5. Two charges with a (charge) ratio of 1:3 are 30cm apart from each other in vacuum (free space).

   1. a) How far do both charges need to be placed in water when we want to achieve the same interaction force in both cases? (εr,water@20°C = 80.1)

1) a car battery is rated at 90 amphour. How much charge is available in the battery?

2) A +2.6 uc point charge is placed at the center of a cube with sides of length 7.5cm. What is the electric flux through two sides of the cube?

3) The amount of charge flowing though a circuit caries with time according to.. q(t)=(0.2t²-0.3t), with q in coulombs and t in seconds. Find the current through the circuit at t = 1.5 seconds.

4) Calculate the acceleration of an electron placed in a uniform electric field of magnitude 4.5*10⁵ N/C.

A conducting single-turn circular loop with a total resistance of 7.50 Ω is placed in a time-varying magnetic field that produces a magnetic flux through the loop given by ΦB = a + bt2 − ct3, where a = 8.00 Wb, b = 15.5 Wb/s−2, and c = 7.50 Wb/s−3. ΦB is in webers, and t is in seconds. What is the maximum current induced in the loop during the time interval t = 0 to t = 1.55 s? (Enter the magnitude.)

Can a person, in principle, travel from Earth to the galactic center (which is about 2.30

1) An evacuated tube uses an accelerating voltage of 44 kV to accelerate electrons to hit a copper plate and produce X-rays. Ignoring relativistic effects, what would be the maximum speed of these electrons?

2) A battery-operated car uses a 12.0-V system. Find the charge the batteries must be able to move in order to accelerate the 600 kg car from rest to 30.0 m/s.

3) I want to accelerate an electron to the speed of sound (343 m/s) by electrostatic force alone. To do so I’ve devised a way to store as much charge as I’d like at a single fixed point which will be located 0.35 m from the electron. How much charge do I need to accumulate to accomplish my goal?

Complete derivation of the infinite square well without the use of dirac delta functions.

Please show every single step.
I know this is long but Thanks Alot.

1. (i) Sketch the relationship between isotherms and heat flow vectors.
(ii) The magnitude of the heat flow vector is proportional to the temperature gradient. Use this to show why a steady-state geotherm must be a straight line in the absence of heat production. 7. Why is it that P waves can convert to SV, but not SH, at a horizontal interface? Explain.

2. The stress and strain tensors are symmetric; that is, _ij = _ji and _ij = _ji . Explain why this is true for the stress tensor.

3. Explain why the following moment tensor is not consistent with an earthquake. What else could have produced it?

M = AI, where A being constant
10. The ray parameter (in a flat Earth) is given by p_x = sin  / c. Use this to find the bottoming depth for a ray in a medium with the linearly increasing velocity profile c = c₀ + kz.

4. A sinusoidal temperature variation at the surface has a characteristic depth of penetration into a half-space z_c = ,for which the temperature as a function of time and depth is T (z,t) = A₀ e^i(t-z/z_c⁾e^-z/z_c. For a rockwith thermal diffusivity of 5×10^-6 m²/s, at what depth will the temperature have its daily maximum when the surface temperature has its daily minimum?

5. A simple-shear displacement field is written as u = x  Show that it contains both strain and rotation components.

Einstein's Theory of General Relativity can be considered a "good theory."

a) What did this theory explain that other theories could also explain?

b) What did this theory explain that other theories could not explain?

c) What did this theory predict that nobody had expected, but which were found experimentally?

Two trains face each other on adjacent tracks. They are initially at rest, and their front ends are 33 m apart. The train on the left accelerates rightward at 1.06 m/s². The train on the right accelerates leftward at 1.02 m/s².

(a) How far does the train on the left travel before the front ends of the trains pass?
m

(b) If the trains are each 150 m in length, how long after the start are they completely past one another, assuming their accelerations are constant?
s

How will voltage and current behave in a circuit with two adjacent batteries (battery-battery-bulb-bulb)? How does this change for two non-adjacent batteries (battery-bulb-battery-bulb)?

A toy car with a mass of 120 g moves to the right with a speed of 0.64 m/s. A small child drops a 36.0-g piece of clay onto the car. The clay sticks to the car and the car continues to the right. What is the change in speed of the car? Consider the frictional force between the car and the ground to be negligible.

Develop an I/O port decoder, using a PLD, that generates 16-bit I/O strobes for the following 16-bit I/O port addresses: 1000H-1001H, 1002H-103H, 1004H-1005H, 1006H-1007H, 1008H-1009H, 100AH-100BH, 100CH-100DH, and 100EH-100FH.

Consider passwords of length 8 using symbols from the set of lower case letters: {a, b, c, ..., z}.

(a) How many such passwords use the letter p exactly two times and the letter q exactly two times? To illustrate, both akpqbqop and quaqpoop satisfy this condition. Include a brief indication of your strategy.

(b) How many such passwords use the letter p exactly once and the letter q exactly once and also have letters arranged so the p is not next to the q? To illustrate, we want to count passwords like amkquoop but not moopguzz or whaqpodo since these have the symbol p next to the q. Include a brief indication of your strategy.

12.64

A dumbbell has a mass m on either end of a rod of length 2a. The center of the dumbbell is a distance r from the center of the Earth, and the dumbbell is aligned radially. If r≫a, the difference in the gravitational force exerted on the two masses by the Earth is approximately 4GmMEa/r3. (Note: The difference in force causes a tension in the rod connecting the masses. We refer to this as a tidal force.)
Suppose the rod connecting the two masses m is removed. In this case, the only force between the two masses is their mutual gravitational attraction. In addition, suppose the masses are spheres of radius a and mass m=43πa3ρ that touch each other. (The Greek letter ρ stands for the density of the masses.)

Part A

Write an expression for the gravitational force between the masses m.

Express your answer in terms of the variables a, ρ, and appropriate constants.

F=?

Part B

Find the distance from the center of the Earth, r, for which the gravitational force found in part A is equal to the tidal force (4GmMEa/r3). This distance is known as the Roche limit.

Express your answer in terms of the variables ME, ρ, and appropriate constants.

r=?

Part C

Calculate the Roche limit for Saturn, assuming ρ=3330kg/m3. (The famous rings of Saturn are within the Roche limit for that planet. Thus, the innumerable small objects, composed mostly of ice, that make up the rings will never coalesce to form a moon.)

Express your answer using three significant figures.

r_S=?

Please explain the answers. Thanks

3.

a) Find the acceleration of gravity at the height of 2.0 x 10⁶ above the earth.

b) A spherical asteroid that is the size of Texas would have a mass about 2.4 x 10²¹kg and radius of 4.7x 10⁵ meters. Find the acceleration of gravity on this asteroid.
c) Name three controls on a car that control acceleration.

d) Explain how the spin cycle of a washing machine removes most of the water from the wet clothes.