Consider,
[tex]{:\implies \quad \displaystyle \sf \langle p\rangle =m\langle v(t)\rangle=m\int_{-\infty}^{\infty}x\bigg\{\dfrac{\partial \Psi^{*}(x,t)}{\partial t}\Psi (x,t)+\Psi^{*}(x,t)\dfrac{\partial \Psi (x,t)}{\partial t}\bigg\}dx}[/tex]
Multiply both sides by ih and simplification will yield
[tex]{:\implies \quad \displaystyle \sf ih\langle p\rangle =m\int_{-\infty}^{\infty}x\bigg[\Psi (x,t)\bigg\{\dfrac{h^2}{2m}\dfrac{\partial^{2}\Psi^{*}(x,t)}{\partial x^2}-V(x)\Psi^{*}(x,t)\bigg\}+\Psi^{*}(x,t)\bigg\{V(x)\Psi (x,t)-\dfrac{h^2}{2m}\dfrac{\partial^{2}\Psi (x,t)}{\partial x^2}\bigg\}\bigg]dx}[/tex]
Some simplification, Then Integrate by parts and then knowing the fact that the wave function vanishes for [tex]{\bf x\to \pm \infty}[/tex] will yield:
[tex]{:\implies \quad \displaystyle \sf \langle p\rangle =\dfrac{ih}{2}\int_{-\infty}^{\infty}\bigg\{\dfrac{\partial \Psi^{*}(x,t)}{\partial x}\Psi (x,t)-\Psi^{*}(x,t)\dfrac{\partial \Psi (x,t)}{\partial x}\bigg\}dx}[/tex]
Integrating by parts and knowing the same fact by some simplification will yield:
[tex]{:\implies \quad \displaystyle \sf \langle p\rangle =-ih\int_{-\infty}^{\infty}\Psi^{*}(x,t)\dfrac{\partial \Psi (x,t)}{\partial x}dx}[/tex]
The momentum is thus contained within the wave function, so we can then deduce that:
[tex]{:\implies \quad \sf p\rightarrow -ih\dfrac{\partial}{\partial x}}[/tex]
[tex]{:\implies \quad \sf p^{n}\rightarrow \bigg(-ih\dfrac{\partial}{\partial x}\bigg)^{n}}[/tex]
[tex]{:\implies \therefore \quad \displaystyle \sf \langle p^{2}\rangle =-h^{2}\int_{-\infty}^{\infty}\Psi^{*}(x,t)\dfrac{\partial^{2}\Psi (x,t)}{\partial x^2}dx}[/tex]
Now the kinetic energy
[tex]{:\implies \quad \displaystyle \sf \langle K\rangle =\dfrac{\langle p^{2}\rangle}{2m}=\dfrac{-h^2}{2m}\int_{-\infty}^{\infty}\Psi^{*}(x,t)\dfrac{\partial^{2}\Psi (x,t)}{\partial x^2}dx}[/tex]
The classical formula for the total energy
[tex]{:\implies \quad \sf \dfrac{p^2}{2m}+V(x)=E}[/tex]
Multiplying this equation by [tex]{\sf \Psi (x,t)=\psi (x)exp\bigg(\dfrac{-iEt}{h}\bigg)}[/tex] and use the above equations and simplify it we will be having
[tex]{:\implies \quad \boxed{\bf{\dfrac{-h^2}{2m}\dfrac{d^{2}\psi (x)}{dx^{2}}+V(x)\psi (x)=E\psi (x)}}}[/tex]
This is the Famous Time-Independent Schrödinger wave equation
Note:- If I write all the explanation then the Answer box willn't allow me to submit the answer
what is the distance of a car travels is its velocity is 30 mph and its time is 2 hours ?
Answer:
distance = 60 miles
Explanation:
Which diagram shows magnets aligned so they will attract each other?
Find the period of small oscillations of a barbell of length l with balls of mass m, located along a homogeneous electric field of intensity E. The charge of the barbell balls is ±q.
An empty hot air balloon weighs 1000 newtons (N). As the balloon is released in the air, the atmosphere provides a lift force of 3300 N. What is the magnitude and direction of the net force?
2300 N upward
4300 N upward
2300 N downward
4300 N downward
[tex]\Large{\green}\fcolorbox{blue}{cyan}{\bf{\underline{\red{\color{red}Answer}}}}[/tex]
2300 N upward
Explanation:
The force by weight of balloon = 1000 N
The atmospheric force experienced by balloon = 3300 N
While weight of balloon is attracted by gravity so the force of weight will act downward
And the atmospheric force gives upward lifting force to the balloon
Net force = atmospheric force - weight of balloon
= 3300 - 1000
= 2300 N
As the atmospheric force is more dominating the balloon will goes upward with 2300 N force
A car accelerates at a rate of 8.8m/s² with a force from the tires of 19,976N. What is the mass of the car?
A.1800kg
B.2270kg
C.1360kg
D2140kg
Answer:
B. 2270 kg
Explanation:
We know that :
Force = Mass x AccelerationWe are given :
Force = 19,976 NAcceleration = 8.8 m/s²Finding mass
19,976 = 8.8 x massmass = 19,976/8.8mass = 2270 kgWhich category of mechanical waves are produced during an earthquake?
A) Gamma wave
B) Radio wave
C) Seismic wave
D) Electromagnetic wave
Answer:
The answer is C. Seismic waves.
Explanation:
Seismic waves are waves of energy that travel through Earth's layers, and are a result of earthquakes.which of the following is a reality based condition with self-defeating patterns?
Answer:
What is a reality based condition with self-defeating patterns?
Terms in this set (35) A psychotic is reality based, yet needs psychotherapy to correct their values. A neurotic is a non-reality based person with self-defeating patterns of behavior.
Explanation:
A magnetic field of 0.0037 T is measured at a distance of 2 cm from a long
straight current carrying wire. What is the magnitude of the current flow in the
wire?
Hi there!
We can use Ampère's Law to derive an expression for the magnetic field strength produced by an infinitely long current-carrying wire:
[tex]\oint B \cdot dl = \mu_0 I_{encl}[/tex]
B = Magnetic Field Strength (T)
dl = Differential length along path
μ₀ = Permeability of Free Space (Tm/A)
I = Enclosed current (A)
The integral is a cross product, so the cosine of the angle between the magnetic field and the path of integration is used. However, for a straight current-carrying wire, the path is ALWAYS parallel to the magnetic field, so since cos(180) = 1, we can disregard the cross product.
Additionally, the path of integration is equivalent to:
[tex]l = 2\pi r[/tex]
[tex]B \cdot l = \mu_0 I_{encl}\\\\B * 2\pi r = \mu_0 I_{encl}\\\\B = \frac{\mu_0 I_{encl}}{2\pi r }[/tex]
Rearrange to solve for enclosed current:
[tex]I_{encl} = \frac{2\pi rB}{\mu_0} = \frac{2\pi (0.02)(0.0037)}{(4\pi *10^{-7})} = \boxed{370 A}[/tex]
what is kinematics ?
name its father and explain its history !
ty ~
Hello There!!
1st QuestionWhat is kinematics?Answer=> Let The Answer be "x"
________________________________
2nd questionName it's fatherAnswer=> He don't have a child so he is not a father
________________________________
3rd QuestionExplain its HistoryAnswer=> Kinematics is a part of science not history.
__________________________________
Hope this helps :D
Answer:
i just wrote this much hope it will help u little
Explanation:
kinematics is the branch of physical which deals with the study of motion as the function of time.Frank reuleaux is known as the father of kinematics.the word *kinematics" comes from a greek word "kinesis" meaning motion.
If the diameter of a wire is tripled and the length is doubled, the resistance would change by a factor of __?
Answer:
it’s going to be times 3
Explanation:
so the answer would be three times which means it will change by a factor of 3.
I’m sorry I wrote it wrong the first time.
What type of bond is most likely to form between two gold (Au) atoms?
Answer:
I believe it would be a metallic bond.
Explanation:
Why the range of a clinical thermometer kept between 35°C and 42°C?
Answer:
Because it is the standard operational range for measuring the body temperature of a living individual.
Explanation:
When making a measuring equipment like a thermometer, you attempt to keep the reading range (Span) as small as possible so that the reading is as accurate as feasible. Because sensors are often rated in percent of span (in this example, span = 45 C–32 C = 13 degrees Celsius), One percent of 13 equals 0.13 degrees Celsius, thus if your sensor has a usual accuracy of 1%, your temperature reading is accurate to roughly 0.1 degrees Celsius.
Your precision would be 0.2 degrees Celsius if you doubled the span. The reading accuracy is now becoming unsatisfactory. Readability is another advantage of analog and mercury clinical thermometers. The markings for 0.1 deg C would be ten times closer together if a mercury thermometer had ten times the range (span). There is a limit to the device's readability.
Which statements correctly describe the effect of distance in determining the gravitational force and the electrical
force? Check all that apply.
The gravitational force has an infinite reach.
The electrical force has an infinite reach.
The gravitational force is inversely proportional to the distance.
U The electrical force is inversely proportional to the distance.
O The gravitational force is inversely proportional to the square of the distance.
O The electrical force is inversely proportional to the square of the distance.
The statements 1,4 and 5 accurately describe the influence of distance on gravitational and electrical forces.
What is Newton's law of gravity?Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.
Gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.
Decreasing the distance would increase the gravity of the planet.
The following statements accurately describe the influence of distance on gravitational and electrical forces.
1. The gravitational force has an infinite reach.
4. The gravitational force is inversely proportional to the square of the distance.
5. The electrical force is inversely proportional to the square of the distance.
Hence, options 1,4 and 5 are correct.
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During a race, a sprinter accelerated 1.8 m/s 2 in 2.5 seconds.How many meters per second did the sprint increase with this amount of acceleration
During a race, a sprinter accelerated 1.8 m/s 2 in 2.5 seconds. The sprint increase with this amount of acceleration by 4.5 m/s.
What is acceleration?Acceleration is the time rate of change of velocity.
Acceleration a = velocity v / time t
1.8 = v/2.5
v = 4.5 m/s
The sprint increase with this amount of acceleration by 4.5 m/s.
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Ahmad pulls a sled across level snow by 75 N . If the sled moves 15 m , how much work does Ahmad do on the sled?
Answer:
1125 J
Explanation:
W=F x s
= 75 x 15
=1125
a
Why do you need a reference
point to determine if an object
has moved?
A. The object will stop moving if you don't
compare it.
B. The object could run into another object.
C. Motion is a change in position relative to a
fixed point.
Answer:
An object is in motion when its distance from another object is changing. A reference point is a place or object used for comparison to determine if something is in motion. An object is in motion if it changes position relative to a reference point.
option C is your CORRECT answer
Calculate the Speed for A + B
Answer:
Speed of A + B = 1 m/s
Explanation:
The speed of B = 0 because the distance does not change with time .
The speed of A = 1 m/s ( the slope of the line)
a simple generator has 200 loop square coil 10 cm on a side .how fast must it turn in a 0.25 T field to produce 24v peak out put
Hi there!
Recall Faraday's Law:
[tex]\epsilon = N\frac{d\Phi_B}{dt}[/tex]
ε = Emf (V)
N = Number of loops
ΦB = Magnetic Flux (Wb)
t = time (s)
Since the magnetic field is constant, we can take this out of the time derivative:
[tex]\frac{d\Phi_B}{dt} = B * \frac{dA}{dt}[/tex]
Therefore:
[tex]\epsilon = N B \frac{dA}{dt}[/tex]
We can express 'A', the area in which the magnetic field passes as:
[tex]A = Acos(\omega t)[/tex]
Taking the time derivative:
[tex]\frac{dA}{dt} = A\omega sin(\omega t)[/tex]
ω = angular speed of coil (rad/sec)
Now, combine with the above expression:
[tex]\epsilon = NBA\omega sin(\omega t)[/tex]
The maximum output will occur when the loop's area vector is PERPENDICULAR to the field, so sin(ωt) = 1.
Therefore:
[tex]\epsilon = NBA\omega \\\\[/tex]
Rearrange to solve for ω:
[tex]\omega = \frac{\epsilon}{NBA}\\\\\omega = \frac{24}{(200 * (.10^2) * 0.25} = \boxed{48 \frac{rad}{sec}}[/tex]
How does the image make the message in the "Mummy, what happens to us if the bomb drops?" poster more clear?
A. The poster shows a clear picture of a girl having a serious talk with her parents.
B. The poster shows all the supplies needed to survive in picture format.
C. The poster provides an emotional picture of a young, innocent girl with a slightly worried expression to make protective feelings.
D. The poster shows the actual bomb attack.
Answer:
C. The poster provides an emotional picture of a young, innocent girl with a slightly worried expression to make protective feelings.
Explanation:
The girl looks quite worried in the poster. Attached is the image:
Newtons second law in words??
Answer:
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object
Explanation:
it's newton's second law
Explain this picture in terms of potential and kinetic energy.
PLEASE HELP ASAP!
Which coefficient is needed in front of NaNO3 to balance the equation Na2S + Zn(NO3)2 → ZnS + _NaNO3? 1, 2, 5, 7,
The coefficient is needed in front of NaNO3 to balance the equation is 2.
What is balanced equation?When in a chemical reaction, both the product elements or compounds should have number of moles equal to that of the elements or compounds of reactants.
In the given chemical reaction equation,
Na2S + Zn(NO3)2 → ZnS + _NaNO3
Number of moles of S is 1 on both the product and reactant side. Zn has 1 mole on both side. NO3 has 2 mole and Na has 2 mole on reactant side. So to balance the equation, Na and NO3 both must have 2 moles on product side.
Thus, the coefficient is needed in front of NaNO3 to balance the equation is 2.
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when a tractor trailer and a smart car collide head on, who hits who with greater force? explain your reasoning
Answer:
The smart car hit with the greater force
Explanation:
Despite the trailers weight, the smart car moves with more speed and momentum than that of the trailer...
I don't even understand what I'm typing
Both will exert equal and opposite force on each other.
When a tractor-trailer and a smart car collide head-on, we can determine the relative forces experienced by each vehicle using Newton's second law of motion.
According to this law, the force acting on an object is equal to the rate of change of its momentum.
Let's consider the tractor-trailer as object 1 with mass [tex]\(M_1\)[/tex] and velocity [tex]\(V_1\)[/tex], and the smart car as object 2 with mass [tex]\(M_2\)[/tex] and velocity [tex]\(V_2\)[/tex].
The force exerted on object 1 due to object 2 [tex](\(F_{12}\))[/tex] can be calculated as:
[tex]\[F_{12} = M_1 \cdot \frac{{dV_1}}{{dt}}\][/tex]
Similarly, the force exerted on object 2 due to object 1 [tex](\(F_{21}\))[/tex] can be calculated as:
[tex]\[F_{21} = M_2 \cdot \frac{{dV_2}}{{dt}}\][/tex]
Since the collision is head-on, the direction of the forces will be opposite for the two objects.
To determine which object experiences a greater force, we need to compare the magnitudes of [tex]\(F_{12}\) and \(F_{21}\)[/tex] = 0 by Newton's third law.
Thus, both will exert equal and opposite force on each other.
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A bug starts from point A, crawls 15cm due east, then 5cm due west, 7cm due south, 3.0cm due west and 5.0cm due north to point B. Calculate the north and east distance of point B from A
Answer:
let i represent due East and j due north
X (displacement) = (15 - 5) i - 7 j - 3 i + 5 j = 7 i - 2 j
Total displacement = (7^2 + 2^2)^1/2 = 7.28 vector displacement
tan θ = -2 / 7 = -15.9 deg or 15.9 deg S of E
note N distance was -2 cm
E distance was 7 cm
A 3.0kg weight W is initially at rest on incline AB, which is raised 40° above the horizontal. The effective coefficient is
mu = 0.3 . Through frictionless pulley and strings of negligible mass, a small mass P, 400g, is at rest on a 200g weighting pan.
Draw a free body diagram representing the situation, and use it to determine the acceleration of the system. Use the value of acceleration calculated to determine the relative weight of P in pounds.
(a) The acceleration of the system is determined as 1.58 m/s².
(b) The relative weight of P is pounds is determined as 0.14 lb.
Acceleration of the system
The acceleration of the system is calculated as follows;
W - T = m₂a --- (1)
T = m₁a ----(2)
μmgsinθ - m₁a = m₂a
(0.3 x 3 x 9.8 x sin40) - (0.4 + 0.2)a = 3a
5.67 - 0.6a = 3a
5.67 = 3.6a
a = 5.67/3.6
a = 1.58 m/s²
Relative Weight of PW = ma
W = 0.4 x 1.58
W = 0.632 N = 0.14 lb
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an ldeal gas with internal energy U at 202°C is heated to 410°C.its internal energy then will be?
Internal energy is directly proportional to temperature
U1T2=U2T1U(273+410)=U2(273+202)683U=475U_2U_2=1.44U,a circular loop carrying a current of 40A produce a field of 3*10^8 T at the center what should be the current in the straight conductor so that it produce the same field at a distance equal to the radius if the loop ?
Hi there!
We can begin by deriving the magnetic field strength for a circular loop at its center.
Using Biot-Savart's Law:
[tex]dB = \frac{\mu_0}{4\pi }\frac{idl \times \^r}{r^2}[/tex]
μ₀ = Permeability of free space (Tm/A)
dl = Differential length element
r = radius (m)
We can rather use 'ds' to represent a differential arc length since we are finding the magnetic field for a circular loop.
We must begin by dealing with the cross-product. Luckily, this derivation is simple since the radius vector is ALWAYS perpendicular to the path of integration along the loop's circumference. (ONLY if we are finding the field for the direct center.) Thus, since sin(90) = 1, we can get rid of the cross-product.
Therefore:
[tex]dB = \frac{\mu_0}{4\pi }\frac{ids}{r^2}[/tex]
Now, we can integrate with respect to ds.
[tex]= \frac{\mu_0}{4\pi }\int\limits^{2\pi r}_0 {\frac{i}{r^2}} \, ds\\\\ = \frac{\mu_0}{4\pi }{\frac{i * 2\pi r}{r^2}} \, ds[/tex]
Simplify:
[tex]B = \frac{\mu_0 i_{circle}}{2r}\\[/tex]
Now, for a straight conductor (assuming of infinite length), we know the magnetic field strength equation to be:
[tex]B = \frac{\mu_0 i_{rod}}{2\pi r}[/tex]
Set the two equal.
[tex]\frac{\mu_0 i_{circle}}{2r}= \frac{\mu_0 i_{rod}}{2\pi r}[/tex]
Cancel out '2', μ₀, and 'r':
[tex]i_{circle}}= \frac{ i_{rod}}{\pi }[/tex]
Plug in the given values and solve.
[tex]40\pi = i_{rod}\\\\i_{rod} = \boxed{125.663 A}[/tex]
A 12 V battery is connected to a device and 24 mA of current is measured. If the device obeys Ohm's law, how much current is present when a(n) 108 V battery is used?
Answer:
Correct answer: Ic₂ = 48 mA = 48 · 10⁻³ A
Explanation:
U₁ = 12 V DC first battery voltage
Ic₁ = 24 mA = 24 · 10⁻³ A Intensity of current with the first battery
U₂ = 24 V DC second battery voltage
Ic₂ = ? Intensity of current with the second battery
The formula that applies to a simple electric circuit under the Ohm's law is:
R = U / Ic
where R is the total resistance in the electrical circuit and it is constant.
R = U₁ / Ic₁ = U₂ / Ic₂ ⇒ U₁ / Ic₁ = U₂ / Ic₂ ⇒ Ic₂ = (U₂ · Ic₁) / U₁
Ic₂ = (24 · 24) / 12 = 48 mA
Ic₂ = 48 mA = 48 · 10⁻³ A
grujan50
Virtuoso
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Q32.4 Sometimes neon signs located near a powerful radio station are seen to glow faintly at night, even though they are not turned on. What is happening?
Neon lamps located near a powerful radio station are seen to glow faintly at night because radio waves may generate a potential difference in the neon gas.
What is a neon lamp?A neon lamp is a lamp containing neon gas as well as other types of gases and two electrodes.
In a neon lamp, the electricity is generated by striping negative electrons from neon atoms, which ionize these atoms.
The radio waves can also ionize atoms in the neon lamp by generating a potential difference in the neon particles of the lamp, thereby glowing faintly at night.
In conclusion, neon signs located near a powerful radio station are seen to glow faintly at night because radio waves may generate a potential difference in the neon gas.
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Which option is it pls help
Answer:
3.74 x 10^12 electrons
Explanation:
.6 x 10^-6 C * 1/( 1.60218 x 10^-19) e /C
= 3.74 x 10^12 electrons