Consider a plane wave of monochromatic green light, ? = 500 nm, that is incident normally upon two identical narrow slits (the widths of the individual slits are much less than ?). The slits are separated by a distance d = 30 µm. An interference pattern is observed on a screen located a distance L away from the slits. On the screen, the location nearest the central maximum where the intensity is zero (i.e., the first dark fringe) is found to be 1.5 cm from this central point. Let this particular position on the screen be referred to as P1.
(a) Calculate the distance, L, to the screen. Show all work.

(b) calculate the ditance between the first and second dark bands in the interference pattern. Shown all work.

(c)In each of the parts below, one change has been made to the problem above (in each case, all parameters not explicitly mentioned have the value or characteristics stated above). For each case, explain briefly whether the light intensity at location P1 would remain zero or not. If not, will P1 become the location of a maximum constructive interference (bright) fringe? In each case, explain your reasoning.

1) One of the two slits is made slightly narrower, so that the amount of light passing through it is less than that through the other.

2) The wavelength is doubled so that ? = 1000 nm.

3) The two slits are replaced by a single slit whose width is exactly 60 µm.

1.On a spacecraft, two engines are turned on for 542 s at a moment when the velocity of the craft has x and y components of v_0x = 2960 m/s and v_0y = 5010 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 3.31 x 10⁶ m and y = 4.76 x 10⁶ m. Find the (a) x and (b) y components of the craft's acceleration.

2.A horizontal rifle is fired at a bull's-eye. The muzzle speed of the bullet is 690 m/s. The gun is pointed directly at the center of the bull's-eye, but the bullet strikes the target 0.028 m below the center. What is the horizontal distance between the end of the rifle and the bull's-eye?

3.A golf ball rolls off a horizontal cliff with an initial speed of 14.0 m/s. The ball falls a vertical distance of 12.7 m into a lake below.(a) How much time does the ball spend in the air? (b) What is the speed v of the ball just before it strikes the water?

4.A rocket is fired at a speed of 85.0 m/s from ground level, at an angle of 38.0

I understand how electrons initially move into another's vicinity, but nowhere can I find a fathomable answer to this. Also, does the pairs forming 'a condensate' mean a Bose-Einstein condensate?

A spherical object has an outside diameter of 60.0cm . Its outer shell is composed of aluminum and is 2.80cm thick. The remainder is uniform plastic with a density of 720kg/m3 .

A) Determine the object's average density.

B) Will this object float by itself in fresh water?

An object with a density of 761.0 kg/m³ and a mass of 1399.0 kg is thrown into the ocean. Find the volume that sticks out of the water. (use ?_seawater = 1024 kg/m³)

Describe how at least one of the laws of thermodynamics relates to your room, or the heating or cooling of your room and Comment on three ways to improve the efficiency of your room.

True or Flase, preferably explain the reasoning behind the answer

a)The electric field inside the solid metal sphere is never zero

b)If the solid sphere is an insulator (instead of metal) with net charge Q, the charges are wherever they were placed, and cannot move around.

c) If the solid sphere is an insulator (instead of metal) with net charge Q, the electric field for r >> R would be the same as that of a conductor with the same shape and charge.

d)The net charge on the inside of the solid metal sphere is neutral.

e)The electric field for the metal sphere at r << R will be the same as the field of a point charge, Q, at the origin

f)The electric field near the metal surface on the outside is parallel to the surface.

List the 8 different types of simple machines. The 8th one is harder and less obvious.

Six similar boxes (A–F) are initially sliding in the positive direction along a frictionless horizontal surface at a speed of 10 m/s. Then a net horizontal force, also in the positive direction, is applied to each box for a period of 10 seconds. The masses of the boxes and the net horizontal force for each case are given below.

Rank the boxes in order of increasing FINAL momentum. That is, put first the box with the smallest final momentum, and put last the box with the largest final momentum.

If B is smallest, then A, C, D, and finally E is largest, enter BACDE.
Note: if final momenta are equal, then enter those cases in the order listed.

A) F = 30 N. . . . . . M = 15 kg
B) F = 80 N. . . . . . M = 10 kg
C) F = 70 N. . . . . . M = 15 kg
D) F = 75 N. . . . . . M = 15 kg
E) F = 95 N. . . . . . M = 25 kg
F) F = 110 N. . . . . . M = 10 kg

explain step by step please

1) A projectile returns to its original height after 4.08 seconds, during which time it travels 76.2 meters horizontally. If air resistance can be neglected, what was the projectile's initial speed?

(Use g = 9.80 m/s2)

When we receive an X-ray at the dentist office why do they place a lead apron on our chest? Why is it lead? What type of radiation?

A parallel plate capacitor with plate area 100.0cm² and air-gap separation .500mm is connected to a 12.0 V battery, and fully charged. The batter is then disconnected.

A.) The plates are now pulled to a separation of 1.00mm. What is the magnitude of the charge on each capacitor plate and the magnitude of the E-field between the plates now? ( ?₀ = 8.85 x 10^-12 C²/Nm²)

B.) What is the potential difference across the plates now?

C.) How much work was required to pull the plates to their new separation?

D.) If a proton was released from the + plate and hit the - plate, what speed would it have?

Thanks :D

A 20 g ball of clay traveling east at 3.0 m/s collides with a 30 g ball of clay traveling north at 2.0 m/s. What is the magnitude and direction of initial momentum for each ball before collision? a. What is the momentum of 50 g blob of clay in x? What is the speed in that same direction? b. What is the momentum of 50 g blob of clay in y? What is the speed in that same direction? c. What is the resultant speed of the blob? d. What is direction of the blob?

A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 23.4 m/s at an angle of 48.0° to the horizontal.

(a) By how much does the ball clear or fall short of clearing the crossbar? (Enter a negative answer if it falls short.)
m
(b) Does the ball approach the crossbar while still rising or while falling?

rising or falling

When a small object approaches a much more massive object, the smaller object can be tidally disrupted. The distance of the closest approach before being tidally disrupted is the Roche limit (recall lecture on rings of plan- ets). If the small object is a star and the large object is a supermassive black hole, the Roche limit is given by

rR= 2.4 * RS * (pBH/p*)^(1/3)

where RS is the Schwarzschild radius, ρ̄BH is the average density of the black hole and ρ̄∗ is the average density of the star.

1. a) Setting the average density of the supermassive black hole equal to its mass divided by the volume contained within the Schwarzschild radius, derive an expression for the mass of a black hole as a function of ρ̄∗ that would have rR = RS.

2. b) If the Sun were to fall into a supermassive black hole, what maximum mass could the black hole have if the Sun would be tidally disrupted before crossing the event horizon (or RS). Compare your answer with typical supermassive black holes in the galactic nuclei.

3. c) If the mass of the supermassive black hole exceeded the mass found above, what would be the implication in terms of the energy release of the infalling star? Could infalling stars effectively power AGNs in this case?