1. (c) Powder diffraction experiment:

   The incident wavelength of a neutron beam is λ = 2.662 Å. The distance between adjacent atoms in a simple cubic crystal structure is 3.26 Å. Calculate the scattering angle of the 1st,

   2nd and 3rd diffraction maximum. Up to which order ’n’ can the diffraction peaks be observed?

A 15.0-L tank containing 1.0 mol of argon gas is at 298 K.

(a) Calculate the initial pressure of the gas and d, the length of the cube containing this volume.

(b) Using your value for d, calculate the energies of the two lowest translational energies for the system E1,1,1 and E2,1,1 and their differences  ΔE .

(c) The tank is opened and the gas is allowed to expand rapidly into a cubical 2000L room such that there is no heat exchange with the surrounding.

Assuming n2,1,1/n1,1,1 remains constant, Determine the new temperature of the gas.

Handwritten answers are preferred.

A proton, moving with a velocity of v_iî, collides elastically with another proton that is initially at rest. Assuming that after the collision the speed of the initially moving proton is 1.40 times the speed of the proton initially at rest, find the following.

(a) the speed of each proton after the collision in terms of v_i

initially moving proton

initially at rest proton

(b) the direction of the velocity vectors after the collision (assume that the initially moving proton scatters toward the positive y direction)

initially moving proton

initially at rest proton

Steam at 100°C is added to ice at 0°C.

The sketch below is a free-body diagram (with all the forces shown) of a bridge. The distance are each 800 cm along the bottome of the bridge, "RL" to "A", "A" to "C", "C" to "B" and "B" to "R". The vertical height shown on the right side of the sketch is 1385 cm. The known forces are A= 5000 N, B= 3000 N and C= 10,000 N. You are to calculate the unknown reactions RLx, RLy and Rr.   

As a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint concerns a stop sign at the corner of Pine Street and 1st Street. Residents complain that the speed limit in the area (55 mph) is too high to allow vehicles to stop in time. Under normal conditions this is not a problem, but when fog rolls in visibility can reduce to only 155 ft. Since fog is a common occurrence in this region, you decide to investigate.

The state highway department states that the effective coefficient of friction between a rolling wheel and asphalt ranges between 0.689 and 0.770, whereas the effective coefficient of friction between a skidding (locked) wheel and asphalt ranges between 0.450 and 0.617.Vehicles of all types travel on the road, from small VW bugs weighing 1430 lb to large trucks weighing 9180 lb.

Considering that some drivers will brake properly when slowing down and others will skid to stop, calculate the minimum and maximum braking distance needed to ensure that all vehicles traveling at the posted speed limit can stop before reaching the intersection.

minimum braking distance: ft

maximum braking distance: ft

Given that the goal is to allow all vehicles to come safely to a stop before reaching the intersection, calculate the maximum desired speed limit.

maximum speed limit: mph

Which factors affect the soundness of your decision?

Drivers cannot be expected to obey the posted speed limit.

Reaction time of the drivers is not taken into account.

Precipitation from the fog can lower the coefficients of friction.

Newton's second law does not apply to this situation.

Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +2q. Sphere B carries a charge of +3q. Sphere C carries no net charge. Spheres A and B are touched together and then separated. Sphere C is then touched to sphere A and separated from it. Last, sphere C is touched to sphere B and separated from it. For the following questions, express your answers in terms of q.

(a) How much charge ends up on sphere C?

  
(b) What is the total charge on the three spheres before they are allowed to touch each other?

(c) What is the total charge on the three spheres after they have touched?

A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 56.0 J and a maximum displacement from equilibrium of 0.258 m.

(a) What is the spring constant?
N/m

(b) What is the kinetic energy of the system at the equilibrium point?
J

(c) If the maximum speed of the block is 3.45 m/s, what is its mass?
kg

(d) What is the speed of the block when its displacement is 0.160 m?
m/s

(e) Find the kinetic energy of the block at x = 0.160 m.
J

(f) Find the potential energy stored in the spring when x = 0.160 m.
J

(g) Suppose the same system is released from rest at x = 0.258 m on a rough surface so that it loses 15.2 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant?
m

A cue ball traveling at 5.0 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is deflected so that it makes an angle of 30° with its original direction of travel.

(a) Find the angle between the velocity vectors of the two balls after the collision.
(b) Find the speed of each ball after the collision.

One billiard ball is shot east at 1.8 m/s . A second, identical billiard ball is shot west at 1.1 m/s . The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90∘ and sending it north at 1.49 m/s .

a) What is the speed of the first ball after the collision? Express your answer to two significant figures and include the appropriate units.

b) What is the direction of the first ball after the collision? Give the direction as an angle south of east. Express your answer to two significant figures and include the appropriate units.

The CM of an empty 1000-kg car is 2.45 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.70 m from the front of the car, and three people sit in the back seat 3.80 m from the front? Assume that each person has a mass of 70.5 kg .

A bullet of mass 1.7×10−3 kg embeds itself in a wooden block with mass 0.980 kg , which then compresses a spring (k = 160 N/m ) by a distance 6.0×10−2 m before coming to rest. The coefficient of kinetic friction between the block and table is 0.53. What is the initial speed of the bullet?

Can you give me an example of translational equilibrium without rotational equilibrium?
I also need an example of rotational equilibrium without translational equilibrium. Thanks!

A 60.0-g object connected to a spring with a force constant of 40.0 N/m oscillates with an amplitude of 7.00 cm on a frictionless, horizontal surface.

(a) Find the total energy of the system.
mJ

(b) Find the speed of the object when its position is 1.30 cm. (Let 0 cm be the position of equilibrium.)
m/s

(c) Find the kinetic energy when its position is 2.50 cm.
mJ

(d) Find the potential energy when its position is 2.50 cm.
mJ