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.

A 30 gallon cylindrical drum is filled with water and is slowly
drained from its base. Let h = the height of water left in the
drum. If the empty drum has a height of 1.4 meters and a
mass of 100 kg, calculate: (a) the mass of water in the drum;
(b) the radius of the drum; (c) the height of the c.o.m. of the
drum plus water left in the drum, as a function of h. (d) At
what value of h is the c.o.m. at its lowest point?

What is drift velocity?

Question 98)

Part 1)

A charged cloud system produces an electric field in the air near Earth's surface. A particle of charge -2.1 × 10^-9 C is acted on by a downward electrostatic force of 4.0 × 10^-6 N when placed in this field. (a) What is the magnitude of the electric field? (b) What is the magnitude of the electrostatic force on a proton placed in this field? (c) What is the gravitational force on the proton? (d) What is the ratio of the electrostatic force to the gravitational force in this case?

Part 2)

A block with a mass of 11.1 g and a charge of +6.70 × 10^-5 C is placed in an electric field with x component E_x = 2.77 × 10³ N/C, y component E_y = -728 N/C, and z component E_z = 0. (a) What is the magnitude of the electrostatic force on the block and (b) what angle does that force make with the positive x direction? If the block is released from rest at the origin at time t = 0, what are its (c) x and (d) y coordinates at t = 2.80 s?

Part 3)

An electron is shot at an initial speed of v₀ = 4.62 × 10⁶ m/s, at angle θ₀ = 40.9 ˚ from an x axis. It moves through a uniform electric field E→ = (5.40 N/C)j→. A screen for detecting electrons is positioned parallel to the y axis, at distance x = 1.84 m. What is the y component of the electron's velocity (sign included) when the electron hits the screen?

The electric potential immediately outside a charged conducting sphere is 220 V, and 10.0 cm farther from the center of the sphere the potential is 140 V.

(a) Determine the radius of the sphere.

. cm

(b) Determine the charge on the sphere.

nC

The electric potential immediately outside another charged conducting sphere is 250 V, and 10.0 cm farther from the center the magnitude of the electric field is 360 V/m. (c) Determine all possible values for the radius of the sphere. (Enter your answers from smallest to largest. If only one value exists, enter "NONE" in the second answer blank.)

(d) Determine the charge on the sphere for each value of r. (If only one value exists, enter "NONE" in the second answer blank.)

3.c Compare and contrast the interference fringe patterns of a Fabry-Perot interferometer and aMichelson interferometer, with each interferometer illuminated in the same way by a divergent laser light beam and with equal path differences contributing to the interference. Be sure to note both how the patterns are similar and why the patterns are different.

To supply heated air to a house, a high-efficiency gas furnace burns gaseous propane (C3H8) with a combustion efficiency of 96 percent. Both the fuel and 40 percent excess air are supplied to the combustion chamber at 25C and 100 kPa, and the combustion is complete. Because this is a high-efficiency furnace, the product gases are cooled to 40C and 100 kPa before leaving the furnace. To maintain the house at the desired temperature, a heat transfer rate of 31,650 kJ/h is required from the furnace. Determine the volume of water condensed from the product gases per day, in Litre/day.

Achondroplasia is a dominant trait that causes a characteristic form of dwarfism. In a survey of 50000 births, five infants with achondroplasia were identified. Two of the affected infants had affected parents, while three had normal parents.

Part A

Calculate the mutation rate for achondroplasia and express the rate as the number of mutant genes per given number of gametes.

Express your answer using two significant figures.

μ =