A man is running at speed c (much less than the speed of light) to catch a bus already at a stop. At t=0, when he is a distance b from the door to the bus, the bus starts moving with the positive acceleration a.
Use a coordinate system with x=0 at the door of the stopped bus.

a)

What is xman(t), the position of the man as a function of time?

Answer symbolically in terms of the variables b, c, and t.

3. The density of CH₃CN 0.786 g/ml and the density of CH₃OH is 0.791g/ml. A solution is made by dissolving 22.5ml of CH₃OH in 98.7ml. Of CH₃CN.

a. What is the mole fraction of methanol in the solution?

b. What is the molality of the solution?

c. Assuming that the volumes are additive, what is the molarity of CH3OH in the solution?

4. Consider two solutions, one formed by adding 10 g of glucose to 1L of water and the other formed by adding 10g of sucrose to 1L of water. Calculate the vapor pressure for each solution at 20oZC; the vapor pressure of pure water at this temperature is 17.5 torr.

A gasoline engine has a power output of 150 kW. If its thermal efficiency is 33%, how much heat must be supplied to keep the engine running for 18 s to reach the end of a street? (in J) (Note: express your answer in scientific notation, for instance: 3.14

An ideal gas with ? = 1.5 is used as the working substance in the cylinder of an engine undergoing a Carnot cycle. The temperature of the hot reservoir is 240?C, that of the cold, 50?C. The gas is expanded isothermally at 240?C from a pressure of 10 atm (1 atm = 1.01 ? 105 N m-2) and a volume of 1 liter to a pressure of 4 atm and a volume of 2.5 liters. Between what limits of pressure and volume does the gas operate when it is in thermal equilibrium with the cold reservoir?

6.   What is the freezing point of a solution (water) that boils at 105.0^oC??

7. The Henry's law constant of helium gas in water at 30^oC is 3.7 X 10-4 M/atm and the constant for Nitrogen (N₂) at 30^oC is 6.0 X10-4 M/atm

          a. How many M of helium are dissolved in a solution if it is at 3 atm?

          b. How many M of Nitrogen are dissolved in a solution if it is at 75 atm?

8.   List the following aqueous solutions in order of decreasing freezing point:

0.04 m glycerine                 0.020 m Kbr                     0.03 m Phenol

Question 29.6 on p. 982 of the textbook university physics 13th edition states that a magnet would reach terminal velocity even if there is no air resistance. How would air resistance change the situation? Is it significant?

03.2 A boat must cross a 190-m-wide river and arrive at a point 30 m upstream from where it starts (see figure). To do so, the pilot must head the boat at an angle ?         = 40

Draw the following circuits:

a. (1 pt) What is the purpose of a rectifier circuit?

b. (2 pts) Half

I am interested in examples of crackpots coming up with correct results in physics.

Why do mainstream physicists look down so much upon "crackpots"?

What basic law of Physics tells us that a laser cannot produce 100% monochromatic light?

Explain the origin of Transverse Electromagnetic Modes (TEM modes) in a commercial laser. Use words and diagrams as necessary.

Explain the concept of collisional broadening in a gas laser

The Kwik-Freez Appliance Co wants you to design a food freezer that will keep the freezing compartment at -5.00?C and will operate in a room at 20.0?C. The freezer is to make 5.80kg of ice at 0 ?C, starting with water at 20.0?C.

a) Find the least possible amount of electrical energy needed to make this ice

b) Find the smallest possible amount of heat expelled into the room.

At launch a rocket accelerates upward at a=2g. After 12 seconds the rocket runs out of fuel and enters freefall.

a.) Determine the rocket's maximum height.

b.) How long after take off does the rocket crash to the ground?

Perturbation theory presumes we have a valid family of models over some continuous (infinitely differentiable, in fact) range for some parameters, i.e. coupling constants. We have some special values for the coupling constants characterizing the unperturbed model, which presumably, is relatively easy to solve. We also assume the family of models transform smoothly under the coupling constants. Then, we perform a Taylor series analysis.

But what if the landscape of valid quantum gravity models is discrete? Even though superstring theory admits a dilaton modulus over 10 uncompactified dimensions, what about the landscape of models we get after compactifying 6 spatial dimensions with nonzero fluxes and some branes, and maybe some orbifolding? We still have moduli when supersymmetry remains unbroken, but what about the metastable states where SUSY is broken? What is the Taylor series of a Dirac delta function?

What about perturbation theory from the perspective of path integrals? With path integrals, the Wheeler-DeWitt constraint shows up in a different guise as a projection operator. We start off with some wavefunctionals, and then take the functional integral over some finite time interval T. In the limit as T goes to infinity, we are left with a projection operator singling out WDW solutions. But what happens when we interchange the order in which we take the limit of the coupling constant going to zero, and T going to infinity? If the spectrum of the Hamiltonian constraint is discrete, and varies with the coupling constant, such an interchange won't be valid! This is a fancy way of saying for most choices of coupling constants, the projection operator is zero.