Engineering Answers

Thermal energies for nucleons in large nuclei are comparable with their

binding energies of about 6 MeV.

(a) To what temperature does this correspond?

(b) Within nuclear matter, identical nucleons are separated by about 2.6 ×

10^−15 m. What is roughly the minimum temperature needed for them

not to be degenerate (i.e., for the number of accessible states to be much

larger than the number of particles.)?

Consider a system of nonrelativistic electrons in a white dwarf star at a

temperature of 10^9 K. Very roughly, what would be their density if the system

is degenerate? How does this compare with typical electron densities in

ordinary matter of about 10^30 electrons/m3?

Consider a system of nonrelativistic electrons in a white dwarf star at a

temperature of 109 K. Very roughly, what would be their density if the system

is degenerate? How does this compare with typical electron densities in

ordinary matter of about 1030 electrons/m3?

Consider a system of two rolled dice, each having six possible states available

to it (six different numbers of dots showing upward). According to classical

statistics, how many different arrangements are available to this system

(a) if the dice are distinguishable,

(b) if the dice are identical.

(c) According to classical statistics, in what fraction of the total number of

different configurations do the two dice show the same number of dots?

(d) What is the true number of distinguishable configurations available to

two identical dice?

(e) For what fraction of the distinguishable configurations in (a) do the two

dice show the same number of dots?

Consider a system of three flipped coins. According to classical statistics,

how many different arrangements are available to this system:

(a) if the coins are distinguishable,

(b) if the coins are identical?

(c) For what fraction of the arrangements in (a) are all three heads or all

three tails?

(d) What is the true number of different heads/tails configurations available

to a system of three identical flipped coins?

(e) For what fraction of these arrangements are all three heads or all three

tails

Given the wavefunction of a standing wave: y(x,t) = A sin(πx)cos(2πt), where x and y are in meters and

t is in seconds. The position of the second anti-node from the end x = 0 is at:

Find the impulse response h[n] for a causal LTI discrete-time systems satisfying the given

difference equations and indicate whether the system is a FIR or an IIR system.

y[n] + y[n - 1] = x[n] - 2x [n - 1]

Find the impulse response h[n] for a causal LTI discrete-time systems satisfying the given 
difference equations and indicate whether the system is a FIR or an IIR system.
y[n] = x[n] + 1/2 x[n - 1] + 2x [n - 2] + 4x[n - 3] - x[n - 5]

Determine the area bounded by the curves y=6x =x^2 and y=x^2 2=2x

Consider a pile group consisting of three piles arranged at the vertices of an equilateral triangle. The total load S is initially distributed evenly over the three piles (each pile carries initially S/3). S is assumed to follow the normal distribution with mean value S and coefficient of variation 30%. The capacity of each pile is also assumed to follow the normal distribution with mean value 25/3 and coefficient of variation 20%. When the first pile fails in this group, its entire load of S/3 is transferred to one of the two surviving piles (the other surviving pile gets no additional load). When the second pile fails, its entire load is transferred to the last surviving pile. Compute the probability of failure of this pile group.