By using the formulae, λ = h/mv, The De Broglie wavelength of the muon is calculated to be 4.13 × 10^10 m, as according to the given data in the question.
Is the nanosecond the shortest?The shortest measured time is 100 attoseconds. A quadrillionth of a minute is a femtosecond. One quadrillionth of a minute is a picosecond. One quadrillionth of a second is a nanosecond.
What is more compact than nano?Particles are smaller than just a nanometer. Depending on the element, an atom is between 0.1 and 0.3 nm in size. Atoms on the a surface in a SEM image.
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The doctor lands his tardis on a planet whose radius is 1. 2x10^7m the acceleration due to gravity is 18m/s^2. What is the mass of the planet
The mass of planet is 3.886×10^25 kg. The radius of planet is 1. 2x10^7m.
What is a planet with half the mass's acceleration caused by gravity?Complete Resolution. If the acceleration caused by gravity on the surface of the earth is given by the formula g, then the acceleration caused by gravity on a planet with a mass half that of the earth and a radius equal to that of the earth is given by the formula g/2. Where G = 6.67 ×10^-11 N m2/kg2 (Newton's gravitational constant).
Is the explanation for the gravitational acceleration independent of mass?As a result, acceleration due to gravity (a) depends on the gravitational constant (G), the mass of the Earth (M), and the radius of the Earth (R), but not on the mass of the body (m).
Given:
Radius of planet (r) = 1. 2x10^7m
Acceleration due to gravity (g) = 18 m/s^2
The acceleration due to gravity at the surface of the planet is,
[tex]g=G\frac{M}{r^2}[/tex]
Where, G = Universal gravitational constant
[tex]G= 6.67*10^-11N.m^2/kg^2[/tex]
[tex]M=\frac{g*r^2}{G}[/tex]
[tex]M=\frac{18*(1.2*10^7)^2}{6.67*10^-11}[/tex]
M =3.886×10^25 kg
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Which of the following is an example of erosion in action ?
Example of erosion: Wind carries small pieces of rock away from the side of a mountain.
Which of the following are examples of erosion?Erosion is the procedure by which the surface of the Earth gets worn down. Erosion can be created by natural elements such as erosion as wind and glacial ice. But everyone who has ever seen a picture of the Grand Canyon knows that nothing strikes the erosion slow steady movement of the water when it comes to commuting the Earth
Rain, rivers, floods, lakes, and the ocean convey away bits of soil and sand and slowly wash away the deposit. Rainfall produces four types of soil erosion: splash erosion, sheet erosion, rill erosion, and ravine erosion.
So we can conclude that Erosion is a ruinous force that wears away land features.
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is often caused by improper loading, not only in terms of the load impedance itself, but in terms of how much capacitive or inductive reactance is part of that impedance.
Resistance and impedance (in AC circuits) are one such pair of synonyms (DC circuits). Technically speaking, they both stand in the way of current flow, but factor ability of impedance also takes resistance into account.
Obviously all, reactance and inductance are also included in this (capacitors).
Impedance, which results from the interaction of reactance and ohmic resistance, is the active resistance to AC of an electric circuit or component. We also describe it as any restriction of an electric current's ability to move energy when voltage is applied.
The more precise meaning is the overall resistance a circuit of electricity provides to an AC current flowing at a single frequency. In conclusion, we measure reactance and resistance in ohms, and we denote this measurement with the sign Z.
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Select the correct answer. A boy is pushing a chair by applying a force of 5 newtons. His mother helps him push it faster by applying an additional force of 7 newtons in the same direction. What is the net force acting on the chair
Answer:
The net force is now 12
Explanation:
The boy is applying a force of 5 newtons + his mother is helping him to apply 7 newtons = 12 newtons.
Some planetary scientists have suggested that the planet Mars has an electric field somewhat similar to that of the earth, producing a net electric flux of -3. 63 × 1016 N⋅m2/C at the planet's surface.
a) Calculate the total electric charge on the planet.
b) Calculate the magnitude of the electric field at the planet's surface (refer to the astronomical data inside the back cover).
c) Find the direction of the electric field at the planet's surface.
d) Calculate the charge density on Mars, assuming all the charge is uniformly distributed over the planet's surface
With a net electric flux of -3. 63 1016 N/m2/C at its surface, the planet Mars has an electric field that is somewhat similar to that of the earth. There will be 3.26 x [tex]10^{5}[/tex] of electric charge throughout the entire earth.
Which best sums up Gauss's law?The electric flux across any closed surface is proportional to the net electric charge q enclosed by the surface, according to Gauss's law of electricity, which reads as = q/0, where 0 is the electric permittivity of free space, which has a value of 8.854 10-12 square coulombs per newton per square meter.
How can the angle of a vector in an electric flux be determined?E is the magnitude of the electric field (with units of V/m), S is the area of the surface, and is the angle between the electric field lines and the normal (perpendicular) to S. If the electric field is uniform, the electric flux (E) travelling through a surface of vector area S is: E = ES = EScos.
Calculation:Ф = q/ε
⇒ 3.69 x [tex]10^{16}[/tex] x = q/ 8.85 x [tex]10^{-12}[/tex]
q = 3.26 x [tex]10^{5}[/tex]
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What is the relationship between the mass of an object and the amount of thermal energy an object has?
The greater the mass of an object, the more particles there are in the sample and the more thermal energy it possesses at the same temperature. Assume you have some boiling hot water at 100 degrees Celsius to demonstrate this concept.
What is thermal energy and what are some examples?Thermal energy is shown by boiling water on a stove. Thermal energy is created when the atoms and molecules of a material vibrate faster as the temperature rises.
What is an example of a mass?Mass is best defined as the quantity of matter contained in any item or body. Everything in our environment has mass. For example, a table, a chair, your bed, a football, a glass, and even air has mass. That being said, all objects are light or heavy because of their mass.
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How were you able to increase the amount of potential the ball had?
Answer:
The potential energy can be increased by increasing the mass of the object, by varying the distance between the two objects, decreasing the kinetic energy of the molecules, by freezing, by compressing or stretching, and so on.
Explanation:
Hope this helped !
What is the velocity of a rocket that goes 700 km north in 25 seconds, and then travels another 700km south in 25seconds?
The rocket's velocity that goes 700 km north in 25 seconds, then travels another 700km south in 25 seconds is 28,000 m/s.
Given,
Distance = 700km, which is 700 * 103m, and Time = 25 seconds.Velocity is known to be equal to displacement times time.Rocket's velocity is 700*103/25, or 28*103 m/s.As a result, the speed is 28,000 m/s.The orbital velocity, which is 7.9 km/s and more than 20 times the speed of sound, is measured in this manner.V equals u ln (m I m). The rocket equation is the name of this outcome. Konstantin Tsiolkovsky, a Soviet physicist, developed it first in 1897. It provides us with the change in velocity that the rocket experiences as a result of burning a mass of fuel that reduces the total mass of the rocket from m0 to m.To know more about Velocity here
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What is the tangential speed of a passenger on a Ferris wheel that has a radius of 42 m and rotates once in 25 sec
Where r is the radius, v is the tangential speed, and is the angular speed The tangential speed is 2.1 m/s as a result.
Any object traveling in a circular motion has a linear speed known as tangential velocity. On a turntable, a point in the center moves less distance in a full rotation than a point near the outside edge. Tangential speed and tangential velocity are not the same thing. The amount of tangential velocity, which is generally referred to as velocity, is what you are referring to. Technically, the nomenclature is incorrect, and speed is actually its magnitude whereas tangential velocity comes with the direction, a.The circle's circumference divided by the duration required for one complete spin gives us the tangential velocity: 2*pi*r/t. The relationship between it and angular velocity is also shown by the formula V = w * r, w.To know more about tangential velocity here
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CANT DO IT
i neeeed herlp For numbers 14a-14d, tell which expressions require you to rename mixed numbers before you can subtract.
14a. LaTeX: 5\frac{2}{5}-2\frac{1}{4}5 2 5 − 2 1 4
[ Select ]
14b. LaTeX: 5\:-\:2\frac{7}{8}5 − 2 7 8
[ Select ]
14c. LaTeX: 7\frac{2}{3}\:\:-\:6\frac{1}{8}7 2 3 − 6 1 8
[ Select ]
14d. LaTeX: 9\frac{1}{6}-5\frac{2}{3}9 1 6 − 5 2 3
[ Select ]
14 a, 14 b, 14 c, and 14 d are the Expressions that require renaming mixed numbers before we can subtract.
Actually, there are a few steps to convert normal fractions into a mixed fractions. The steps are as follows:
firstly, we have to find the whole number to do this we divide the numerator by the denominator. secondly, Get the new numerator: To get a new number we should calculate in step one and multiply it by the original denominator. The result of that multiplication is then subtracted from the original numerator.After that Our mixed fraction, we need to put the whole number together with our new numerator and original denominator.finally, Simplifying our fraction.Solving one by one with the help of the given options:
1) 14a
[tex]5\frac{2}{5}-2\frac{1}{4} \\\\\frac{17}{5} -\frac{9}{4} \\\\\frac{68-45}{20}\\\\ \frac{23}{20} =1\frac{3}{20}[/tex]
2)14b
[tex]5-2\frac{7}{8} \\\\\frac{5}{1} -\frac{7}{8} \\\\\\\frac{40-23}{8}\\\\ \frac{17}{8} =2\frac{1}{8}[/tex]
3)14c
[tex]7\frac{2}{3} -6\frac{1}{8} \\\\\frac{23}{3} -\frac{49}{8} \\\\\frac{184-147}{8} \\\\\frac{37}{24} =1\frac{13}{24}[/tex]
4)14d
[tex]9\frac{1}{6} -5\frac{2}{3}\\\\ \frac{55}{6}-\frac{17}{3}\\\\ \frac{165-102}{18} \\\\\frac{63}{18}=3\frac{9}{18}[/tex]
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The length of nylon rope from which a mountain climber is suspended has a force constant of 1.2×104 N/m.
a. What is the frequency, in Hz, at which he bounces, given his mass and the mass of his equipment is 98 kg?
b. How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 1.8 m before the rope runs out of slack?
c. What is the frequency, in Hz, at which he bounces, given his mass and the mass of his equipment is 98 kg if the rope is twice as long?
d. How much would this rope stretch, in centimeters, to break the climber's fall if he free-falls 1.8 m before the rope runs out of slack if he rope was twice the length?
The length of nylon rope from which a mountain climber is suspended has a force constant of 1.15 ✕ 104 N/m.
What is the force constant measured in?Spring constant is the common name for the force constant. Hooke's law states that F=-kx. k=N/m is used to replace units in the equation where F is force, x is displacement, and k is force constant (spring constant) to determine the SI unit of force constant (spring constant).
What is a graph's force constant?The slope (gradient) of the graph equals the force constant. The proportionality constant, or k, is also known as the force constant in physics. A spring that is more rigid will have a higher value for k. The graph is no longer a straight line beyond point A since the gradient has changed and the formula F = Kx is no longer valid.
Calculation:Maximum speed is at equilibrium where:
F = kx ⇒x =F/k
Now, F x=1/2mv²+1/2kx²
Solving we get,
V=F/√mk=Vmax
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An object with mass of 50kg moves with
velocity of 11. 2m/s and an event occur
whereby it transfers 1539 of energy to
another objects as work.
What is the new
velocity of the object after the event??
The new velocity of the object after the event is 7.99m/s.
We are given that,
Mass = m = 50kg
Initial velocity = v = 11.2m/s
Energy = E = 1539j
The kinetic energy of object can be calculated as,
K= (1/2)mv²
K = (50×125.44)/2
K = 3136J
Consequently, since both the initial kinetic energy and the total amount of energy transferred are known. The article's resulting energy is easily discernible.
Final energy = initial kinetic energy - the ending energy
Final energy = 3136-1539= 1597 joules
Therefore, using the equation for kinetic energy derivation, the speed of the object can now be determined.
K.E = 1/2MV²
1597 = 50/2V²
3194 = 50V²
V = 7.99m/s
Therefore , the new velocity of the object after the event would be 7.99m/s.
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On what interval is the factor by which the office noise is related to the standard threshold of hearing
The interval by which the factor by which the office noise is related to the standard threshold of hearing is (100,000, 10,000,000].
The factor by which the office noise is related to the standard threshold of hearing is given by x = 10^(d/10), where d is the sound intensity in decibels. Since the decibel reading was consistently above 50 but never above 70, we can calculate the range of x using the following:
50 < d <= 70
10^(50/10) < x <= 10^(70/10)
To find the range of x, we need to calculate the 10^(50/10) and 10^(70/10)
10^(50/10) = 10^5 = 100000
10^(70/10) = 10^7 = 10000000
Therefore, the range of x, the factor by which the office noise is related to the standard threshold of hearing is (100,000, 10,000,000].
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Your question is incomplete but most probably the complete question is:
Sound intensity, in decibels, d, can be written using a comparison factor, x, that compares sound intensity to the standard threshold of hearing. d = 10log(x) A sensor measures the sound intensity, in decibels, of an office over time. The decibel reading was consistently above 50, but never above 70. On what interval is the factor by which the office noise is related to the standard threshold of hearing? (17, 18.5) (17, 18.5] (100,000, 10,000,000] (100,000, 10,000,000)
A 63.0-kg sprinter starts a race with an acceleration of 3.20 m/s2. If the sprinter from the previous problem accelerates at that rate for 20.0 m, and then maintains that velocity for the remainder of the 100.0-m dash, what will be his time for the race
At his current velocity the sprinter will complete the 100.0-m dash in 28.53 s.
What is velocity?
Velocity is a vector quantity that describes the rate of change of an object's position. It is a measure of how fast an object is moving and in what direction. Velocity is measured in units of meters per second (m/s) or miles per hour (mph) and is often represented by the symbol "v".
We can use the equations of motion to calculate the time for the sprinter to complete the race.
First, we can use the equation:
v = u + at
to find the final velocity of the sprinter after accelerating for 20.0 m. Here, u is the initial velocity (which is 0 m/s since the sprinter is at rest at the start of the race), a is the acceleration of 3.20 m/s^2, and t is the time it takes for the sprinter to accelerate for 20.0 m.
v = 0 + (3.20 m/s^2)(t)
We know that the sprinter accelerates for 20.0 m, so we can use the equation:
s = ut + 1/2at^2
to find the time t:
20.0 m = (0 m/s)(t) + 1/2(3.20 m/s^2)(t^2)
t^2 = (20.0 m) * 2 / (3.20 m/s^2) = 12.5
t = sqrt(12.5) = 3.53 s
So the time it takes for the sprinter to accelerate for 20.0 m is 3.53 s.
Next, we can use the equation:
v = d/t
to find the time it takes for the sprinter to cover the remaining 80.0 m of the race at his final velocity. Here, d is the remaining distance of 80.0 m and v is the final velocity found before.
t = d/v = 80.0 m / (3.20 m/s) = 25.0 s
So the time it takes for the sprinter to cover the remaining 80.0 m of the race at his final velocity is 25.0 s
So the total time for the race is the sum of the time it takes to accelerate and the time it takes to cover the remaining distance at a constant velocity:
t = 3.53 s + 25.0 s = 28.53 s
Hence, at his current velocity the sprinter will complete the 100.0-m dash in 28.53 s.
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Now let's think about a balloon. We know the gas particles inside of the balloon are bumping against the sides. What keeps those gas particles from forcing the balloon to expand
The elasticity of the balloon's material keeps the 1particles from forcing it to expand. The material stretches as the gas particles bump against the sides, allowing the balloon to expand to a certain point before contracting again.
The elasticity of the balloon's material is an important factor in determining the balloon's shape and size. In general, the more elastic the material is, the more the balloon will be able to stretch and expand. When the material is not elastic enough, it will not be able to stretch and the balloon will remain in its original shape.
The elasticity of the material also affects the amount of air pressure within the balloon. A more elastic material will be able to hold more air pressure, while a less elastic material will not be able to hold as much pressure. This is why balloons with a higher pressure will usually be larger than balloons with a lower pressure.
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The wheel in the simplified engine of Figure 1 has radius of 0. 250 m and rotates so that the piston oscillates at angular frequency of 12. 0 rad/s. At = 0, the piston is located at =. Calculate the piston’s position, velocity and acceleration at = 1. 15 s.
The piston's position, velocity, and acceleration at t = 1.15 s are :
Position: 3.45 m
Velocity: 3 m/s
Acceleration: 0 m/s^2
To calculate the piston's position, velocity, and acceleration at t = 1.15 s, we need to know the angular position, velocity, and acceleration of the wheel.
The angular position of the wheel at t = 1.15 s is given by
θ = ωt + [tex]A_{0}[/tex]
where ω is the angular frequency, t is the time, and [tex]A_{0}[/tex] is the initial angular position.
Since the angular frequency is given as 12 rad/s and the initial angular position is 0, the angular position of the wheel at t = 1.15 s is
θ = 12 x 1.15 = 13.8 radians
The piston's position is given by
r = Rθ
where R is the radius of the wheel.
Substituting the value of R and θ,
r = 0.25 x 13.8 = 3.45 m
The velocity of the piston is given by
v = r' = Rθ' = Rω
Substituting the values
v = Rω = 0.25 x 12 = 3 m/s
Acceleration of the piston is given by
a = v' = Rθ'' = Rω' = R(ω^2)θ
As the angular frequency is constant, the angular acceleration is 0 so the linear acceleration is also 0.
Note: Linear acceleration is not equal to the derivative of linear velocity, it is equal to the derivative of velocity with respect to time, which is zero in this case.
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Complete this sentence. If the cone of force is facing an observer, the impact comes from the ________ side of the observer.
left
same
right
opposite
If the cone of force is facing an observer, the impact comes from the opposite side of the observer.
What is Newton's third law of motion?
Newton's third law of motion states that action and reaction force are equal and opposite. That is for every action, there is an equal and opposite reaction.
Mathematically, the formula for Newton's third law of motion is given as;
Fa = - Fb
where;
Fa is the impact force or force exerted on BFb is the reaction force of B due to applied force of AThus, when a force is applied from a side, the observed force or reaction will be directed in opposite direction. The force exerted and the reaction force are both equal in magnitude but occurs in opposite direction.
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A baseball player throws a ball giving it a change in momentum of 6. 5
kg. M
over 90 ms.
S
What is the magnitude of the net force on the ball?
A baseball player throws a ball which has a certain change in momentum. The magnitude of the net force on the ball is 72.22 N.
Given that,
Change in momentum Δp = 6.5 kg m/s
Time t = 90 ms = 90 × 10⁻³ s
Change in momentum can be written as,
Δp = m Δv = F×t
As we need net force on the ball,
Δp = F×t
Making F as subject and putting the values we have,
F = Δp/t = 6.5/(90 × 10⁻³) = 72.22 N
Thus, the required net force on the ball is calculated to be 72.22 N.
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Why do we calculate torque?
Torque is one of the key ideas to comprehend in order to solve problems with rotational motion. Torque is the tendency of a force to produce or change rotational motion.
Why is torque calculation important?Torque is a measure of an engine's capacity to control a load and generate a certain level of power to turn the engine on its axis. which is an important part of an automobile engine's power-generating process. Per foot (ft) of rotation about a single point, the force is expressed in pounds (lb).
Why does the torque exist?The force that can cause an object to revolve around an axis is measured in torque. In linear kinematics, force causes an item to accelerate, and torque causes an object to produces the angular acceleration of an object. A vector quantity is a torque.
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A continuous line of charge lies along the x axis, extending from x = +x0 to positive infinity. The line carries positive charge with a uniform linear charge density λ0. (a) What is the magnitude of the electric field at the origin?(b) What is the direction of the electric field at the origin?
The E = -kλo/xo is the magnitude of the electric field at the origin, negative sign the direction is towards the origin.
What is electric field ?
The force per unit charge imposed on a positive test charge that is at rest at a given position is mathematically defined as the electric field, which is a vector field that can be associated with any point in space.
What is magnitude ?
According to the physics definition, magnitude is just "distance or quantity." It demonstrates how an object moves as it is moving, including whether the movement is absolute, relative, or of a particular size. It serves as a means of describing the size or scope of something. Physicists use the word "magnitude" to indicate size or distance.
a)Lets take an element dx at x distance from origin
Field due to that element of origin; E = k*((λo)dx)/x2 (E = kq/r2)
Integrating from xo to ∞
E =integral( kλo/x2 dx )(xo to ∞)
E = -kλo/xo
b)As we have negative sign the direction is towards the origin
Therefore, E = -kλo/xo is the magnitude of the electric field at the origin, negative sign the direction is towards the origin.
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SOMEONE PLS HELP ME ITS DUE TOMORROW
Answer:
1) -5 N, Left
2) 14 N, Up
3) 13, Right
4) 10, Right
5) 22, Down
6) 9, Left
Explanation:
IF: Left or Down, then Negative
1) 15+15=30
Left= 30
Right= 25
30-25=5
30>25
2) 60+10=70
Down= 70
84-70= 14
70<84
3) Left= 62
75-62= 13
The image below shows the combined wave for Sound A + B, where Sound A has a higher frequency than Sound B. What is the frequency of Sound A?
The frequency of Sound A is 440.3 Hz.
What is the resultant frequency of the two sound waves?The resultant frequency of the sound A and sound B is calculated as follows;
Mathematically, the relationship between period and frequency of a wave is given as;
F = 1 / T
where;
T is the period of the waveThe resultant frequency from the given graph is calculated as;
The period of the sound in the image = 0.3 s
F = 1 / T
F = 1 / 0.3 s
F = 3.3 Hz
If sound B = 437 Hz, the frequency of sound A which is greater is calculated as;
F ( A ) = 437 Hz + 3.3 Hz
F ( A ) = 440.3 Hz
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A passenger elevator operates at an average speed of 8 m/s. if the 60th floor is 219 m above the first floor,how long does it take the elevator to go from the first floor to the 60th floor?
Answer:
27s
Explanation:
Time = distance/speed
Time = 219/8
Time = 27.375 s
The hanging mass is referred to as M and it sets the centripetal force.
True
False
Answer:
False
Explanation:
The centripetal force is the force that points towards the center and is responsible for keeping an object in a curved path. This force is provided by the tension in the string, not the mass of the object.
Two particles P and Q are initially at rest 1.64 m apart, P has a mass of 1.43 kg and Q a mass of 4.29 kg. P and Q attract each other with a constant force of 1.79 x 10-2 N. No external forces act on the system. (a) Describe the motion of the center of mass. (b) At what distance from P’s original position do the particles collide?
(a)The center of mass of the system has no acceleration, and remains at the same position as it was earlier.
(b)The particle P, collide at a distance 1.23m from P's original position.
What is acceleration?Vector quantities include accelerations. The direction of the net force imposed on an object determines its acceleration in relation to that force.Acceleration in a body is the result of imbalanced forces.The three main categories of accelerated motions are uniform, non-uniform, and average acceleration. When an item moves in a straight path with an increase in speed occurring at regular intervals of time, this motion is referred to as having uniform acceleration.Any modification of motion's speed or direction is referred to as acceleration. When anything is speeding up, slowing down, or not traveling straight ahead, it is said to be accelerating.To learn more about acceleration refer to:
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The volume of the balloon is
14 000 cm³
The density of the helium in the balloon is 0.180 kg/m³
Calculate the mass of helium in the balloon
1 cm³ = 1 x 10-6 m³
The balloon's helium has a mass of 2.52 KG.
The definition of density.The quantity of things—which could include humans, animals, plants, or objects—in a given space is referred to as density. To determine density, divide the number of objects by the area's measurement. The number of people in a country divided by its area in square kilometers or miles is known as its population density.
Simply put, what is density?The term "density" refers to the ratio between the volume (the amount of space taken up by an object or substance) and the amount of matter contained therein (its mass). The amount of mass per unit of volume is another method to define density.
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A RL circuit is driven by an AC generator as shown in the figure. sin(ot) The voltages across the resistor and generator are ??.
O always out of phase O always in phase sometimes in phase and O sometimes out of phase Submit
Sometimes in phase and sometimes out of phase.The voltage across the resistor and generator will depend on the phase difference between the current and voltage in the circuit.
The voltage across the resistor and generator will depend on the phase difference between the current and voltage in the circuit. If the phase difference is 0°, then the voltage across the resistor and generator will be in phase. If the phase difference is 180°, then the voltage across the resistor and generator will be out of phase. In any other scenario, the voltage across the resistor and generator will be somewhere in between in phase and out of phase.
Sometimes in phase and sometimes out of phase.
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(TCO A) The primary reason for networking standards is to
Student Answer:simplify cost accounting for networks. Make it more difficult to develop hardware and software that link different networks. Ensure that hardware and software produced by different vendors can work together. Ensure that all network components of a particular network can beprovided by only one vendor. Lock customers into buying network components from one vendor
Make sure that software and hardware developed by various manufacturers can cooperate.
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You can just say if its A B C or D.
Thank you!
Suppose the particles in the preceding problem have masses The velocities of the particles are (a) Calculate the angular momentum of each particle about the origin. (b) What is the total angular momentum of the four-particle system about the origin?
Part A: The angular momentum of each particle about the origin
The angular momentum of the first particle is -0.4 kg.m²/s.The angular momentum of the second particle is 0.The angular momentum of the third particle is 1.3 kg.m²/s.The fourth particle's angular momentum is 0.Part B: The total angular momentum of the four-particle system is 0.95 kg.m²/s.
The expression used to calculate angular momentum L is:
L = r x mv
Here, r is the position vector of the object m is the mass and v is the velocity vector.
According to the superposition principle, the resultant angular momentum due to many particles is the vector sum of the individual angular momentum.
L = L₁ + L₂ + L₃ + ...
Here, L₁ is the angular momentum of a particle, L₂ is the angular momentum of the particle, and so on.
In the question
Mass of a particle = 5.0 kg
vector r = (2.0i - 3.0j) m
vector v = (3.0i) m/s
Part A (seen in the picture for instruction)
For particle 1
The position vector is 2.0j m
Substitute 0.10 kg from m₁, 2.0j from r, and 2.0i m/s for v₁ in the expression of angular momentum
L = r x mv
L₁ = (2.0jm) x [(0.10 kg)( 2.0i m/s)]
L₁ = -4.0 kg.m²/s
The angular momentum for the first particle is -4.0 kg.m²/s.
For particle 2
Position vector is (2.0i - 2.0j) m
Substitute 0.20 kg from m₂, (2.0i - 2.0j) m from r, and (3.0i - 3.0j)m/s for v₂ in the expression of angular momentum
L₂ = (2.0i - 2.0j) m x [ (0.20 kg) (3.0i - 3.0j) m/s]
L₂ = 0
The angular momentum for the second particle is 0
For particle 3
The position vector is (-3.0i + 1.0j) m.
Substitute 0.30 kg from m₃, (-3.0i + 1.0j) m from r, and -5.0j m/s for v₃ in the expression of angular momentum
L₃ = (-3.0i + 1.0j) m x [((-3.0i + 1.0j) m) ( -5.0j m/s)]
L₃ = 1.35 kg.m²/s
The angular momentum for three particles is 1.35 kg.m²/s.
For particle 4
The position vector is 4.01i m.
Substitute 0.40 kg from m₄, 4.0i m from r, and -4.0i m/s for v₄ in the expression of angular momentum
L₄ = (4.0i m) x [(0.40 kg) (-4.0i m/s)
L₄ = 0
The angular momentum for four particles is 0.
Part B
Formula used: L = L₁ + L₂ + L₃ + L₄
The total angular momentum of the four-particle system is calculated as follows:
By superposition principle
L = L₁ + L₂ + L₃ + L₄
L = -4.0 kg.m²/s + 0 + 1.35 kg.m²/s + 0
L = 0.95 kg.m²/s
Hence, the total angular momentum of the four-particle system is 0.95 kg.m²/s.
Your question is incomplete but most probably your full question was:
Suppose the particles in the preceding problem have masses m₁ =0.10 kg, m₂=0.20 kg, m₃ = 0.30 kg, m₄ = 0.40 kg. The velocities of the particel are v₁= 2.0i m/s,v₂= (3.0i - 3.0j) m/s, v₃= - 1.5j m/s, v₄= -4i m/s.
(a) Calculate the angular momentum of each particle about the origin.
(b) What is the total angular momentum of the four-particle system about the origin?
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