Two kg of water is contained in a piston–cylinder assembly, initially at 10 bar and 200°C. The water is slowly heated at constant pressure to a final state. If the heat transfer for the process is 1740 kJ, determine the temperature at the final state, in °C, and the work, in kJ. Kinetic and potential energy effects are negligible. (Moran, 01/2018, p. P-23) Moran, M. J., Shapiro, H. N., Boettner, D. D., Bailey, M. B. (01/2018). Fundamentals of Engineering Thermodynamics, Enhanced eText, 9th Edition [VitalSource Bookshelf version]. Retrieved from vbk://9781119391388 Always check citation for accuracy before use.

2: For this problem the heights are low enough that the acceleration due to gravity can be approximated as -g. (Note: even at low Earth orbit, such as the location of the International Space Station, the acceleration due to gravity is not much smaller then g. The apparent weightlessness is due to the space station and its occupants being in free-fall.)

A rocket is launched vertically from a launchpad on the surface of the Earth. The net acceleration (provided by the engines and gravity) is a₁ (known) and the burn lasts for t₁ seconds (known). Ignoring air resistance calculate:

a) The speed of the rocket at the end of the burn cycle.

b) The height of the rocket when the burn stops.

The main (now empty) fuel tank detaches from the rocket. The rocket is still propelled with the same acceleration as before due to the secondary fuel tank.

c) Calculate how long it takes for the main tank to fall back to the ocean back on the surface of the Earth in order to be recovered for next use.

d) Calculate the height of the rocket at the time when the tank hits the ocean.

e) At the time the main tank hits the ocean the secondary fuel tank runs out of fuel. Calculate the maximum height above the surface of the Earth that is reached by the rocket.

A satellite moves in a circular earth orbit that has a radius of 7.49 x 106 m. A model airplane is flying on a 24.1-m guideline in a horizontal circle. The guideline is nearly parallel to the ground. Find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.

1. A 2.00 kg ball is thrown straight upward from the top of a 50.0 m high building with an initial speed of 10.0 m/s. (25 points)

       Given: (1 point)

       a. What is the total energy at the top of the building? (6 points)

       b. What is the total energy at the ground? (6 points)

       c. What are the potential and kinetic energies at the ground? (6 points)

       d. What is its speed at the ground? (6 points)

Imagine a superfast fish that is able to swim faster than the speed of sound in water. Would this fish produce a “sonic boom”?

Use the concepts from this module to explain why flying bees buzz.

If the handle of a tuning fork were to be handled firmly against a table, would the sound from the tuning fork change? If so, what would change?

The strings of a harp have different length in order to produce different notes. However, given that the strings in a guitar have all the same length, how are the different notes produced?

The pitot static system of Cessna 172 is used to determine the indicated airspeed at which the aircraft is flying. Determination of airspeed on the airspeed indicator is based on using sea level density in the Bernoulli’s equation. If the pressure difference between the pitot tube on the wing and the static pressure probe on the fuselage side of the airplane is 40.9 lb/ft^2, determine the indicated airspeed of the aircraft in knots. If the aircraft is cruising at 5,500 feet in a standard atmosphere, determine the true airspeed in knots.

Define the following in plasma physics : 1- Larmor radius or Gyro- radius
2- Guiding-center
3- adiabatic invariants
4- first adiabatic invariant
5- The magnetic flux
   6- Harris field

Describe the conditions which are favorable for ozone destruction in polar regions. Include what occurs in polar spring which causes the rather abrupt commencing of ozone destruction.

What happens in polar summer that reverses some of the effects of ozone destruction that occur in polar spring?

Two eagles fly directly toward one another, the first at 15.0 m/s and the second at 24.2 m/s. Both screech, the first emitting a frequency of 3643 Hz and the other one of 3800 Hz. What frequencies do they receive if the speed of sound is 330 m/s? (Enter your answers to at least the nearest 10 Hz.)

Fill in blank space with the following words:

Black Hole

Law of Universal Gravitation

Efficiency

Power

Weight

Rotational Speed

Torque

1. A concentrated mass resulting from gravitational collapse near which gravity is so strong not even light can escape is called a                      ].
2. The ratio of the output energy for a machine to the total input energy is called the                        of the machine.
3. “For any pair of objects, each body attracts the other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass.” This is a statement of                              .
4.                     is the rate at which work is done or energy is transformed: work/time.
5.                     is the number of rotations per unit time.
6. The product of the force and the lever arm on a body which imparts a rotational acceleration on the object is called               .

7. The force of an object on a surface, usually due to gravity, is called

how much energy is needed to place four positive charges, each of magnitude +5.0 mc, at the vertices of a square of side 2.5 cm? choose one way of assembling the charges and calculate the potential at each empty vertex as this set of charges is assembled. be sure to clearly describe the order of assembly.

Consider the ground state energy of the hydrogen atom E₀.

Enter the expression you use to verify that the ground state energy is 13.6 eV? Use fundamental constants e, m_e, k and h.

E₀ = ?

a) If you have five capacitors with capacitances 1.1 × 10^-6 F, 3.5 × 10^-6 F, 5.5 × 10^-6 F, and two 8.6 × 10^-6 F in series. What is the equivalent capacitance of all five?

b) Initially the capacitors are uncharged. Now a 7 V battery is attached to the system. How much charge is on the positive plate of the 5.5 × 10^-6 F capacitor?

c)What is the potential difference between the plates of the 5.5 × 10^-6 F capacitor?

d) How much energy is stored in the entire capacitor system?

e) If you have five capacitors with capacitances 1.1 × 10^-6 F, 3.5 × 10^-6 F , 5.5 × 10^-6 F, and two 8.6 × 10^-6 F in parallel. What is the equivalent capacitance of all five?

f) If one attaches a 7 V battery to the system, how much charge is on the positive plate of the 5.5 × 10^-6 F capacitor?

g)What is the potential difference between the plates of the 5.5 × 10^-6 F capacitor?

h) How much energy is stored in the entire capacitor system?

Let’s look at some gravitational potentials and the density profiles that can generate them.

i) For ρ(r) = ρ◦r ◦^2/r^2 , what is the corresponding gravitational potential?

ii) For Φ(r) = −GM/[b + √ (b ^2 + r ^2)], what is the corresponding density profile?

iii) For Φ(R, z) = Φ◦ln[ (R ◦^2+R ^2+(z ^2/q^2))/R◦^2 ], what is the corresponding density profile ρ(R, z)? In this expression, the constant q controls the axis ratio of the potential, where q = 1 would be spherically symmetric and q < 1 means that the potential is “flattened” a bit along the z-axis. Does something strange happen along the z axis if q < 0.7 ?

In this exercise, the first of a series, we will make connections between the physics you have been learning (in this case, kinematics) and how it is used by people in their work and research. Today we consider an example from kinesiology research, based on a 2000 paper from the Journal of Measurement in Physical Education and Exercise Science (nota bene: you do not have to read this paper, or any of the hyperlinks to follow the exercise – it is only provided here for your interest).

Jumping is an activity common to many sports, such as basketball, volleyball, and others. An important part of training to improve jumping ability is tracking your progress: how else will you decide if your chosen routine is working? Researchers in the field , as well as professional athletes and their coaches , use a variety of techniques to accurately measure the vertical jump height. One approach is straightforward: just "see" how high you jump! To do it accurately, however, you need high speed cameras, a way of calculating the position of the body's centre of mass, balancing torques... very complicated. Or you can use the old "reach" method, having subjects jump and touch the highest point they can reach with a chalk-covered palm – but now you have to correct for differential arm length, swing timing... rather crude.

However, with your knowledge of kinematics, you can get away with as little as a stopwatch, saving valuable time and money. Below we will get you to follow in the footsteps of pioneering kinesiologists and exercise scientists and re-invent two of these physics-based methods. (By the way, this kind of use of mechanics in biology is called biomechanics.)

a) (Please refrain from looking at the rest of the question until you have given this part some thought: not to worry, no wrong answers here!) Given your knowledge of kinematics, what variable would you want to measure to be able to calculate someone's vertical jump height? Please explain in a few words how you would go about doing this.

b) Suppose you could measure the time of flight ?flight. How would you calculate the vertical jump height ℎ? (Unsurprisingly, this is called the time-of-flight method . Calculate the predicted height for the following times-of-flight: 0.827 s (LeBron James), 0.846 s (Michael Jordan), 0.864 s (Wilt Chamberlain), 0.53 s (the author of this exercise).

c) What about if you measured the vertical take-off velocity ?=(0,??) instead? (This is known as the impulse-momentum method , because of the way the take-off velocity is calculated using a force platform). Calculate the predicted height for the following take-off velocities: 3.91 m/s (LeBron James), 4.00 m/s (Michael Jordan), 4.09 m/s (Wilt Chamberlain), 2.60 m/s (the author of this exercise).

d) Suppose you have both numbers: would you expect them to be consistent, i.e., to give the same predicted vertical jump height? Give your reasons. How might you check for consistency?

e) Use the two datasets from the previous parts of this problem to check consistency. Were you right? If you found an inconsistency, list some of the reasons behind this inconsistency. If not, explain why you should expect them to be consistent.