The deflection of a pointer in a centrifugal force experiment can be found by measuring the angle between the initial position of the pointer and its final position after rotation in a circular path.
The deflection of a pointer in a centrifugal force experiment can be determined by measuring the angle between its initial position and its final position after it has been rotated in a circular path.
This angle can then be used to calculate the magnitude of the centrifugal force that was applied to the pointer. By measuring the deflection of the pointer, scientists can gain a better understanding of the effects of centrifugal force on objects in motion.
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an object is placed 40.0 cm from a concave mirror of radius 20.0 cm. (a) find the location of the image. (b) what is the magnifi cation of the mirror? is the image real or virtual? is the image upright or inverted?
Provided that the concave mirror's given focal length is 20 cm long.The object is 40 cm away, which indicates that it is at the center of the curve.
When a concave mirror with a 20 cm focal length is put 40 cm away from the object? Provided that the concave mirror's given focal length is 20 cm long.The object is 40 cm away, which indicates that it is at the center of the curve.As a result, a real, inverted image that is the same size and precisely in the focus will be produced.As a result, the picture is created 10 centimeters in front of the mirror.The image's distance from the mirror is 40 cm, and the image is reversed at that distance.The image is 40 cm away from the viewer.To learn more about concave mirror refer
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A 30 kg child moving at 5 m/s jumps onto a 50 kg sled that is initially at rest
on a frictionless sheet of ice. Determine the speed of the child-sled system after
the child jumps onto the sled.
The speed of the child-sled system after the child jumps onto the sled is 3 m/s.
What is speed?An object's speed is the rate at which it moves in any direction. Speed is measured as the ratio of the distance travelled to the time required to cover that distance. Speed is a scalar quantity since it only has a direction and no magnitude.
Apply momentum conservation perfect inelastic.
p(before) = p(after)
m1v1i = (m1 + m2)vf
(30)(5) = (50)vf
vf = 3 m/s
Hence, speed of the child-sled system after the child jumps onto the sled is 3 m/s
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how many revolutions does the object make during the first 3.4 s s ? express your answer using two significant figures. view available hint(s)
Number of revolutions the object make during the first 3.4 s is, 8.4.
The nature of the graph of the angular velocity vs time gives information about the angular acceleration of the body and the angular displacement of the body.
Revolutions is given by, the angular displacement divided by the total angular replacement in full circle.
Total angular replacement in full circle is 2π.
Looking at the graph, the angular displacement in time t is given by,
20 + (10 t)
The angular displacement in first 3.4 seconds.
20+ 10(3.4) = 54
Using the formula for number of revolutions,
Number of revolutions = 54/2π
Number of revolutions = 8.4
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you play a sine wave from an omnidirectional speaker in the middle of an empty field. the power from the speaker at a certain distance d from the speaker varies proportional to which exponential power of d?
Exponential power refers to the power to which a base number (often represented as "e") is raised.
Exponential power is used to represent exponential functions, which describe growth or decay over time, among other things.
For example, the exponential power of d can be used to describe how a quantity changes with increasing d.
When the exponential power of a variable is negative, the quantity decreases with increasing the variable; when it's positive, the quantity increases.
Exponential functions can also be represented as exponential series, which are infinite sums of increasing powers of the base number e.
These series can be used to approximate functions that are otherwise difficult to solve exactly, or to represent functions with properties that are difficult to obtain using other methods.
Exponential powers are an important part of mathematics and are widely used across a range of scientific and engineering fields. Understanding exponential powers is essential for solving many problems and analyzing complex systems in a variety of disciplines.
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When a swimmer stands on a high diving board, he has 5800 J of PE relative to the surface of the water. What is his PE and KE the instant he steps off the board when he is half way to the water just before he hits the water
(a) When the swimmer steps off the diving board, his initial PE is 5800 J and his initial KE is zero.
(b) At the instant he is half way to the water just before he hits the water, then PE = KE = 0.5 * 5800 J = 2900 J.
The conservation of energy principle states that the initial potential energy (PE) plus the initial kinetic energy (KE) is equal to the final PE plus the final KE. When the swimmer steps off the diving board, his initial PE is 5800 J and his initial KE is zero.
As he falls towards the water, some of his potential energy is converted into kinetic energy (KE = 1/2 mv²). At the instant he is half way to the water just before he hits the water, half of his initial PE has been converted into KE, so his PE and KE are both equal to half of his initial PE:
PE = KE = 0.5 × 5800 J = 2900 J
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how does a change in electrical potential energy from –4 j to –7 j reflect on the stability of a system?
The system has grown more stable when the potential energy drops. Remember that negative numbers are more negative and have a lower value when their absolute values are larger than when they are less.
Electric potential V is given as potential energy per charge.
Mathematically, V = PE/q
where, q is charge
PE is potential energy
The work done on q by the electrostatic or Coulomb force is independent of the direction taken because it is a conservative force. The gravitational force in the absence of dissipative forces like friction is exactly identical to this. When a force is conservative, it is possible to define a potential energy that goes along with the force. Because the potential energy varies solely on position, managing it is typically simpler than calculating the work directly.
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8. A 50.0 kg woman, riding on a 10 kg cart, is moving east at 5.0 m/s. The woman jumps off the front of the cart and lands on the ground at 7.0 m/s eastward. What is the final velocity of the cart
Answer:
To find the final velocity of the cart, we can use the conservation of momentum principle. Momentum is defined as mass times velocity, and in an isolated system, the total momentum before an event equals the total momentum after the event.
Before the woman jumps off the cart, the total momentum of the system is (50 kg)(5 m/s) = 250 kg m/s. After the woman jumps off, the total momentum of the cart is (10 kg)(v), where v is the final velocity of the cart.
Using the conservation of momentum principle, we can write the following equation:
(50 kg)(5 m/s) = (10 kg)(v) + (50 kg)(7 m/s)
Solving for v, we get:
v = (250 kg m/s - (50 kg)(7 m/s)) / 10 kg
v = -25/10
v = -2.5 m/s
So the final velocity of the cart is -2.5 m/s (westward direction)
a solenoid has 21 turns per centimeter of its length. the solenoid is twisted into a circle so that it becomes shaped like a toroid. what is the magnetic field at the center of each turn of the toroid? the current is 57 ma m a .
The magnetic field is 228π x 10⁻¹⁰ T.
To calculate the magnetic field at the center of each turn of the toroid, we can use the formula for magnetic field produced by a solenoid:
B = μ x n x I / L
where:
B is the magnetic field
μ is the magnetic constant
n is the number of turns per unit length of the solenoid
I is the current flowing through the solenoid
L is the length of the solenoid
For the toroid, we need to find the magnetic field at the center of each turn. We can assume that the number of turns per unit length is equal to the number of turns per centimeter of the original solenoid.
So, substituting the given values:
B = (4π x 10⁻⁷) x 21 turns/cm x 57 x 10⁻³ A / 1 cm = 228π x 10⁻¹⁰ T.
Magnetic field is a field that surrounds a magnetic object and influences the behavior of moving charges within it. It is characterized by its direction and magnitude, and it can be represented by magnetic field lines. The magnetic field is proportional to the amount of current flowing through a conductor or a wire, and it can also be created by moving charged particles.
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what is the rms current in an rl circuit when a 50.0 hz 120 v rms ac voltage is applied, where r = 1.20 kω , and l = 370 mh ?
The RMS current in an RL circuit when 50 hertz 120 volts RMS ac voltage is applied is 82.68 mA
RMS or root mean square current/voltage of the alternating current/voltage represents the d.c. current/voltage that dissipates the same amount of power as the average power dissipated by the alternating current/voltage. For sinusoidal oscillations, the RMS value equals peak value divided by the square root of 2.
Inductive reactance
XL= 2xpixfxL
=2pix50x0.37
XL=116.24 ohms
Impedance
Z= √[R^2+XL^2] =√[2900^2+116.24^2]
Z=2902.35 ohms
Rms current
I,rms=V,rms/Z
=240/2902.35
I,rms=0.08268 A or 82.68 mA.
Therefore , The RMS current in an RL circuit when 50 hertz 120 volts RMS ac voltage is applied is 82.68 mA
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With the settings used in the simulation, you were unable to produce the 1st harmonic in either Part A or Part B. Why not? What specific changes to the simulation settings would enable you to see the 1st harmonic in each part? Write out your answer in a clear and well supported paragraph. Is the speed of the wave constant in Parts A and B? How did you determine this for each part? If the speed is not constant, how does it change as a function of harmonic number? Write out your answer in a clear and well supported paragraph.
insufficient data or simulation software constraints If the medium is heterogeneous or anisotropic, the wave's speed can change with harmonic number to produce the first harmonic in a simulation.
Numerous factors, such as improper simulation settings, software restrictions, or insufficient data, could prevent a simulation from producing the first harmonic. The simulation settings must be configured to accurately resolve the first harmonic frequency in order to produce the first harmonic in a simulation. This can be accomplished by changing parameters like the simulation's time step size, frequency range, or number of harmonics.
The medium through which the wave is propagated determines the wave's speed. travelling as well as the characteristics of that medium, such as its elastic modulus and density. The wave's speed is constant for each harmonic if the medium is homogeneous and isotropic. However, the wave's speed can vary with harmonic number if the medium is heterogeneous or anisotropic. In order to calculate the speed using the equation v = f,
where v is the speed, f is the frequency, and is the wavelength, the frequency and wavelength of the wave in Parts A and B must be measured.
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7. Two campers dock a canoe. One camper steps onto the dock. This camper has a mass of 80 kg and moves forward at 4.0 m/s. With what speed and direction do the canoe and the other camper move if their combined mass is 110 kg?
Answer:
Explanation:
Ths question is about conservation of momentum. The momentum of the camper on the dock is the same as the momentum of the other camper and the canoe.
[tex]m_1v_1=m_2 v_2[/tex]
[tex]80 kg . 4.0 m/s = 110 kg . v_2[/tex]
[tex]v_2 = \frac{320 kgm/s}{110 kg}[/tex]
[tex]v_2 = 2.9 m/s[/tex]
The canoe will move backward (away from the dock) at 2.9 m/s
as seen from the earth, what was the angle between the direction to the sun and the direction to mars on december 3, 1999?
On December 3, 1999, the angle between the direction to the sun and the direction to Mars, as seen from the Earth, was approximately 26.6 degrees.
The angle between the direction to the Sun and the direction to Mars from the Earth is determined by the relative positions of Earth and Mars in their respective orbits. On December 3, 1999, Mars was at opposition, meaning that it was on the opposite side of the Sun from Earth. At this time, the angle between the two was approximately 26.6 degrees.
The angle between the two changes over time, depending on the relative positions of Earth and Mars. When the two planets are on the same side of the Sun, the angle between them is at a minimum, and when they are on opposite sides of the Sun, the angle between them is at a maximum. This is why the angle between the two is always changing and is never exactly the same.
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a karate expert breaks a pine board, 2.2 cm thick, with a hand chop. strobe photography shows that his hand, whose mass may be taken as 580 g, strikes the top of the board with a speed of 9.5 m/s and comes to rest 2.8 cm below this level. (a) calculate the time duration of the chop (assuming a constant force). (b) calculate the average force applied.
A) The time duration of the chop 5.8 millisecond.
B) The applied average force Fav would be 830 N.
What is Velocity ?Velocity is a vector quantity that describes the rate of change of an object's position. It is equal to the displacement of an object divided by the time interval over which the displacement occurred. Velocity has both magnitude and direction, and its units are typically meters per second (m/s). The velocity of an object can change over time due to acceleration, and if an object is moving in a circular path, it also has a component of velocity perpendicular to its direction of motion, known as centripetal velocity.
a) The average speed Vav during the time the hand is in contact with the board is half of the initial speed.
Thus, Vav = (9.5 m/s) /2
= 4.8 m/s
To obtain the time duration t of the chop, substitute 2.8 cm for y and 4.8 m/s for vav
in the equation t=y/ Vav,
t=y/ Vav
=(2.8 cm)/(4.8 m/s)
= (2.8 cm×10⁻² m/1 cm)/(4.8 m/s)
= 5.8×10⁻³ s
= (5.8×10⁻³s) (1 ms/10⁻³s)
= 5.8 ms
Therefore the time duration t of the chop will be 5.8 ms.
b.
To obtain the applied average force Fav, substitute 5.1 N.s for J and 5.8 ms for t in the equation Fav = Jlt,
Fav=Jlt
=(5.1 N.s)/(5.8 ms)
=(5.1 N.s)/(5.8 ms×10⁻³s/1 ms)
= 880 N
From the above observation we conclude that, the applied average force Fav would be 830 N.
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a truck with a mass of 2400 travels at a constant speed of 90 km/hr. what average force would be required to stop the truck in 8 seconds?
We need a force of 7500 in the opposite direction of the motion of the truck.
According to the first equation of motion
V= U + a t
t = time taken
V= final velocity =0 (as truck will come to rest)
U = initial velocity = 90 km/hr = 25 m/sec
a = acceleration
a= V- U / t
a = 0- 25 / 8
a = - 3.125 m/[tex]sec^{2}[/tex]
According newtons second law
F= m a
F = 2400 (- 3.125 m/[tex]sec^{2}[/tex])
F= - 7500 Newton
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two bodies begin a free fall from rest from the same height 1.0 seconds apart. how long after the first body begins to fall will the two bodies be 10 m apart?
One second apart, two bodies start free falling from the same height after coming to rest. When the two bodies are 10 m apart, the first body will start to fall, taking 1.73 seconds.
To solve this problem, we will use the equation for the acceleration due to gravity, which is a = g = 9.8 m/s2. We can use this equation to calculate the time it will take for the first body to fall 10 m, starting from rest.
The equation for distance travelled (s) due to a constant acceleration (a) is
s = ut + 0.5at2
Where u is the initial velocity (in this case, 0 m/s) and t is the time taken.
Putting values, we get
10 = 0 + 0.5 x 9.8 x t2
Solving for t, we get
t = √(20/9.8) = 1.73 s
Therefore, it will take 1.73 seconds for the first body to fall from a height 10 m, starting from rest.
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what is the gauge pressure inside the reservoir? express your answer with the appropriate units.
The difference between the inner and external pressures is measured by the pressure gauge on a reservoir. When the oxygen (O2) tank is full, it holds 12.0 kg of the gas at a gauge pressure of 40 atm.
The oxygen (O2) tank holds 12.0 kg of the gas at a gauge pressure of 40 atm when it is fully filled. Gauge pressure is the common name for this type of reading since the gauges measure pressure in relation to atmospheric pressure, which serves as the zero point. However, anything that is not a complete vacuum is considered to be under some type of pressure. In daily life, gauge pressure is frequently utilized. Tire pressure, for instance, is assessed in relation to atmospheric pressure. When an automobile ascends a mountain, the gauge pressure rises as the air pressure falls, but it is assumed that the tire's absolute pressure stays constant.
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Let the angle be the angle that the vector A makes with the +x-axis, measured counterclockwise from that axis. Find the
angle for a vector that has the following components.
Ax=1.50, Ay=1.30
The angle formed by the vector and the positive or counterclockwise of x-axis is 40.91°
What are Vectors ?The term "vector" is used informally to describe constituents of particular vector spaces or some values that cannot be described by a single integer.
A quantity or phenomena with independent qualities for both size and direction is called a vector. The word can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
Any vector with a two-dimensional direction may be conceived of as having two distinct parts. The impact of a single vector in a certain direction is described by its component.
The components are
Aₓ = 1.50
Ay = 1.30
We can find the angle of the vector by using the formula
[tex]tan\theta = \frac{A_{y} }{A_{x} }[/tex] = [tex]\frac{1.30}{1.50} =[/tex]
⇒[tex]\theta = tan\x^{-1}(1.3/1.5)[/tex]
⇒θ = 40.91°
The angle formed by the vector and the positive or counterclockwise of x-axis is 40.91°
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g an insulating rod is positively charged, and an electrically neutral conducting sphere is mounted on an insulating stand. the rod is brought near to the sphere on the left, but they never actually touch. which image that best represents the resulting charge distribution on the conducting sphere?
The image where the rod is held near to the left side of the sphere on the stand, making the left side of the sphere become positively charged, best represents the resulting charge distribution on the conducting sphere.
Since the rod is too far away to contact the remaining portion of the sphere, it will remain neutral. The electrons in the sphere's substance will be drawn away from the positive charge on the left side of the sphere, leaving a region of positive charge there. The electrons will stay put on the right side of the sphere, creating a neutral charge there.
The image is provided below
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suppose that yesterday you had a mass of 50.0 kg. this morning you stepped on a scale and found that you had gained weight. what happened, if anything, to your mass? what happened, if anything, to the ratio of your weight to your mass?
If you gained weight, your mass increased. The ratio of your weight to your mass would have increased as well, since weight is directly proportional to mass.
Weight is the force of gravity on an object, and is equal to the mass of an object multiplied by the acceleration due to gravity. Therefore, if the mass of the object increases, the weight of the object increases as well.
Additionally, the ratio of weight to mass will increase as the mass increases. Since weight is directly proportional to mass, as the mass increases, the ratio of weight to mass will increase as well. This is because when the mass is larger, the weight of the object will be greater compared to its mass.
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the escape velocity from earth at point a is 5.6 km/s. how far is point a from the earth center? the earth's escape velocity at its surface is 11.2km/s and the radius of the earth is r km. group of answer choices 4r km r/4 km r/2 km 2r km
The escape velocity is 5.6 km/s at a point 4R kilometer from the center of the Earth, if R is the radius of the Earth.
Escape velocity is formulated as: v = √(2GM/R)
Escape velocity at the surface of the Earth, v₁ = 11.2 km/s
Let at the height of h km the escape velocity, = 5.6 km/s
Let the radius of the Earth = R
v² = 2GM/R
11.2² = 2GM/R....equation (1)
5.6² = 2GM/h....equation (2)
On dividing equation (1) by equation (2)
11.2²/5.6² = [2GM/R]/[2GM/h]
125.44/31.36 = h/R
h = 4R
Hence option A is correct.
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--The given question is incomplete, the complete question is:
"The escape velocity from earth at point a is 5.6 km/s. how far is point a from the earth center? the earth's escape velocity at its surface is 11.2km/s and the radius of the earth is r km. group of answer choices are A) 4R km B) R/4 km C) R/2 km D) 2R km"--
process of an object changing position from one location
to another
location of an object within a physical frame of reference
set of points or objects used to determine relative
movement
measure of the total pathway taken between two points
linear distance and direction between two points of
reference
size of a quantity
quantities that are described by magnitude alone
quantities that are described by both magnitude and
direction
[Choose ]
[Choose]
[Choose ]
Distance
[Choose]
[Choose ]
[Choose ]
[Choose]
The answers include the following:
The process of an object changing position from one location to another - MotionThe location of an object within a physical frame of reference - Reference frameSet of points or objects used to determine relative movement - Reference pointMeasure of the total pathway taken between two points - DistanceLinear distance and direction between two points of reference - PositionSize of a quantity - measurementQuantities that are described by magnitude alone - scalar Quantities that are described by both magnitude and direction - vectorWhat is a Scalar quantity?This is referred to as quantities that are fully described by a magnitude (or numerical value) alone while on the other hand vector quantity is described by both magnitude and direction.
Reference point is referred to as the set of points or objects used to determine relative movement.
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As Column A gets heated, what happens to the ball?A. It moves left along the beamB. It falls straight down from its current positionC. It moves right along the beamD. Nothing(look figure)
As Column A gets heated, the balI moves left along the beam. The solid ball cannot fit through the ring because it grows larger and expands when heated.
Heat causes a substance's molecules and atoms to vibrate more quickly. Atoms that vibrate more swiftly separate themselves from one another. The state of matter of a substance is determined by the velocity and spacing of the particles. The thing finally grows and takes up more space as a result of increased molecular mobility. Heat causes the molecules in the thermometer's red liquid to flow more swiftly. This movement causes the molecules to spread out a little bit further, which competes with their mutual attractions. They can only get out by climbing the tube.
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explain why the air bubble moved up the capillary tube.
Air bubbles move up in the capillary tube due to the upward buoyant force applied by the water on bubbles.
According to the Archimedes' principle, when an object floats in a liquid, it experiences an upward exerted by the liquid. This force is equal to the weight of the liquid displaced by the volume of the floating or sinking object.
When air bubbles are present in capillary tube, then the upward force exerted by the water on bubbles is more than the weight of the air bubbles, as the density of the air is very less than that of the water. That's why the air bubbles move up in capillary tube.
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assume that the starting temperature of the metal is -18ºc (or 0ºf); show all calculations.
The starting temperature of the metals is -18ºc (or 0ºf) then
255.37222222 K is Celsius to Fahrenheit
-17.77777778ºc is Fahrenheit to Celsius
1. Fahrenheit to Celsius:
To convert from Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature, then divide by 1.8.
To convert from Celsius to Fahrenheit, you need to use the following formula:
F = (C x 1.8) + 32
To convert -18ºC to Fahrenheit:
F = (-18 x 1.8) + 32
F = 0ºF-18ºc = 0ºf
0ºf - 32 = -32
[tex]\frac{-32 }{ 1.8} = -17.77777778ºc[/tex]
-17.77777778ºc is the temperature of metal at Fahrenheit to Celsius
2. Celsius to Kelvin:
To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature.
[tex]-17.77777778ºc + 273.15 = 255.37222222 K[/tex]
255.37222222 K is the temperature of metal at Celsius to Kelvin.
The temperature of metal varies depending on the type of metal in question. Most metals have a melting point between 1,000 and 1,500 degrees Fahrenheit (538 and 816 degrees Celsius).
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which is correct in reference to electrical resistance? group of answer choices two electrical devices will have the same combined resistance if they are connected in series as they will have if connected in parallel. if one of three bulbs in a parallel lighting circuit is removed, the total resistance of the circuit will become greater. an electrical device that has a high resistance will use more power than one with a low resistance with the same applied voltage.
The correct statements are;
If one of three bulbs in a parallel lighting circuit is removed, the total resistance of the circuit will become greater. An electrical device that has a high resistance will use more power than one with a low resistance with the same applied voltage.What is electrical resistance?Electrical resistance is the measure of a material's opposition to the flow of electric current, resulting in energy loss as heat.
We have to note that the resistance of the object would determine the magnitude of the electrical current that can be able to pass through the material.
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22r6 r2⇒r2 is used to transform a matrix. determine the row operation that will transform the matrix back to its original form. use r1, r2, etc. to represent the rows r1, r2, etc.
Row operation 22R6 + R2 R2 changes the matrix by adding row 6 to row 2 twice. To reverse this procedure and restore the matrix to its original shape, subtract row.
6 twice from row 2. This can be written as: -22R6 + R2 ⇒ R2 As a result, the row operation that will return the matrix to its original form is: -22R6 + R2 ⇒ R2 This procedure can be used to reverse the results of the previous operation and restore the matrix to its original state. 22r6 r2⇒r2 is used to transform a matrix. determine the row operation that will transform the matrix back to its original form. use r1, r2, etc. to represent the rows r1, r2, etc. Row operation 22R6 + R2 R2 changes the matrix by adding row 6 to row 2 twice. To reverse this procedure and restore the matrix to its original shape, subtract row.
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a point charge of 8.00×10−12 c is located at the center of a cubical gaussian surface. what is the electric flux φface through each face of the cube?
When a point charge of 8.00×10−12 c is located at the center of a cubical gaussian surface, 143.84 x 10^3 is the electric flux φface through each face of the cube.
The electric flux through a face of a cube is given by the product of the electric field and the area of the face. The electric field due to a point charge can be calculated using Coulomb's law:
=> E = k x Q / r^2
here,
E is electric field,
k is C constant (8.99 x 10^9),
Q is charge,
r is distance from the point charge to the surface,
In this case, the charge is
= 8.00 x 10^-12 C
and the distance from the point charge to the surface is equal to half the length of one side of the cube,
So, r = a/2
here,
a is length of a side of the cube.
The area of one face of the cube is a^2,
The electric flux of face is:
=> φface
= E x a^2
= k x Q / (a/2)^2 x a^2
= 2k x Q / a^2
Since there are six faces of the cube in the total electric flux is:-
=> φtotal
= 6 x φface
= 6 x 2k x Q / a^2
adding values, we get:
=> φtotal
= 6x2x8.99 x 10^9 Nm^2/C^2 x 8.00 x 10^-12 C / (a/2)^2
The electric flux of each face is :-
=> φface
= φtotal / 6
= 2 x 8.99 x 10^9 Nm^2/C^2 x 8.00 x 10^-12 C / a^2
= 143.84 x 10^3
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The center of the moon is 0.0026 AU (3.890 x 10⁸ m ) from the center of the Earth and has a relative mass of 0.0123. (a) Locate the cm of the Earth-Moon system with respect to the center of the Earth. (b) With respect to the center of the Moon. (c) Find the ratio of orbital velocities of the Earth and Moon about the cm of the system. (d) If the orbital velocity of the Moon is 1012 m/s , what is the approximate orbital velocity of the Earth about the cm of the Earth-Moon system? .
A) centre of mass will be 3.843 x 10⁸ m from the centre of moon
B) r₁ = 3.843 x 10⁸m
r₂ = 0.047 x 10⁸ m
C) Ve /Vm = 0.01226
A) Let the centre of moon be considered as point of origin.
therefore centre of mass = Mm x 0 + Me x 3.89x 10⁸/ Mm + Me
Mm = mass of moon
Me = mass of earth
Mm = 0.0123 Me
Centre of mass = 3.89 x 10⁸ / 1.0123 m
So centre of mass will be 3.843 x 10⁸ m from the centre of moon or it will be at a distance of 0.00256 Au from the centre of the moon.
B) For moon G Mm Me /r² = Mm Vm² /r²
For earth G Mm Me / r² = Me Ve² / r₂²
r₁ = 3.843 x 10⁸m
r₂ = 0.047 x 10⁸ m
C) Mm Vm² / r₁ = Me Ve² / r₂
(Ve/Vm)² = Mm r₂ / Me r₁
Ve/Vm =√ 0.047 x 0.0123/ 3.843
Thus Ve /Vm = 0.01226
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A) centre of mass will be 3.843 x 10⁸ m from the centre of moon B) r₁ = 3.843 x 10⁸m r₂ = 0.047 x 10⁸ m C) Ve /Vm = 0.01226 A) Let the centre of moon be considered as point of origin.
therefore centre of mass = Mm x 0 + Me x 3.89x 10⁸/ Mm + Me Mm = mass of moon Me = mass of earth Mm = 0.0123 Me Centre of mass = 3.89 x 10⁸ / 1.0123 m So centre of mass will be 3.843 x 10⁸ m from the centre of moon or it will be at a distance of 0.00256 Au from the centre of the moon. B) For moon G Mm Me /r² = Mm Vm² /r² For earth G Mm Me / r² = Me Ve² / r₂² r₁ = 3.843 x 10⁸m r₂ = 0.047 x 10⁸ m C) Mm Vm² / r₁ = Me Ve² / r₂ (Ve/Vm)² = Mm r₂ / Me r₁ Ve/Vm =√ 0.047 x 0.0123/ 3.843 Thus Ve /Vm = 0.01226 The center of the moon is 0.0026 AU (3.890 x 10⁸ m ) from the center of the Earth and has a relative mass of 0.0123. (a) Locate the cm of the Earth-Moon system with respect to the center of the Earth. (b) With respect to the center of the Moon. (c) Find the ratio of orbital velocities of the Earth and Moon about the cm of the system. (d) If the orbital velocity of the Moon is 1012 m/s , what is the approximate orbital velocity of the Earth about the cm of the Earth-Moon system
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Three horizontal force are pulling on a ring, at ret. F1 i 6. 25 N at a 180 angle, and F2 i 8. 90 N at a 2430 direction. What i the y-component of F3?
According to the question of force, the y-component of F3 is -2.719 N.
What is force?
Force is a fundamental concept in physics that describes the interaction between two objects or systems. It is a vector quantity, meaning it has both magnitude and direction, and can be described mathematically. Force is a push or pull that can cause an object to accelerate, change its direction, or change its shape. Force is a function of mass and acceleration, as described by Newton's second law of motion.
The y-component of F3 can be calculated using the equation F3y = F1y + F2y. Since F1 is at a 180° angle, its y-component is 0. The y-component of F2 can be calculated using the equation F2y = F2 × sin(θ), where θ is the angle of F2. In this case, θ is 2430°, so the y-component of F2 is 8.90 × sin(2430°) = 8.90 × -0.3105 = -2.719 N. Therefore, the y-component of F3 is -2.719 N.
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what is the dirction and magnitude of the angular momentum vector of an irregular object in free fall
The angular momentum vector of an irregular object in free fall direction will be perpendicular to the plane of rotation and Magnitude depends on mass distribution and rotation speed, constantly changing in free fall.
When an irregular object is in free fall, its angular momentum vector is perpendicular to the plane of rotation and its magnitude is determined by its mass distribution and its rotational speed.
Since an object in free fall is constantly changing its velocity, the magnitude of its angular momentum is also constantly changing. It is important to take this into consideration when attempting to calculate the angular momentum vector of an object in free fall, as its direction and magnitude will be constantly shifting.
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