in the above equation
t = 32.9 x 10 ^ -6
v = 1.7 x 10 ^ 8 x m / s
Then, f = 1 / t
Then, f = 1 / t
f= 1/3.2 x 10 - 6 s - So,
s = 1.7 x 10 x 1/3.2 x 10-
= 1.7/3.2 x 10 (8 + 6)
= 0.531 x 10 14
= 53.1
The depth of the ice would therefore be s/2 since the wave covers the distance twice in the specified time period.
Ice depth = 53.1 x 1012/2
Ice depth = 26.55 x10 12 x m
26.55 x 10 ^ 12 x m
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Additionally, the radio wave is moving at the speed of light, or 3 10 8 m/s. As a result, radio waves travel for 12.58 minutes.
What exactly are radio waves?
A transmitter emits nonparticulate radiation, which is sensed by a receiver. An antenna allows a transmitter to transfer energy into house and a receiver to pick up energy from space. Transmitters and receivers are typically designed to operate on a limited range of frequencies.
The ice depth is then 26.55 x 1012 m.
Let's call the radio wave's speed 'v.'
Let the frequency of the radio wave be represented as 'f'.
Let's call the radio wave's distance's.'
Let's call the radio wave's time period 't.'
Distance formula:
v=s/t
v=s/1/t
The inverse of time period is frequency. As a result, 1/t in the preceding formula can be substituted by f.
v=sxf
filling in the blanks in the above equation
t = 32.9 x 10 ^ -6
v = 1.7 x 10 ^ 8 x m / s
Then, f = 1 / t
Then, f = 1 / t
f= 1/3.2 x 10 - 6 s - So,
s = 1.7 x 10 x 1/3.2 x 10-
= 1.7/3.2 x 10 (8 + 6)
= 0.531 x 10 14
= 53.1
The depth of the ice would therefore be s/2 since the wave covers the distance twice in the specified time period.
Ice depth = 53.1 x 1012/2
Ice depth = 26.55 x10 12 x m
26.55 x 10 ^ 12 x m
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A Ferris wheel with a diameter
of 40 m makes one revolution
every 20 minutes. What is its
average speed in meter/min?
Answer:
6.3 m/min
Explanation:
Circumference of a circle = 2πr
r = D/2 = 40m/2 = 20m
C = 2π(20m) = 125.7 m
speed = distance/time = (125.7 m) / (20 min) = 6.3 m/min
The actual usage for grain depends on which llamas show up at feeding time, thus there is an average need for 50 pounds of grain each day with a standard deviation of five pounds. In addition, there is some variability in how long it takes the feed store to whip up a batch of llama feed. The standard deviation of the feed prep is one day. The farm is willing to tolerate a 2% chance of running out of feed before they can get some more hauled in. Which adjustment to their system would have the greatest impact on the reorder point?.
The adjustment that would have the greatest impact on the reorder point would be reducing the standard deviation of the feed prep time.
By reducing the standard deviation of the feed prep time, the farm would be able to order the feed earlier, thus reducing the chance of running out of feed. This would have the effect of lowering the reorder point, as there would be less time between when the feed is ordered and when it arrives.
Additionally, reducing the standard deviation of the feed prep time would be more effective than trying to reduce the standard deviation of the grain usage, as the former is more controllable and can be adjusted more precisely.
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a2.25m segment of wire supplying current to the motor of a submerged submarine carries750a and feels a3.5n repulsive force from a parallel wire 5.00 cm away. what is the magnitude of the current in the other wire in a?
For a 2.25 m segment of wire supplying current to the motor of a submerged submarine, which carries 750 a and feels a3.5 n, the magnitude of the current in the other wire is I2 = 518 A.
where,
The current in wire 1 is equal to 750 in I1. A
I2 is the wire 2 current, and it needs to be computed.
The wire's length is 2.25 m, while the spacing between the two wires is 5.00 cm, or 0.050 m.
Force is attractive if they are carrying current in the same direction.
Force is repellent if they are carrying the opposing stream.
The force in the question is 3.5 N and is repulsive in nature.
The current in wire 2 that is causing the force on wire 1 must be calculated. I2 = 3.5N*2*pi*0.05/Mo*750A*2.25m I2 = 518A can be expressed as the result of the equation above.
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Gravitational force between objects ____________ as objects move farther apart, and it is ___________ between objects that are closer together.
Gravitational force between objects gets weaker as objects move farther apart, and it is stronger between objects that are closer together.
The gravitational force between two objects is given by:
F = G x M x m / r²
Where:
G = constant of gravity
M = mass of object 1
m = mass of object 2
r = distance between two objects
If the masses are constant, then the gravitational force is inversely proportional to the square of distance between those objects, or mathematically:
F ∝ 1/r²
By inversely proportional means if the distance between two objects decreases, the gravitational force increases or gets stronger; and if the distance between two objects increases, the gravitational force decreases or gets weaker.
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a 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg m2 is rotating freely with an angular speed of 1.0 rad/s. two people, each of mass 60 kg, are standing right outside the edge of the merry-go-round and suddenly step onto the edge with negligible speed relative to the ground. what is the angular speed of the merry-go-round right after the two people have stepped on?
Angular speed = 0.4 rad/s , when a 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg m2 is rotating freely with an angular speed of 1.0 rad/s.
radius = 5 m
moment of inertia = 2000 kg-m²
angular speed = 1.0 rad/s
mass = 60 kg
to find out
angular speed
solution
Rotational momentum of merry-go-round = I?
The momentum we experience here is expressed as
momentum = 2000 × 1
momentum = 2000 kg-m²/s
and
Inertia of people will be here as
Inertia of people = mr² = 60 × 5²
Inertia of people = 1500 kg-m²
so Inertia of people for two people
1500 × 2 = 3000
and
Currently, angular momentum conservation
(Momentum + People's Inertia) = Moment of Inertia Angular Speed angular velocity
2000 × 1 = (2000 + 3000 ) ω
solve we get now
ω = 0.4 rad/s
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According to Newton's 2nd law, when something is traveling 50cm with changing forces (in Newtons), why does acceleration = 1/t^2? Use kinematics to show/prove this.
The relation between acceleration and mass is inversely proportional, according to Newton's second law, and there is a direct relationship between acceleration and net external force.
What are the relation in forces and acceleration?One of the most significant laws in all physics is Newton's second law. F = ma, where F (force) and a (acceleration) are both vector values, can be used to represent a body whose mass m is constant. A body is accelerated according to the equation if there is a net force acting on it.
Therefore, An object will remain at rest or move in a straight path at constant speed in the absence of acceleration. A force that is not balanced causes an object to accelerate.
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an astronaut of mass 60 kg is on a space walk when suddenly someone throws a 3 kg book to her with speed 4m/s. she catches the book in an inelastic collision. find: a. the velocity of the astronaut book system after the collision. b. the initial kinetic energy of the system c. the final kinetic energy of the system d. the impulse exerted by the book on the astronaut..
There are 4 questions here that need to be solved.
a. The velocity of the astronaut & book system after the collision (using conservation of momentum) is 0.19 m/s
b. The initial kinetic energy of the system is 24J
c. The final kinetic energy of the system is 1.14J
d. The impulse exerted by the book on the astronaut is 11.43 kg.m/s
What is kinetic energy?In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during acceleration, the body maintains this kinetic energy unless its speed changes.
Now, let's answer the question.
a.
m1 book = 3kg
m2 astronaut = 60kg
vi1 = 4m/s
vi2 = 0m/s
Vf = final speed after collision
Now, let calculate using conservation of momentum formula
ρi = ρf
m1 * vi1 + m2 * v2 = (m1 + m2) * vf
3 * 4 + 60 * 0 = (3 + 60) * vf
12 = 63vf
vf = 0.19 m/s (rounded)
So, the velocity of the astronaut-book system after the collision is 0.19 m/s.
b. Initial kinetic energy will be calculated using kinetic energy formula
KEi = 1/2 * m1 * Vi1^2
= 1/2 * 3 * 4^2
= 24J
So, the initial kinetic energy of the system is 24J
c. Final kinetic energy will be calculated as follows
KEf = 1/2 * (m1 + m2) * vf^2
= 1/2 * (3 + 60) * 0.19^2
= 1.137J
So, the final kinetic energy of the system is 1.137J
d. To calculate the impulse, it is basically the change in momentum of the book, calculated as follows
I (impulse) = m1 * (Vi1 - Vf)
= 3 * (4-0.19)
= 11.43 Kg.m/s
Therefore, the impulse exerted by the book on the astronaut is 11.43 Kg.m/s
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The velocity of a vehicle is typically expressed relative to which of the following?
A
other vehicles on the road
B
the surface of the road
C
the speed of Earth rotating
D
the speed of the tires rotating
The velocity of a vehicle is typically expressed relative to ground.
What is velocity?Velocity is the speed of something that is given direction.
velocity is the measurement to a body's "pace of change of the displacement in relation to time" whenever the main body is traveling through along a straight route.
It is common knowledge of that the word "linear" refers to be something that is totally straight; therefore, when the body moves in a straight path, it is said to be linear velocity .
Alternatively, velocity is the distance traveled by a body traveling in a specified to the direction during of a predetermined period of time. Thus, the fundamental idea of linear velocity is the provided by the union of these two quantities.
Because it always has the direction of velocity is a vector.
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brandon is on one side of a river that is 70 m70 m wide and wants to reach a point 300 m300 m downstream on the opposite side as quickly as possible by swimming diagonally across the river and then running the rest of the way. find the minimum amount of time if brandon can swim at 2 m/s2 m/s and run at 4 m/s.at 4 m/s. (use decimal notation. give your answer to two decimal places.) the minimum amount of time is s
The minimum time required to get there is 79.5 s.
What does downstream mean?The direction of or nearer to the mouth of a stream.
On one side of a river is Brandon.
The river is 70 meters wide.
Brandon can swim at a speed of 2 m/s.
Brandon moves at a running pace of 6 m/s.
Let's assume that the included angle is 45 degrees.
Therefore, Brandon covered 99 meters in water.
Given that Brandon swims at a speed of 2 m/s
Time = distance / time
t = 99/2 = 49.5
The remaining distance to be covered while running is 250 - 70 = 180 m, hence the time required to do it is 180/6 = 30 s.
The time needed to get there is therefore 49.5 + 30 = 79.5 s.
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A 1,000 kg car experiences a net force of 3,500N from its engine.
Answer:Magnitude of the car's acceleration is 3.5 m/s²
Given:
Mass of car = 1,000 kg
Net force applied by car = 3,500 N
Find:
Magnitude of the car's acceleration
Computation:
Net force = Mass × Acceleration
So,
3,500 = 1,000 × Acceleration
Acceleration = 3,500 / 1,000
Acceleration = 3.5 m/s²
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gold is sold by the troy ounce (31.103 g). what is the volume in cm3 of 1 troy ounce of pure gold (19300 kg/m3)?
The volume of the gold with given specs is 1.610 cm³.
Density of the gold as given in the question : 19300 kg/m³
Density of the gold in changed units i.e g/cm³ : 19.3 g/cm³
The measure of how densely a material is packed together is called density. As the mass per unit volume, it has that definition. Density Formula: = m/V, m is the object's mass, and V is its volume.
Density = Mass / volume
=> Volume = Mass / density
Substituting the values :
Volume = (31.103)/(19.3)
Volume = 1.610 cm³
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calculate the velocity of a non-relativistic electron whose de broglie wavelength is 3.637 nm.
The velocity of a non-relativistic electron whose de broglie wavelength is 3.637 nm is 5.82 x 10^6 m/s.
The velocity of a non-relativistic electron can be calculated using the formula v = h / mλ, where h = Planck's constant, m = the mass of the electron, and λ = the de Broglie wavelength of the electron.
Assuming the mass of the electron is 9.11 x 10^-31 kg, the velocity of the electron can be calculated as follows:
v = (6.63 x 10^-34 m^2 kg / s) / (9.11 x 10^-31 kg * 3.637 x 10^-9 m)
This works out to be approximately 5.82 x 10^6 m/s.
However, it's important to note that the de Broglie wavelength of a particle is generally only considered to be a meaningful quantity when the particle is moving at speeds that are comparable to the speed of light.For non-relativistic particles, such as an electron moving at a low velocity, the de Broglie wavelength is not a well-defined concept. Therefore, it's not meaningful to calculate the velocity of an electron based on its de Broglie wavelength.To know more about electrons visit:
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a coil with a self-inductance of 16 mh and a resistance of 6.0 w is connected to an ac source whose frequency can be varied. at what frequency will the voltage across the coil lead the current through the coil by ? f
The frequency of the voltage across the coil is 60 Hz.
The tendency of a coil to resist internal current fluctuations is known as self-inductance. Every time a coil's current varies, an EMF is produced that is inversely proportional to the rate of change of the coil's current.
Given the self-inductance (L) is 16 mH and resistance is 6.0 Ω.
L = 16×10⁻³ H
The frequency can be calculated using the inductive resistance formula, [tex]f=\frac{X_L}{2\pi L}[/tex] where, XL is inductive resistance and L is inductance.
First, we have to find inductive resistance using the phase angle formula.
[tex]\begin{aligned}\tan\phi&= \frac{X_L-X_C}{R}\\X_L&=R\tan\phi\\&=6\times \tan 45^{\circ}\\&=6\times1\\&=\mathrm{6\;\Omega}\end{aligned}[/tex]
Then, frequency is
[tex]\begin{aligned}f&=\frac{6}{2\pi \times 16\times 10^{-3}}\\&=\mathrm{60\;Hz}\end{aligned}[/tex]
The answer is 60 Hz.
The complete question is -
A coil with a self-inductance of 16 mH and a resistance of 6.0 Ω is connected to an ac source whose frequency can be varied. At what frequency will the voltage across the coil lead the current through the coil by 45°?
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Why is sleep important for safety?
Sleep is very crucial for safety. Proper sleep helps persons to behave well and choose correct decision during chaos .Exa-Crossing the road.
Sleep isn't just significant for generally speaking energy level at work, however fundamental for our general medical issue. Unfortunate rest propensities can prompt circulatory strain issues, which thus can prompt various medical problems. In this issue we'll be taking a gander at rest, why it makes a difference for work environment wellbeing, and how to urge all your staff to get a decent night's rest.
A laborer's body needs to dial back and rest to keep the heart solid. A very much refreshed body is connected to a sound, serious areas of strength for heart framework and diminished degrees of stress. Rest is significant for wellbeing and the connection among rest and security is obviously significant too.
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An olympic-size pool is 50. 0 m long and 25. 0 m wide. How many gallons of water (density = 1. 0 g/ml) are needed to fill the pool to an average depth of 4. 8 ft?.
In order to fill the pool to an average depth of 4.8 ft., the water needed is 483,101 gallons
The formula for the volume of rectangular cuboid is:
V = l x w x h
Where:
l = length
w = width
h = height
Parameters given in the problem:
l = 50 m
w = 25 m
h = 4.8 ft. = 1.463 m
Plug these parameters into the formula:
V = 50 x 25 x 1.463
V = 1,828.75 m³
1 m³ = 264.17 gallons
Hence,
V = 1,828.75 m³ = 1,828.75 x 264.17 gallons
V = 483,101 gallons
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