Explain how the latest technology is used in the investigations of fingerprints, DNA, and firearms?

The mass flow rate of steam through an ideal Rankine turbine ( with an isentropic turbine and an isentropic pump) is 30lbm/s. The water and or steam is at a pressure of 1000 psia throughout the boiler and superheater and exits the superheater at a temperature of 600 F. The condenser is at a pressure of 2 psia, and the water exits the condenser as a saturated liquid. Calculate the following.

(a) the power output of the turbine

(b) the overall thermal efficiency of the cycle

(c) The Carnot efficiency of the cycle based on the boiler and condenser temperatures

3. There are several techniques for determining body composition. One method is hydrostatic weighing, or “underwater weighing”. To do this measurement, the person is weighed while standing in air on a regular scale and weighed again while completely immersed in water. By comparing these scale readings, the average density of the person can be calculated. From that density, the body fat percentage of the person can be calculated. Imagine you are a physical therapist, determining the body composition of a patient. The scale reading of your patient standing in air on a regular scale is 177 pounds, and while completely immersed in water is 2.5 pounds. NOTE: In this problem, a fair amount of precision is needed, so please: use g = 9.8 m/s2 , not the estimate of 10 m/s2 for converting units of force, use 1.0 pound = 4.45 Newtons

(a) Draw two free body diagrams of the patient: one when they are weighed in air on a regular scale, and one when they are weighed while immersed in water. Label each of the forces with its name.

(b) Determine the magnitude of each of the forces on your diagrams. (Recall the magnitude of a force is how big that force is.) Include units!

(c) Determine the mass of your patient. Include units!

(d) Determine the density of your patient. Give your answer both kilograms per cubic meter and in grams per cubic centimeter. Include units!

The body is made up of essentially two components: fat mass (the total fat of an individual) and fat-free mass (everything else: bone, water, lean tissue, etc.) Studies have determined that the densities of these two components are: Density of fat mass = 0.90 grams per cc Density of fat-free mass = 1.10 grams per cc (In physics, we write cubic centimeter as cm3 . In medicine, cubic centimeter is written as cc.) A person with a density of 0.90 g/cc would have 100% body fat, and a person with a density of 1.10 grams/cc would have zero percent body fat. Real people fall between these two extremes.

(e) Given the above information, assess your result for your patient’s density. Do you have confidence that your answer is reasonable? Explain why or why not.

(f) You discover that the scale reading of 2.5 pounds was actually obtained with the patient submerged in seawater, not fresh water. Which of the following is true? Circle one answer. Explain.

A. The calculated value of density is higher than the person’s actual density.

B. The calculated value of density is lower than the person’s actual density.

C. The patient’s density would be calculated correctly

Consider the data for a block of mass

m = 0.245 kg

given in the table below, which gives the position of a block connected to a horizontal spring at several times. Friction is negligible.

(a) What is the mechanical energy of the block–spring system?
J

(b) Write expressions for the kinetic and potential energies as functions of time. (Use the following as necessary: t. Assume K and U are measured in joules. Do not include units in your answer.)

Momentum, Impulse, and Collisions:

A 1050kg sports car is moving westbound at 15.0m/s on a level road, when it collides with a 6,320kg truck driving east on the same road at 10.0m/s. The two vehicles remain locked together after the collision.

What is the velocity (magnitude & direction) of the two vehicles just after the collision?

At what speed should the truck have been moving so that both it and the car are stopped in the collision?

Find the change in kinetic energy of the system of two vehicles for the situations of part a) and b). 

For which situation is the change in kinetic energy greater in magnitude?

Orbital Mechanics:

A small space probe is put into circular orbit about a newly discovered moon of Saturn. The moon’s radius is known to be 550 km. If the probe orbits at a height of 1500 km above the moon’s surface and takes 2.0 earth days to make one orbit, determine the moon’s mass. Consider the total radial distance required to solve this problem. Be sure to perform all the necessary dimensional conversions to mks units.

A boy on a carnival bungee ride is released from rest at the bottom of the ride and oscillates up and down with an amplitude of 8 meters and a period of 4s. How long after he is released does he first get to a height 10m above the place where he started? [Hint: Choose the top of the poles as y=0, and measure positive downward.]

A) For hydrogen, find the frequency of light emitted in the transition from the 130th orbit to the 122th orbit.


B) For hydrogen, find the frequency of light absorbed in the transition from the 168th orbit to the 173th orbit.

A bullet with mass 25g and initial horizontal velocity 320m/s strikes a block of mass 2kg that rests on a frictionless surface and is attached to one end of a spring. The bullet becomes embedded in the block. The other end of the spring is attached to the wall. The impact compresss the spring a maximum distance of 25cm. After the impact, the block moves in simple harmonic motion.

1. What is the frequency of the oscillation?

2. Sketch graphs for the block’s position, velocity, and acceleration as a func- tion of time (x vs. t, v vs. t, a vs. t). Check to make sure your graphs are consistent.

3. Write an description of what is happening to the energy in this system from the time the bullet is fired until the block returns to its starting position for the first time. Meaning, tell a story about how the energy changes form or moves from one object to another.

4. Prove that if there are two operators A, ˆ Bˆ, such that their commutator [A, ˆ Bˆ] = λ where
λ is a constant. Show that (6 points)

exp[μ(Aˆ + Bˆ)] = exp(μAˆ) exp(μBˆ) exp(−μ
2λ/2)

where given an operator Xˆ; exp(tXˆ) = 1 + tXˆ +
1
2
t
2Xˆ 2 + ... +
1
n!
t
nXˆ n + ... (the usual

exponential series implemented for operators).

1. You release a disk (momentum of inertia Idisk=(1/2)mr2 ) with mass m = 100 g and radius r = 10 cm from height 15 cm on a ramp with angle 15°, write down the energy conservation equation for the object at the bottom of the ramp.

2. Use the energy conservation equation you wrote down from step 1, solve for the velocity of the disk at the bottom of the ramp.

3. Does your answer of the final velocity of the disk depend on its mass or radius? Explain your answer.

4. If the disk you rolled down the ramp were twice as heavy (i.e., if it had twice the mass), how would this affect your results?

5. If the disk you rolled down the ramp were twice as large (i.e., if it had twice the radius), how would this affect your results?

6. If you rolled any disk down a ramp 15 cm high, what is its speed at the bottom?

7. If you rolled any ring down a ramp 15 cm high, what is its speed at the bottom? Note that for the ring, its momentum of inertia Iring = mr2 .

8. If you rolled a sphere, disk, and ring at the same time, in what order do they reach the bottom? Assume the height is 15 cm.

9. If you dropped a sphere, disk, and ring at the same time, in what order do they hit the ground? Assume the height is 15 cm.

Derive T=MBsin(θ)=NIABsin(θ)

A dockworker loading crates on a ship finds that a 34-kg crate, initially at rest on a horizontal surface, requires a 73-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 50 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor

A bullet weighing 0.1 lb is fired vertically downward from a stationary helicopter with a muzzle velocity of 1200 ft/sec. The air resistance (in lbs) is numerically equal to 16^-5v², where v is the velocity of the bullet in ft/sec.

a)If the helicopter is 3,000 ft high, how long does it take for the bullet to hit the ground?