Briefly describe Millikan’s oil drop experiment and what do the results tell us about electric charge.

There are many subtle effects that must be taken into account in calculations involving GPS satellites. Estimate just the effect of the time dilation of special relativity.

(a) Find the speed of a GPS satellite (height is 20,200 km above the surface of Earth). Hence, find the time difference between a clock in the satellite and one on the ground after one complete orbit, assuming they were originally synchronized (ignore all effects except time dilation).

(b) Suppose we forgot to allow for this time difference. Estimate the resulting error in the calculation of our position.

A hollow sphere of radius 0.230 m, with rotational inertia I = 0.0739 kg·m² about a line through its center of mass, rolls without slipping up a surface inclined at 22.5° to the horizontal. At a certain initial position, the sphere's total kinetic energy is 18.0 J. (a) How much of this initial kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at the initial position? When the sphere has moved 0.840 m up the incline from its initial position, what are (c) its total kinetic energy and (d) the speed of its center of mass?

At a particular moment, three charged particles are located as shown in the figure below. Q1 = −4.5 μC, Q2 = +5.5 μC, and Q3 = −7.0 μC. Your answers to the following questions should be vectors. (Recall that 1 μC = 1 ✕ 10−6 C. Assume that the +x axis is to the right, the +y axis is up along the page and the +z axis points into the page. Express your answers in vector form.) (a) Find the electric field at the location of Q3, due to Q1. E1 = −2.5e7 Incorrect: Your answer is incorrect. N/C (b) Find the electric field at the location of Q3, due to Q2. E2 = N/C (c) Find the net electric field at the location of Q3. Enet = N/C (d) Find the net force on Q3. Fnet,3 = N (e) Find the electric field at location A due to Q1. E1 = N/C (f) Find the electric field at location A due to Q2. E2 = N/C (g) Find the electric field at location A due to Q3. E3 = N/C (h) What is the net electric field at location A? EA = N/C (i) If a particle with charge −6.0 nC were placed at location A, what would be the force on this particle? Fon A =

3 moles of an ideal gas with 2 atoms under 308 K temperature and 5 atm are expanded reversible to 1 atm end pressure. Calculate w, q, ΔU, ΔH values ​​in case of expansion of this expansion by isothermal and adiabatic way.

A block with mass 0.460 kg sits at rest on a light but not long vertical spring that has spring constant 85.0 N/m and one end on the floor.

a)How much elastic potential energy is stored in the spring when the block is sitting at rest on it?

b) A second identical block is dropped onto the first from a height of 4.10 mm above the first block and sticks to it. What is the maximum elastic potential energy stored in the spring during the motion of the blocks after the collision?

c)What is the maximum distance the first block moves down after the second block has landed on it?

Two metal spheres of identical mass m = 3.60 g are suspended by light strings 0.500 m in length. The left-hand sphere carries a charge of 0.765 µC, and the right-hand sphere carries a charge of 1.61 µC. What is the equilibrium separation between the centers of the two spheres?

At time t = 11.5 sec, a particle of mass M = 5 kg is at the position (x,y,z) = (4,4,6) m and has velocity (2,1,-2) m/s.

1) What is the x component of the particle's angular momentum about the origin?

Answer: -70 kg m²

2) What is the y component of the particle's angular momentum about the origin?

Answer:100 kg m²

3) What is the z component of the particle's angular momentum about the origin?

Answer: -20 kg m²

4) Now an identical particle is placed at (x,y,z) = (-4,-4,-6) m, with velocity (-2,-1,2) m/s. What is the x component of the pair's total angular momentum about the origin?

Answer: -140 kg m²

5) What is the y component of the pair's total angular momentum about the origin?

Answer: 200 kg m²

6) What is the z component of the pairs's total angular momentum about the origin?

Answer: -40 kg m²

7) Finally a thin rod of mass 11 kg is added between the two particles Since the particles are moving perpendicular to the line separating them and in opposite directions (you should convince yourself that this is true), then the particles + rod system rotates about its center of mass. What the angular frequency of rotation of the rod + particles system? (Note: The particles are moving perpendicular to the line separating them and in opposite directions (you should convince yourself that this is true), then the particles + rod system rotates about its center of mass.)

Answer: 0.364 rad/sec

8) What is the magnitude of the total angular momentum of the system (particles plus rod)?

Please solve number 8!

A hydrostatic system consists of 0.1 moles of an ideal gas whose specific heat capacity at constant volume, ??, is equal to 3?2 where R is the gas constant equal to 8.31 J mol–1 K–1. Its initial pressure and volume are 32 Pa and 8 m3. In its final state, the pressure is just 1 Pa and its volume increases eightfold. The particular thermodynamic process can be represented on an indicator diagram as a straight line joining the initial and final states.
(a) Determine a relationship between the pressure and the volume of the gas that represents the thermodynamic process.

(b) Establish a relationship between the temperature and the volume of the gas valid for the thermodynamic process.

(c) Determine the volume of the gas when the temperature is a maximum.

(d) Determine the temperature of the gas at the initial and final states, and the maximum temperature attained by the gas in the process.

(e) Imagine that the gas, while following the thermodynamic process outlined above, is at some arbitrary state such that its volume is V. This state is somewhere between the initial and final states. Determine the heat exchange that occurs while the gas is traversing (along the process) from the initial to the arbitrary state. Your expression should be a function of V only.

(f) With reference to part (e), determine that volume which corresponds to maximum heat exchange. Hence determine the corresponding temperature.

1 - The plates of a spherical capacitor have radii of 38.9 mm and 40.2 mm.

(i) Calculate the capacitance. (in F)

(ii) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance? (in cm^2)

______________

2 - Now in another experiment, The plates of a spherical capacitor have radii of 37.6 mm and 43.6 mm.

i) Calculate the capacitance. (in F)?

(ii) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?(in cm^2)

What happens to the observer's local night sky as the observer's latitude gradually changes:

A. from the equator gradually towards the north pole

B. as local time passes from sunset to sunrise?

C. as local time passes over the course of several weeks and months?

6. A one-dimensional diatomic crystal contains 2 different atoms with masses ?1 and ?2, with ?1< ?2, in each of its unit cell. Assume that there is interaction between every nearest neighbor atoms that can represented by a spring with spring constant ?. Derive the phonon frequency dispersion relation ?(?) of the crystal. Indicate which one is the acoustic branch and which one is the optical branch.

A 2 km diameter thunderstorm produces 4.2 cm of rainfall in 4 hours.  What is the power production from latent heat of condensation of this storm, in megawatts?  A megawatt is a million watts and the average coal-fired plant in the US produces 677 megawatts.

What is PET— what kind of image does it create and how?

Why use PET with CT rather than CT alone? Give the main reason/application.

What sort of radiation is involved? Is PET “perfectly safe”? If not, what are the dangers?