Starting from the 2D time-independent Schr ̈odinger Equation, and using your knowledge
of the 1D harmonic oscillator, write down the normalized ground-state and the first
excited state, with both position and time dependence included. Come up with a way
of writing these states in shorthand using kets.
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Three infinite straight wires are fixed in place and aligned parallel to the z-axis as shown. The wire at (x,y) = (-13.5 cm, 0) carries current I1 = 3.2 A in the negative z-direction. The wire at (x,y) = (13.5 cm, 0) carries current I2 = 1.4 A in the positive z-direction. The wire at (x,y) = (0, 23.4 cm) carries current I3 = 5.1 A in the positive z-direction.
1)
What is Bx(0,0), the x-component of the magnetic field produced by these three wires at the origin?T
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2)
What is By(0,0), the y-component of the magnetic field produced by these three wires at the origin?T
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3)
What is Fx(1), the x-component of the force exerted on a one meter length of the wire carrying current I1?N
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4)
What is Fy(1), the y-component of the force exerted on a one meter length of the wire carrying current I1?N
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5)
What is Fx(2), the x-component of the force exerted on a one meter length of the wire carrying current I2?
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a) Determine the mass of water vapor, initially at 130 ° C, needed to heat 200 g of distilled water in a 100 g glass container, to go from 20 ° C to 50 ° C.
The specific heat of water vapor is 2.01x103 J / kg ° C, the specific heat of distilled water is 4.19x103 J / kg ° C, the latent heat of condensation of water vapor is 2.26x106 J / kg and the Specific heat of the glass is 837 J / kg ° C
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Derive the expression for the time averaged heating in the metal in which AC current of frequency ω flows – use the expression for the AC conductivity and P= ⋅EJ relation for instant power
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Draw an experimental setup in the Laboratory in which you are working, where only interference is observed. Explain why you use each element you use in the setup.
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A gymnast is performing a floor routine. In a tumbling run she spins through the air, increasing her angular velocity from 3.00 to 4.10 rev/s while rotating through two-thirds of a revolution. How much time does this maneuver take?
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A person walks first at a constant speed of 4.90 m/s along a straight line from point circled A to point circled B and then back along the line from circled B to circled A at a constant speed of 2.90 m/s. Find the average Velocity for the time interval of 1.80s to 2.80s and also the average velocity for the time interval of 1.85s to 2.25s.
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Which statement below is most precise?
a. Deceleration means that the acceleration is negative
b. Acceleration tells us how quickly the speed changes
c. When the acceleration and the velocity have the same sign the object's speed Increases
d. A positive acceleration always points to the right
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This all counts as 1 question in class because it's supposed to be already known. So please answer all of them. I just want to be sure I'm right.
Question 1
Which of the following statements are true regarding momentum? Check all that apply.
| The total momentum of an isolated system is conserved, but internal forces can change the total momentum of the system |
|
pinitial = (m1v1)i + (m2v2)i + (m3v3)i + … |
|
pfinal = (m1v1)f + (m2v2)f + (m3v3)f + … |
| The x and y components of momentum are independently conserved |
| Total momentum is conserved, but angular momentum is not. |
| A figure skater spins faster when she draws in her arms because torque is conserved. |
| Momentum points in the same direction as the applied force |
| Angular momentum points in the same direction as the net applied torque |
| Momentum points in the same direction as the velocity of the object |
Question 2
A bug and the windshield of a moving car collide. Indicate which of the following statements are TRUE. (Select all that apply)
| The impulse on the bug and the car are the same magnitude |
| The impact force on the bug and the car are the same magnitude |
| The change in velocity of the bug and the car are the same |
| The change in momentum of the bug and the car are the same magnitude |
| None of the above |
Question 3
A running thief is being chased by the police, and he jumps on a stationary skateboard hoping he will be able to go faster. That is a good idea because:
| Momentum is conserved, and thus his velocity will increase when he jumps on the skateboard (which has a smaller mass). |
| Angular momentum is conserved, so that the wheels on the skateboard can spin much faster than his feet can run on the ground. |
| Momentum is conserved, and since his mass combined with the skateboard is larger, he can go faster. |
| Momentum is conserved, which means he will go a little slower on the skate, but will look cooler as he does so. |
Question 4
Which of these are forms of energy? Check all that apply:
| Kinetic Energy |
| Gravitational Potential Energy |
| Spring Potential Energy |
| Friction Energy |
| Thermal Energy |
| Inertial Energy |
| None of the above |
Question 5
Bob pushes a 1-meter wide bookcase with a force of 100 N for 10 seconds, but the bookcase does not move due to friction. How much work has Bob done?
| 100 Nm |
| 1000 Nm |
| 10 Nm |
| None of the above |
Question 6
Which of the following are units of Work?
|
kg / s2 |
| N m |
| Joules |
| Calories |
| Degrees |
|
(kg m / s)2 / kg |
| None of the above |
Question 7
If an object has kinetic energy, then it also must have... (check all that apply)
| Speed |
| Impulse |
| Acceleration |
| Force |
| None of the above |
Question 8
When an object is lifted 10 meters, it gains a certain amount of potential energy. If the same object is lifted 20 meters, its potential energy is:
| Less |
| The same |
| Twice as much |
| Four times as much |
| None of the above |
Question 9
Which of the following statements are true? Check all that apply:
| Work is the what you get when a force acts over a certain distance. Therefore, without distance or force there would be no work. |
| Work and Distance are related because force is acted over a long distance. |
| Without work you do not have force. |
| Energy is the ability to do work or make work, and work is not done without it. |
| Energy causes a change, and work is needed for energy to exist. |
| Energy is the ability to do work or cause a change, and work is the transfer of energy. |
| Kinetic energy is the energy of motion, and potential energy is stored energy. |
| Potential energy is the energy of weight, and kinetic energy is the energy of nuclear atoms. |
| None of the above |
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Let's say you want to produce a (roughly) uniform electric field using a very large nonconducting sheet. However, you still want to be able to access the regions above and below the sheet, so a drill a small hole with a radius of 1.80 cm into the sheet. You can assume that very large means "infinite" in this context. The sheet has a surface charge density of 4.50 pC/m2. What is the magnitude of the electric field at a point 2.56 cm above the sheet after the hole is drilled into the sheet? You drill the hole such that the point we are considering lines directly above the center axis of the hole.
Hint: Remember that electric fields obey the superposition principle. What charge distribution can you add on top of the sheet to create the absence of charge (i.e., not net charge) in "hole" region?
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A crate of mass 100.0 kg rests on a rough surface inclined at an angle of 37.0° with the horizontal. A massless rope to which a force can be applied parallel to the surface is attached to the crate and leads to the top of the incline. In its present state, the crate is just ready to slip and start to move down the plane. The coefficient of friction is 80% of that for the static case
a. What is the coefficient of static friction?
b. What is the maximum force that can be applied upward along the plane on the rope and not move the block?
c. With a slightly greater applied force, the block will slide up the plane. Once it begins to move, what is its acceleration and what reduced force is necessary to keep it moving upward at constant speed?
d. If the block is given a slight nudge to get it started down the plane, what will be its acceleration in that direction?
e. Once the block begins to slide downward, what upward force on the rope is required to keep the block from accelerating downward?
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1-state the relationship between a wave's velocity wavelength and frequency?
2- What is the principle of superposition?
3- The distance between two nodes or two antinodes in a standing wave is …………………. Wavelength?
4- - The distance between an antinode and a node in a standing wave is …………………. Wavelength?
5- A string, which has a mass of 0.50 kg and a length of 3.0 meters, is clamped on both ends. If the tension in the string is 25 Newtons, what are the lowest 3 natural frequencies of oscillation of the string? For each case, include a sketch of the standing wave pattern.
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An RLC series circuit consists of a 450-Ω resistor, a 3.00-mF capacitor, and a 1.00-H inductor. The circuit is driven by a power source that oscillates at 20.0 Hz and has an Erms value of 30.0 V . The power source is switched on at t = 0 and at that instant the emf is at its maximum value.
Part A Calculate the power supplied at t = 0.0200 s.
Part B Calculate the power supplied at t = 0.0375 s.
Part C Calculate the power supplied at t = 0.0500 s.
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