A ) A 2-?C point charge is embedded in the center of a solid Pyrex sphere of radius R = 15 cm.

(1) Calculate the electric field strength E just beneath the surface of the sphere. (in N/C ) - Answer them in term of "e" like [ ex. : 1.43e+05? ]

(2) Assuming that there are no free charges, calculate the strength of the electric field just outside the surface of the sphere. ( in N/C ) Answer them in term of "e" like [ ex. : 1.43e+05? ]?

(3) What is the induced surface charge density ?ind on the surface of the Pryex? (in C/m^2) Answer them in term of "e" like [ ex. : 1.43e+05? ]?

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B) Trying with diffrent variables, a 1-?C point charge is embedded in the center of a solid Pyrex sphere of radius R = 12 cm.

(1) Calculate the electric field strength E just beneath the surface of the sphere.( in N/C )? Answer them in term of "e" like [ ex. : 1.43e+05? ]?

(2) Assuming that there are no free charges, calculate the strength of the electric field just outside the surface of the sphere.( in N/C )? Answer them in term of "e" like [ ex. : 1.43e+05? ]?

(3) What is the induced surface charge density ?ind on the surface of the Pryex?(in C/m^2) Answer them in term of "e" like [ ex. : 1.43e+05? ]

A) Plot the first five particle in a box wavefunctions for an electron in a 10 Å box

(starting at n = 1). Choose two of these and plot their probability density. Offer a brief

interpretation.

B) (10) Calculate the probability you would find the electron in the right-hand . of the

box (right-hand meaning larger values of the spatial variable) if the electron were

described by your fifth wavefunction (highest energy where n = 5). Calculate the

probability you would find the electron in the left-hand 1/4 of the box

C) (15) Suppose your electron were described as an equal superposition of the first and

second wavefunctions. Normalize this new function and then calculate the probability

you would find the electron in the right-hand 1/4 of the box. Calculate the probability

you would find the electron in the left-hand 1/4 of the box.

A 190 Ω resistor, a 0.875 H inductor, and a 5.75 μF capacitor are connected in series across a voltage source that has voltage amplitude 32.0 V and an angular frequency of 270 rad/s.

A. What is v at t= 22.0 ms ?

B. What is v_R at t= 22.0 ms ?

C. What is v_L at t= 22.0 ms ?

D. What is v_C at t= 22.0 ms ?

E. Compare v_C+v_L+v_R and v at this instant:

vC+vL+vR<v

vC+vL+vR>v

vC+vL+vR=v

which is true?

F. What is V_R?

G. What is V_C?

H. What is V_L?

I. Compare V and VL+VC+VR:

VL+VR+VC=V

VL+VR+VC<V

VL+VR+VC>V

Which is true?

1. A pendulum with a length of 30 cm swings back and forth as shown in the figure above, at each turn around point it stops and it starts accelerating until reaching maxium velocity at the botton (equilibrium position), at which point it starts slowing down. If the maximum angle is 11 degrees, what is its maximum velocity in m/s? (Use g = 10.0 m/s² and assume there is no friction).

2. A car (mass 955 kg) is traveling with a speed of 48 mi/h. A bug (mass 5 mg) is traveling in the opposite direction. What speed would the bug need in (millions of mi/h) in order to slow down the truck by 4 mile per hour in a big bug splash (i.e., final speed 44 mi/h)?

8. A cart slides down an inclined plane with the angle of the incline θ starting from rest. At the moment the cart begins to move, a ball is launched from the cart perpendicularly to the incline.

(a) Choosing an x-y-coordinate system with the x-axis along the incline and the origin at the initial location of the cart, derive the equation of the trajectory that the ball assumes from the perspective of this coordinate system.

(b) Determine where the maximum of this trajectory is located and at what location along the chosen x-axis the ball will fall back into the cart.

(c) Sketch the trajectory in this coordinate system. What does the trajectory look like in an x-y-coordinate system where the x-axis is horizontal?

9. We discussed in lecture that from the perspective of a viewer in the cart sliding down the incline, the ball will always be seen as hovering above the cart, ultimately falling back into the cart. Describe what a viewer sitting in the classroom would see. Are the cart and the ball still advancing in lockstep from that perspective? To help you put this into numbers, calculate where the ball and cart will be located (x- and y-coordinate of each)

(a) at a time equal to the flight time to the peak of the parabolic trajectory and

(b) at twice the flight time to the peak. We choose an angle of the incline of 30o and v .

Please use heat expansion formula s = r* theta The answer should be a) 1.13 degrees b) 3212.1 Celsius

A bimetallic strip is made of copper and steel fused together. The length of each piece is 23 cm at 25 Celsius and the thickness of the copper is .6mm and the steel is .8mm.

a) If the temperature of the strip goes from 25 to 35 Celsius, what is the subtended angle of the arc that the strip makes? [Assume that the thickness does not change appreciably compared to the length of the pieces]

b) To what temperature should the strip be heated so that it curls up to the shape of a complete circle?

Explain (in detail) Nuclear Fission and Nuclear Fusion, why is one radioactive vs the other?What is the nuclear process in a reactor (Fission, or fusion), and what kind of decays is it going through (alpha, beta, or gamma)?What is Critical Mass in nuclear physics?

A spring is mounted over an air track in such a way that the one end of the spring is fixed and the other is connected to a spring scale. When the spring is stretched to 0.01 m a force of 1 N is registered on the spring scale. The spring is relaxed and a glider of 0.43 kg (resting on the air track) is connected to it. The glider-spring system is then pulled to the right through a distance of 0.01 m. Calculate the following:

(a) The spring constant k. (1 mark)

(b) The period of motion. (1 mark)

(c) The angular frequency. (1 mark)

(d) Calculate the amplitude and phase angle of the spring-glider system, if the initial velocity and position of the glider is 0.3 m/s and 0.72 m, respectively.

(e) Utilize all the information already calculated and set up equations for the displacement, velocity and acceleration as function of time.

For the 1S to 2P (Lyman α) transitions in the hydrogen atom, calculate the total integrated absorption cross section.

If you go to a crafts store and buy “glitter beads,” you get a little plastic tube of tiny, metal covered glass or plastic beads. On a nice dry day, you can get a charge on the beads, and some of them will “hover” in the air inside the tube, maybe 4 mm apart from each other. It’s pretty cool.

A. To make it even more cool, let’s estimate how much charge there is on a bead. For that, let’s just assume there are only two beads, one under the other, and it’s the electrostatic repulsion that’s holding the top bead up. If the beads are 4 mm apart, they each have a mass of about 0.1 grams, and we can assume they have the same charge, about how much is that charge?

B. If the amount of the charge on the beads were to drop by 1/2, what would you expect to happen to the distance between them?

C. And how much of a difference in the mass of a bead does that amount of accumulated charge make? That is, how much more or less mass does a charged bead have than a neutral one?

Car A has a mass of 2000 kg and speed of 10 miles per hour. Car B has mass of 1000 kg and speed of 30 miles per hour. The two cars collide to each other and stick together after collision in three different situations. Calculate the velocity of the two cars after the collision.

1. Car A moves East and car B moves West and had a head to head collision. Calculate the velocity of the two cars after the collision (speed and direction).

2. Car B follows car A and both head toward the East. Car B had a head to tail collision with car A. Calculate the velocity for the two cars after the collision(speed and direction).

3.Car A moves to the East and car B moves to the North and collide in a cross road. Calculate the velocity for the two cars after the collision (speed and the angle of the velocity).

explain in detail einsteins theory of general relativity. how so black holes effect gravity according to his theory?

how do,*

A 2.00 kg ball is thrown straight upward from the top of a 50.0 m high building with an initial speed of 10.0 m/s.

       Given:

       a. What is the total energy at the top of the building?

       b. What is the total energy at the ground?

       c. What are the potential and kinetic energies at the ground?

       d. What is its speed at the ground?

Two kg of water is contained in a piston–cylinder assembly, initially at 10 bar and 200°C. The water is slowly heated at constant pressure to a final state. If the heat transfer for the process is 1740 kJ, determine the temperature at the final state, in °C, and the work, in kJ. Kinetic and potential energy effects are negligible. (Moran, 01/2018, p. P-23) Moran, M. J., Shapiro, H. N., Boettner, D. D., Bailey, M. B. (01/2018). Fundamentals of Engineering Thermodynamics, Enhanced eText, 9th Edition [VitalSource Bookshelf version]. Retrieved from vbk://9781119391388 Always check citation for accuracy before use.

2: For this problem the heights are low enough that the acceleration due to gravity can be approximated as -g. (Note: even at low Earth orbit, such as the location of the International Space Station, the acceleration due to gravity is not much smaller then g. The apparent weightlessness is due to the space station and its occupants being in free-fall.)

A rocket is launched vertically from a launchpad on the surface of the Earth. The net acceleration (provided by the engines and gravity) is a₁ (known) and the burn lasts for t₁ seconds (known). Ignoring air resistance calculate:

a) The speed of the rocket at the end of the burn cycle.

b) The height of the rocket when the burn stops.

The main (now empty) fuel tank detaches from the rocket. The rocket is still propelled with the same acceleration as before due to the secondary fuel tank.

c) Calculate how long it takes for the main tank to fall back to the ocean back on the surface of the Earth in order to be recovered for next use.

d) Calculate the height of the rocket at the time when the tank hits the ocean.

e) At the time the main tank hits the ocean the secondary fuel tank runs out of fuel. Calculate the maximum height above the surface of the Earth that is reached by the rocket.