Since light travels at a finite speed, if we witness an object 13 billion light years distant, the light has been moving in our direction for 13 billion years. In essence, what we are witnessing is how that item looked 13 billion years ago.
The cosmos is 13.7 billion years old, but how can we know this?
Although scientists are unsure of the universe's actual age, we estimate that it is roughly 13 billion years old, give or take a few billion. Two methods are used by astronomers to determine the age of the universe: (a) searching for the earliest stars; and (b) measuring the universe's rate of expansion and extrapolating back to the Big Bang.
The age of the universe is 13.8 billion light-years?
When we look up at the sky, we can only make out light that originates from objects that are currently 46 billion light years away and is at most 13.8 billion years old. Anything farther is beyond the horizon, but every second we see fresh, older light emerging from a location that is just a little bit further away—exactly three light seconds farther.
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If a man hoot a pear at a place where he ee the fih inide water i it poible that it will hit the fih?
The pear will not hit the fish where he eyes the fish in the water.
Please note that fish in the water will not be the same as what our eyes see. Where the location of the position will be different because it follows the refraction of light obtained so that it can be concluded that the position of the fish is not the actual position. The fish swims forward and the shooter looks at the water from above as if the fish is looking up.
This event is caused by the process of refraction of light. Refraction is the deflection of the direction of propagation of light when it enters a medium of different densities.
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2. a student places an object with a mass of m on a disk at a position 0.2m from the center of the disk. the student starts rotating the disk. when the disk reaches a speed of 0.8 m/s, the object starts to slide off the disk. what is the coefficient of static friction between the object and the disk? (4 pts)
The coefficient of static friction when the speed of the disk is given, is calculated to be 0.065 / r.
The maximum velocity of an object moving in a curve beyond which it will slide off the curve is given by the relationship,
v = √(μ* g* r) ----(1)
where is the coefficient of friction between the object and the surface of the curve, g is acceleration due to gravity and r is the radius of the curve.
Given that,
v = 0.8 m/s
g = 9.8 m/s²
r = ?
μ = ?
Making μ as subject, we have,
μ = v²/(g*r) ----(2)
As we were not given the value of r, we can just substitute other known values, then solve and leave the answer in terms of r.
μ = (0.8)²/(9.81* r) = 0.64/ (9.81* r) = 0.065 / r
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where are elliptical galaxies most likely to be found? in the central regions of clusters on the outskirts of clusters in small clusters in between clusters
Elliptical galaxies most likely to be found in the central regions
Galaxies with an elliptical form are known as elliptical galaxies. Since an ellipse has an oval shape, these galaxies also have an oval shape. Elliptical galaxies are those with little to no gas and dust. The elliptical galaxies are the most abundant type of galaxies. Elliptical galaxies are most likely to be found in the central regions of galaxy clusters. Galaxy clusters are large groups of galaxies that are bound together by gravity and are some of the largest structures in the universe.
Elliptical galaxies are characterized by a lack of distinct features, such as spiral arms or a visible nucleus. These galaxies are thought to have formed through the merger of smaller galaxies and are generally found in high-density environments such as the centres of galaxy clusters. They are less common on the outskirts of galaxy clusters and are rarely found in small clusters or in between larger clusters.
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if particle 3 is of unknown charge is to be located such that the net electrostatic charge from particles 1 and 2 is zero, what must be the x and y coordinates
For the distance between q 3 and q 1, the formula is: = 3 L 0 = 3 1 L = 3 1 10 cm 14 cm. Q3 should therefore be positioned at x=14 cm along the x-axis.
For q 3, there is no equilibrium position.
between two fixed changes because one is pulling it and the other is pushing it
L is set at 10 cm, and L 0 is taken to be positive. We cancel k and q 3 and set this equal to zero as the problem specifies. As a result, we get L 0.
∣q 1\s\s ∣\s\s − \s(L+L \s0\s\s)\s∣q \s2\s\s ∣\s\s =0 ⇒(\sL \s0
L+L \s0\s
\s ) \s2\s = \s∣\s∣\s∣\s∣\s∣\s
q \s1\s
q \s2\s
∣\s∣\s∣\s∣\s∣\s\s = \s∣\s∣\s∣\s∣\s∣
+1.0 μC\s−3.0 μC
=3.0 results in L 0 after taking the square root.
L+L \s0\s
For the distance between q 3 and q 1, the formula is: = 3 L 0 = 3 1 L = 3 1 10 cm 14 cm. Q3 should therefore be positioned at x=14 cm along the x-axis.
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The gravitational force of a lunar rover is 1,607.2 Newtons on Earth. What will the rover’s gravitational force be on the Moon?
On Earth, g = 9.8m/s2.
On the Moon, g = 1.62 m/s2.
Answer: Fg = 265.68 N
Explanation:
Fg = m * g
m = Fg / g
m = 1607.2 N / 9.8 m/s^2
m = 164 kg
Fg = m * g
Fg = 164 kg * 1.62 m/s^2
Fg = 265.68 N
you're in a boat with a big rock, in a swimming pool. you toss the rock overboard. what happens to the level of the water in the pool?
You're in a boat with a big rock, in a swimming pool. You toss the rock overboard. Level of water will increase as of the mass of big rock to the level of the water in the pool.
The buoyancy of any floating object partially or totally submerged in a fluid can be computed thanks to Archimedes' principle. The weight of the thing alone exerts a downward mass on it. The upward or buoyant force acting on the object is what is meant by the aforementioned Archimedes' principle. The difference between the buoyant force and the object's weight is therefore the net force acting on it. In the event that this net force is positive, the item will rise; in the event that it is negative, the object will sink; and in the event that it is zero, the object will be neutrally buoyant, remaining stationary. Simply said, when a body is partially or entirely submerged in a fluid, the Archimedes' principle applies. Consider a cuboid submerged in a fluid, with its top and bottom facing in the direction of gravity, which is considered to be constant throughout the length of the cube. Each face of the fluid will experience a normal force, but only the normal forces on the top and bottom will result in buoyancy. The height directly affects the pressure difference between the top and bottom faces (difference in depth of submersion). A net force on the cuboid is created by multiplying the pressure difference by the area of a face.
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A ball is kicked with an initial horizontal velocity of 3.6 m/s off of a 19.6 m cliff. How
far away will the ball land from the cliff?
If a ball is thrown at an initial horizontal velocity of 3.6 meters per second off of a cliff that is 19.6 meters high, it will land 35.28 meters away from the cliff.
What is velocity?The vectoral expression of a particle and object's motion with respect towards time is called its velocity. The recognized unit for measuring magnitude of velocity is indeed the meters per second (m/s), which is frequently referred to as speed. Velocity is the rate at which an object's position is changing as perceived from a particular point of view and so as measured by a certain unit of time. It refers to the direction speed of the an object in motion.
How do you calculate velocity?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Speed in the SI is expressed in m / sec. The average speed (S) is calculated using the equation S = d/t, where d is the entire distance traveled and t denotes the total time. One can determine an object's beginning velocity by dividing the time it took the thing to go a specific distance by the total distance.
Briefing:D = (1/2) gt2 where g = 9.8 m/s2
It takes time to descend the 19.6-meter cliff.
19.6 = 1/2(9.8)t2
19.6/4.9 = t2
Square root 90.4 = about 9.8 sec.
3.6 m/s x 9.8 sec = 35.28 m
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calculate the work done on a 1500 kg elevator by its cable to lift it 40 m at a constant speed and friction
Work done on a 1500kg elevator by its cable to lift it 40m at a constant speed is 592000N.
The work done by a force is calculated as the product of the force(F) and the displacement of the object on which the force is acted.
Work done = F×d
downward forces are weight of lift and frictional force
upward force is only tension of string.
T = Frictional force + Mg
Mg = 1500× 9.8 = 14700N
given frictional force is 100N
So, Tension in string = (100+ 14700) N
= 14800N
work done by tension in lifting = tension force ×
displacement of lift
= 14800 × 40
= 592000N.
hence, work done on a 1500 kg elevator by its cable to lift it 40m at a constant speed is 592000N.
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Which of the following is a true statement?
14) (10 pts) a series lr circuit contains an emf source of having no internal resistance, a resistor, an inductor having no appreciable resistance, and a switch. i) (6 pts) if the emf across the inductor is of its maximum value after the switch is closed, what is the resistance of the resistor?
The resistance of the resistor is 1.8Ω
Consider the voltage across the inductor 4 sec after the switch is closed is V(4)
The voltage across the inductor 4 sec after the switch is closed is 80% of its maximum value, i.e., V(4)=0.8[tex]V_{0}[/tex]
Consider the expression for the voltage across the RL circuit.
V(t)=[tex]V_{0}e-\frac{t}{T}[/tex]
Where [tex]V_{0}[/tex] is the maximum voltage, t is the time, V(t) is the voltage at time
t and T is the time constant.
Substitute the values of ,[tex]V_{0}[/tex], V(t) and t in the above expression.
[tex]$$\begin{aligned}0.8 \mathrm{~V}_0 & =\mathrm{V}_0 \times \mathrm{e}^{-\frac{4}{\tau}} \\0.8 & =\mathrm{e}^{-\frac{4}{\tau}} \\\frac{1}{0.8} & =\mathrm{e}^{\frac{4}{\tau}}\end{aligned}$$[/tex]
Take natural log on both the sides.
[tex]$$\ln \left(\frac{1}{0.8}\right)=\frac{4}{\tau}$$[/tex]
Rearrange the above expression.
[tex]$$\begin{aligned}\tau & =\frac{4}{\ln \left(\frac{1}{0.8}\right)} \\& =17.9 \mathrm{~s}\end{aligned}$$[/tex]
Now consider the expression for time constant.
[tex]$$\tau=\frac{\mathrm{L}}{\mathrm{R}}$$[/tex]
Where R is the inductance and L is the resistance.
Rearrange the above expression.
R = [tex]\frac{L}{T}[/tex]
Substitute the values of T and L in the above expression.
[tex]R=\frac{34}{17.9}\\ R=1.8[/tex]Ω.
Therefore, the resistance of resistor is 1.8Ω
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Calculate the work done by the electrostatic field in moving a charge of 2 coulomb from one point to another, if the potential of the first point is 20V, and the second - (5V)
Answer:
To calculate the work done by the electrostatic field in moving a charge from one point to another, you can use the formula:
work = charge * (final potential - initial potential)
In this case, the charge is 2 coulombs, the initial potential is 20V, and the final potential is -5V. Plugging these values into the formula, we get:
work = 2 coulombs * (20V - (-5V))
= 2 coulombs * (25V)
= 50 Joules
Therefore, the work done by the electrostatic field in moving the charge from one point to another is 50 Joules.
patricia places an electrically charged object next to an uncharged object to see what will happen. for her experiment, what control does she need?
A negative object so it takes in the charge object and nothing will happen until something else would touch it.
what is the charge?Electric charge is the property of a material that makes it feel a force when subjected to an electromagnetic field. Protons and electrons most typically carry positive and negative charges, which are the two forms of electric charges.
What does "unit of charge" mean?The basis of the SI system of physical units is the coulomb It is referred to as C. A coulomb is the unit of power that a one-ampere current can carry in one second.
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an object has a kinetic energy of 36.0 j. an object with three times the mass moving at the same speed will have a kinetic energy of
The kinetic energy of another body having three times the mass of the given object will be 108 J
Kinetic energy-In physics, the kinetic energy of an object is the energy it has due to motion. It is defined as the work required to accelerate a body from a given mass from rest to a specified speed.
The kinetic energy of a body is given by [tex]K.E= \frac{1}{2}Mv^{2}[/tex] (first equation)
Given K.E= 36J
Now the mass of second body is m=3M
also the second body is moving with the same speed v
So kinetic energy of second body K.E₂= [tex]\frac{1}{2}mv^{2} =\frac{1}{2}(3M)v^{2}[/tex]=36×3
=108J (from first equation)
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8) why can we not determine distances to galaxies by the same method used to measure the parallaxes of stars?
They are so distant that the parallax is too small to be measured since parallax varies inversely with distance.
Parallaxes can be measured accurately out to distances of approximately 100 light-years. The nearest galaxies are about 50,000 to 80,000 light-years from the Sun. Therefore, there is no perceptible change in the apparent position of any galaxy as we view it from opposite sides of Earth's orbit.
Because of the influences of the Earth's atmosphere, it is highly challenging to estimate parallax angles of less than 0.01 arcsec from Earth. Due to this, telescopes on Earth can only measure the distances to stars that are 1/0.01 or 100 parsecs distant.
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a metal crystal is made up of metal ions held together by an ""electron sea"" of valence electrons. why does this configuration make metals good electrical conductors?
The motion of the free electron sea causes the electrical conduction.
Metals that are near to one another have valence electrons that do not only remain on their own atom but also easily migrate throughout the entire metal complex. They seem to be floating through an sea of electrons, like a solitary water molecule floating freely in the sea. For this reason, it is often referred to as the electron sea model.
These atoms become positively charged cations because each metal atom is free to move around. These cations resemble a positively charged island because they are encircled by a sea of negatively charged electrons. Because of these free-moving electrons, metal is a good conductor of electricity.
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a wire carries an electric current straight upward. what is the direction of the magnetic field due to the current north of the wire
The current north of the wire fliws upwards as of the electric current straight upward.
The proper-hand thumb rule suggests the path of the magnetic area for a recognise path of the modern-day. If the thumb of the proper-hand factors alongside the path of modern-day then the curled arms of that hand offers the path of the magnetic area because of the modern-day.
The path of the magnetic area is perpendicular to the twine and is withinside the path the arms of your proper hand might curl in case you wrapped them across the twine together along with your thumb withinside the path of the modern-day.A vertical twine wearing a modern-day withinside the upward path is located in a horizontal magnetic area directed toward north.
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The box is being pushed to the right with a force of 300 newtons, and to the left with a force of 400 newtons. What is the magnitude of the net force on the box?.
pushed to the right = 300 newtons
pushed to the left = 400 newtons
[tex]400-300=100[/tex]
[tex]\fbox{100 Newtons to the left}[/tex]
a solenoid of length 2.50 cm and radius 0.550 cm has 45 turns. if the wire of the solenoid has 1.15 amps of current, what is the magnitude of the magn
According to the given statement 11.38 T is the magnitude of the magnetic field inside the solenoid.
What is vector and magnitude?By using the symbol |v|, the strength of a vector theorem can be utilized to determine the length for such a given vector (let's say v). This amount is essentially the distance between the vector's beginning point and ending point. The range calculation, which we will go over in this section, is used to determine the vector's magnitude.
Briefing:Length of solenoid, L = 2.5 cm = 0.025 m
Radius of solenoid, r = 0.55 cm = 0.0055 m
Number of turns, N = 45 turns
Current, I = 1.15 A
Magnetic field, B, is given as:
B = (N*r*I) /L
B = (45 * 0.0055 * 1.15)/0.025
B = 11.38 T
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The complete question is-
A solenoid of length 2.50 cm and radius 0.550 cm has 45 turns. If the wire of the solenoid has 1.15 amps of current, what is the magnitude of the magnetic field inside the solenoid?
Jimi is pushing a large cart at work toward the left side of the store using 10N of force. His friend Jonah comes up and pushed the cart with 8 N of force toward the right side of the store. What is the net force and direction of the cart
The net force acting on the cart is 2 N in left direction.
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. Newton is the SI unit of force.
Jimi is pushing a large cart at work toward the left side of the store using 10N of force.
Jonah pushed the cart with 8 N of force toward the right side of the store.
Hence, the net force acting on the cart in left direction = ( 10 N - 8 N) = 2 N.
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find the work done by a force of 12 newtons at 25 degrees pulling an object 10 meters up a ramp inclined at 4 degrees
The work done by a force is 40.14 J
The work done is calculated to include both the force applied to the body and the overall movement of the body. There is a constant force F in front of this block. The purpose of this force is to move an object a certain distance d in a straight line in the direction of the force.
The cart is lifted to a height, h:
h = (10meters) ×sin(4) = 0.69 m
The force in the vertical direction is:
Fy = 12N×sin(29o) = 58.177N
Work = F×d = (58.177)×(0.69) = 40.14 joules
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uppose that a flat loop of wire with an area of 0.050 m2 lies in a magnetic field normal to the loop. if the magnetic field changes at a uniform rate from 0.30 t to 1.5 t it induces an emf of 1.2 volts in the loop. find the time interval for the change. group of answer choices 0.023 sec 0.050 sec 0.073 sec 0.085 sec
When we calculate a function's average rate of change over a certain interval, we are computing the average number of units that the function moves up or down per unit along the xx-axis.
Given the function and interval of interest (f(x)f(x) and [x ₁,x₂]), [x\s₁,x₂ ]), our first step is to compute the value of our function at both ends of the interval. Then we plug those numbers and the interval's ends into our algorithm to calculate the average rate of change.
The average rate of change formula is
{x₂-x₁}
x f = x₂ x 1 f(x₂ )
within the interval [x₁,x ₂][x ₁,x ₂ ].
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the intensity levels of two people's speech are 60.5 db and 65.5 db, respectively. what is the intensity level of the combined sounds?
the intensity level of the combined sounds is 67.76 dB
Calculation :
Sound Intensity level L= 63 dB
We know L = 10 log(I/Io)
63 = 10 log(I/Io)
6.3 = log (I/Io)
I /Io = [tex]10^{6.3}[/tex]
I = [tex]10^{6.3}[/tex] Io
= [tex]10 ^{6.3 }[/tex]x [tex]10 ^{-12}[/tex]
= [tex]10^{ -5.7}[/tex] W/m 2
= 1.995 x[tex]10 ^{-6}[/tex] W/m 2
Sound Intensity level L '= 66 dB
We know L ' = 10 log(I '/Io)
66 = 10 log(I '/Io)
6.6 = log (I'/Io)
I ' /Io = [tex]10 ^{6.6}[/tex]
I ' = [tex]10 ^{6.6}[/tex] Io
= [tex]10 ^{6.6}[/tex] x [tex]10 ^{-12}[/tex]
= [tex]10 ^{-5.4}[/tex]W/m ^2
= 3.981 x[tex]10 ^{-6}[/tex] W/m^ 2
Combined intensity I " = I + I ' = 5.976 x10 -6 W/m 2
the intensity level of the combined sounds L " = 10 log(I" / Io)
L " = 10 log [( 5.976 x[tex]10 ^{-6}[/tex] )/([tex]10 ^{-12}[/tex] ) ]
= 10 log [5.976 x10 6]
= 10(6.776)
= 67.76 dB
Intensity is the amount of energy a wave transports in one unit of area per unit time and is also equal to the energy density multiplied by the wave velocity. Usually measured in watts per square meter. Intensity depends on wave strength and amplitude.
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in an experiment with n = 14 and preal = 0.10, what is the power using a = 0.012 tail?
In an experiment with n = 14 and preal = 0.10, then the power using a = 0.012 tail will be 0.997
Power is the capacity to shape or direct events, other people's behavior, or both. It is the ability to decide what to do and then do it. It might be either physical—like power—or mental—like wisdom. Power may also be social, political, or economic. It can be employed constructively, such as to effect change and defend human rights, or destructively, such as to repress and exert control. Power may be utilized to both bring about and stop change. Politics, economics, and culture all exhibit it since it is an essential component of all social relations.
N = 14
Mean, mu=0.10,
s=sqrt [0.10(1-0.10)/14]=0.08,
cumulative probability, 0.003,
Power=1-0.003=0.997
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. a single strand of wire of adjustable length is wound around the circumference of a round balloon that has a diameter of 21.0 cm. a uniform magnetic field with a magnitude of 2.00 t is perpendicular to the plane of the loop. if the balloon is blown up such that its diameter and the diameter of the wire loop increase to 31.0 cm in 0.036s, what is the magnitude of the average value of the emf induced in the loop?
The magnitude of the average value of the emf induced in the loop is 2.26 V.
The initial area of wire loop is:
A(initial) = π d² / 4
= 3.14 × ( 0.21 m )² / 4
= 0.0346 m²
And, The wire loop's final location is at:
A(final) = π d² / 4
= 3.14 × ( 0.31 m )² / 4
= 0.0754 m²
It is given that the magnetic field is normal to the loop of wire.
Therefore, angle made by the magnetic field with the normal to the loop
is :
θ = 0°
Applying Faraday's law, the average emf induced in the loop is:
ε = B × ( A(final) - A(initial) ) × cosθ / Δt
ε = 2.00 T × ( 0.0754 - 0.0346 ) m² × cos0° / 0.036 s
ε = 2.26 V
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the radius of our sun is 6.96 108 m, and its total power output is 3.85 1026 w.
The Sun's surface emits as a black body its surface temperature is [tex]$5.78 \times 10^3 \mathrm{~K}$[/tex].
The sun's surface area is,
A 3D object's surface area is the entire area that all of its faces cover. If we need to figure out how much paint is needed to paint a cube, for example, we may use the cube's surface area. It is consistently expressed in square units.
[tex]A=4 \pi r^2[/tex]
The sun's radius, r, is indicated here.
Substitute [tex]$6.96 \times 10^8 \mathrm{~m}$[/tex] for r.
[tex]A & =4 \pi\left(6.96 \times 10^8 \mathrm{~m}\right)^2 \\& =6.09 \times 10^{18} \mathrm{~m}^2[/tex]
The radiated power is, according to Stefan's law
Energy that emanates from an origin and moves through space at the speed of light is referred to as radiation. This radiation has wave-like qualities and is accompanied by an electric field and a magnetic field.
[tex]P & =\sigma A e T^4 \\T^4 & =\frac{P}{\sigma A e} \\T & =\left(\frac{P}{\sigma A e}\right)^{\frac{1}{4}}[/tex]
Substitute [tex]$6.09 \times 10^{18} \mathrm{~m}^2$[/tex] for A,
[tex]5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2. \mathrm{K}^4$[/tex] . for [tex]$\sigma$[/tex],
and [tex]$3.85 \times 10^{26} \mathrm{~W}$[/tex] for P.
[tex]T & =\left(\frac{3.85 \times 10^{26} \mathrm{~W}}{\left(5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}^4\right)\left(6.09 \times 10^{18} \mathrm{~m}^2\right)(1)}\right)^{\frac{1}{4}} \\& =\left(1.12 \times 10^{15} \mathrm{~K}^4\right)^{\frac{1}{4}} \\& =5.78 \times 10^3 \mathrm{~K}[/tex]
The temperature is [tex]$5.78 \times 10^3 \mathrm{~K}$[/tex].
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Note:- The correct question would be as follow,
The radius of our Sun is [tex]$6.96 \times 10^8 \mathrm{~m}$[/tex], and its total power output is [tex]$3.85 \times 10^{26} \mathrm{~W}$[/tex]. (a) Assuming the Sun's surface emits as a black body, calculate its surface temperature.
which construct can be used in a shell script to read standard input and place it in a variable?
We use a construct that can be used in a shell script the read built-in Bash command to read user input. It assigns user input to the variable after receiving it. It simply takes one line from the Bash shell to read. The syntax for implementing it is listed below.
read <variable_name>
What is the read bash command?A built-in tool in Bash allows you to read text from standard input. The utility provides a wide range of user input reading capabilities that assist make Bash scripts interactive. Through various examples and use situations, this article demonstrates how the Bash read command functions. access to a terminal or command line.
The "read" command in Bash scripting is used to get human input. It's essential to comprehend the "read" command if you want to make your code more interactive. The "read" command is used to retrieve user-inputted data. This article demonstrates how to communicate with users using Bash's "read" command.
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calculate the rotational inertia of a wheel that has a kinetic energy of 24 400 j when rotating at 602 rev/min.
The moment of inertia is measured in units of mass times squared distance, such as kgm2. The rotational kinetic energy of an item in rotation about an axis is K = 12I2.
Moment of inertia divided by half equals rotational kinetic energy (angular speed). Where 0 0 is the starting angular velocity, = 0 + t (constant) and = 0 + t (constant). The equation is the same as the linear version, with the exception that the angular equivalents of the linear variables. It is necessary to specify the moment of inertia in relation to a selected axis of rotation. The moment of inertia for a point mass is equal to the mass times the square of the distance perpendicular to the rotation axis, or I = mr2.
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Prove the property a × b = − b × a of this theorem. Let a = a1, a2, a3 and b = b1, b2, b3 . Then a × b = __ = (−1) __ =− b × a.
If a = a1, a2, a3 and b = b1, b2, b3 . Then [tex]& \vec{a} \times \vec{b}=(-1)(\vec{b} \times \vec{a})[/tex] Or [tex]& \vec{a} \times \vec{b}=-\vec{b} \times \vec{a}[/tex]
As per the details share in the above question are as bellow,
The provided data are follow,
The product of two or more integers that remain the same, regardless of the sequence in which they are multiplied, is referred to as the commutative property formula for multiplication. The commutative property formula for multiplication is (A x B) = (B x A).
Let us consider, Let a = a1, a2, a3
And b=b1, b2, b3
We have the property that a × b = − b × a.
Then a × b = __ = (−1) __ =− b × a.
[tex]& \vec{a}=a_1 i+a_2 j+a_3 k \\ \vec{b}=b_1 i+b_2 j+b_3 k[/tex]
Then,
[tex]$$\vec{a} \vec{x} \vec{b}=\left|\begin{array}{ccc}i & j & k \\a_1 & a_2 & a_3 \\b_1 & b_2 & b_3\end{array}\right|$$[/tex]
[tex]$$=i\left(a_2 b_3-a_3 b_2\right)+j\left(a_3 b_1-a_1 b_3\right)+k\left(a_1 b_2-a_2 b_1\right)$$[/tex]
So further we get,
[tex]& =i\left(b_2 a_3-a_2 b_3\right)+j\left(a_1 b_3-a_3 b_1\right)+k\left(a_2 b_1-a_1 b_2\right) \\& =-\left[i\left(a_2 b_3-a_3 b_2\right)+j\left(a_3 b_1-a_1 b_3\right)+k\left(a_1 b_2-a_2 b_1\right)\right.[/tex]
So, we get,
[tex]\vec{a} \times \vec{b}=\left[i\left(a_2 b_3-a_3 b_2\right)+j\left(a_3 b_1-a_1 b_3\right)+k\left(a_1 b_2-a_2 b_1\right)\right.[/tex]
We get,
[tex]& \vec{b} \times \vec{a}=-[\vec{a} \times \vec{b}][/tex]
Or [tex]& -\vec{b} \times \vec{a}=\vec{a} \times \vec{b}[/tex]
Then,
[tex]& \vec{a} \times \vec{b}=(-1)(\vec{b} \times \vec{a})[/tex]
Or [tex]& \vec{a} \times \vec{b}=-\vec{b} \times \vec{a}[/tex]
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what is the electric flux through the surface shown in the figure? assume that e=300n/c.
Electric flux through the surface is [tex]1.5 Nm^2/C[/tex].
As per the detail share in the above question are as bellow,
Given an area A with a unit normal vector n, the electric flow through that region is given by Φ = E.(An) = |E|Acosθ
Where angle between vectors E and n =θ .
Also Magnitude of E = |E|
When the magnitude of n is |n| = 1
The normal n and the electric field vector E make an angle of,
θ = 90 - 30 = 60 degrees,
Therefore magnitude of,
|E| = 300N/C
And A= 0.1 x 0.1 = 0.01 m.
Thus,
Φ = |E|Acosθ
Substitute the value in above equation we get,
=300 x 0.01 x cos(60)
=3 x 0.5
[tex]= 1.5 Nm^2/C[/tex]
Electric flux=Φ=[tex]1.5 Nm^2/C[/tex]
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Note : The correct question would be as follow,
what is the electric flux through the surface shown in the figure? assume that e=300n/c.
a sinusoidal transverse wave is traveling on a string. any point on the string: a) moves in the same direction as the wave b) moves in simple harmonic motion with a different frequency than that of the wave c) moves in simple harmonic motion with the same angular frequency as the wave d) moves in uniform circular motion with a different angular speed than the wave e) moves in uniform circular motion with the same angular speed as the wave
There is a transverse sinusoidal wave on a string that flows in a straightforward harmonic fashion and has an angular frequency that matches the wave. (Chose c.)
How physically act waves?An energetic disturbance called a wave moves from one place to another. Every time a wave moves, energy is changed, regardless of the change. The substance through which a wave passes is known as the medium. Back and forth oscillations occur repeatedly in that medium.
How could waves be described?A wave is a disruption or variation that progressively moves energy from one location in a medium to another. It could manifest as an elastomeric deformation or a shift in pressure, magnetic or electric field strength, electric potential, or temperature.
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