A racing bus rounds a corner on a banked bus-racing track. The radius of curvature of the turn is R and the curve is banked with a grade G. If the coefficient of static friction between the tires and the road is μ, determine the range of speeds at which the bus can take the turn without slipping off the road.

[Answer: √ (?−?)/(1−??) < ? √?? < √ (?+?)/(1+??) ]

Prove the product of a compact space and a countably paracompact space is countably paracompact.

Discuss the reduced zone-scheme for representing electron energy band structures and show how the periodic zone scheme and the reduced zone-schemes are equivalent.

Two objects with masses of 3.20 kg and 8.00 kg are connected by a light string that passes over a frictionless pulley, as in the figure below. (a) Determine the tension in the string. (Enter the magnitude only.) N (b) Determine the acceleration of each object. (Enter the magnitude only.) m/s2 (c) Determine the distance each object will move in the first second of motion if both objects start from rest. m

Suppose that you have obtained spectra of several galaxies and have measured the observed wavelength of the H-alpha line (rest wavelength = 656.3nm) to be:

Galaxy 1: 659 nm. Galaxy 2: 666.5 nm. Galaxy 3: 676.6 nm.

10. [4pt] Calculate the redshift, z, for each of these galaxies.

11. [4pt] Calculate the radial velocity of each of these galaxies.

12. [4pt] Assuming a Hubble Constant of 69.6 km/s/Mpc, cal- culate the distance to each of these galaxies (answer in Mpc).

Summarize the Source-Filter Theory. Be sure to incorporate glottal spectrum, resonance, bandpass filter, variable resonator, and the three functions.

a) Consider 1.3 moles of an ideal gas at an initial temperature of 400 K and in a 1.2 m³ closed container. If the gas goes through an isochoric process to twice the initial temperature, what is the new pressure of the gas in Pa?

b) Consider 1.3 moles of an ideal gas at an initial temperature of 400 K and in a 1.2 m³closed container. If the gas goes through an isothermal process to 3.6 m³, what is the new pressure of the gas in Pa?

c) Consider 1.3 moles of an ideal gas at an initial temperature of 400 K and in a 1.2 m³ closed container. If the gas goes through an isobaric process to 3.6 m³, what is the new temperature of the gas in Kelvin?

Photolithograph or e-beam lithography is known as a top-down approach to nanostructures while chemical synthesis is known as a bottom-up approach to nanostructures. Compare the advantages and disadvantages of these two different approaches in terms of a. cost, b. capital investment, c. control, d. precision, e. volume of production, and f. diversity of materials.

Estimate how often stars collide in the Milky Way (using the model of a cylinder with radius = disc scale length and height = 2* disc scale height)

Estimate how often galaxies collide in a galaxy cluster, i.e., the stellar component of one galaxy passing through another.(Model the average galaxy as a sphere with a radius of 10 kpc).

A 200 g hockey puck is launched up a metal ramp that is inclined at a 30° angle. The coefficients
of static and kinetic friction between the hockey puck and the metal ramp are #5 = 0.40 and pk =

0.30, respectively. The puck's initial speed is 14.9 m/s. What speed does it have when it slides back
down to its starting point?

questions 1) : How to control the polarization of light and intensity and phase of light ????

questions 2) : How to control the polarization, intensity, phase of liquid crystal ???

As a physics demonstration, you want a special bowling ball made to demonstrate exactly 1 kg·m2, so that your students can rotate the ball about its center of mass to get a "feel" for how "big" 1 kg·m2 is. The bowling balls most familiar to your students has a weight of 15.4 pounds and have a circumference of 25.5 inches, but do not have a moment-of-inertia equal to 1 kg·m2. Since the sporting goods manufacturer has no understanding of how \"big\" 1 kg·m2 is, calculate the diameter of the demo bowling ball (in inches) it will need to manufacture. Assume that bowling balls are solid, with a constant density.

63. Use Max Planck’s quantum theory to explain the following behaviour of photoelectrons.

a) Low-intensity light does not release any photoelectrons. What will happen if the light

is made brighter? Explain your reasoning.

b) Low-intensity light releases photoelectrons. What will happen if the light is made

brighter? Explain your reasoning.

c) Low-intensity light does not release any photoelectrons. What will happen if the

frequency of the light is gradually increased? Explain your reasoning.

3. List some types of optimization algorithms for photons and for protons planning.
Compare the dose distribution of Photon IMRt with the proton IMPT.
How are the organs at risk protected in photon therapy and how are in Proton therapy?