For example it is stated that if supersymmetry breaking is soft then stability of gauge hierarchy can be still maintained.

Imagine, if you will, a string background with an extremely tiny value for the string coupling. The Planck scale is many orders of magnitude smaller in size than the string scale. Is the UV/IR mixing scale the Planck scale, or the string scale? What happens at intermediate scales?

Gravitons are string modes, and as such, their spatial extent is the string scale. They can never resolve anything smaller than that. On the other hand, D-branes are more sensitive

A 80 kg man weighs himself at the north pole and at the equator. Which scale reading is higher? (The radius of the earth at the equator is 6.37 x 10⁶m). By how much? ____N

Find the electric field (magnitude and direction) for the following situations:

A) At a point 1.0x10-3 m away from a 5.00 pC charge. (4.5x104 N/C, away)

B) Halfway between a 6.0 ?C and a -8.0 ?C charge, which are 10.0 m apart. (5040 N/C towards -8 ?C*)

C) 1.0 m from the end of a 3.5 m long uniformly charged rod, which has a 4.0 nC net charge. (8.00 N/C away from rod)

Two 1.20-m long, uniformly charged wires are perpendicular to each other, as shown below: + 2Q . P -Q

A) If Q = 2.5 ?C, find the electric field at point

An ideal monatomic gas expands adiabatically from an initial temperature of 384 K and volume of 4.6 m³ to a final volume of 10 m³. If the initial pressure is 1.5 ? P_atm, how much work is done on the gas?

A grappling hook is fired from a cannon at ground level with an initial speed of 40 m/s at an angle of 50 degree above the ground. It is a fired at a vertical cliff. The cliff is very high and we are very close. So we are sure that the hook will hit the face of the cliff.

1. Determine the x component of the initial velocity, and how that the y-component of the initial velocity is 30.6 m/s up.

1. It takes 4.0 second for the hook to hit the well. Determine the height of the hook at the point it hits the well and the y-component of the velocity at the time of impact.

1. Draw a graph of the y-component of the velocity vy as a function of the time for those 4.0 second the axes should be labeled, include units, and be to an appropriate scale.

1. Discuss the types of energy transformations that are involved in the following devices or events. (For example, for (a) striking a match transforms the chemical energy in the match head into thermal (heat) and radiant (light) energy).

a. striking a match

b. windmill

c. microphone

d. flashlight

e. water behind a dam flowing past a turbine to generate electricity

A 0.50-�F and a 1.4-�F capacitor (C1 and C2, respectively) are connected in series to a 17-Vbattery.

1. Calculate the potential difference across each capacitor. What is V1, V2? Express your answers using two significant figures separated by a comma.

2. Calculate the charge on each capasitor. What is Q1, Q2? Express your answers using two significant figures separated by a comma.

3. Calculate the potential difference across each capacitor assuming the two capacitors are in parallel. Express your answers using two significant figures separated by a comma.

4. Calculate the charge on each capasitor assuming the two capacitors are in parallel. What is Q1, Q2? Express your answers using two significant figures separated by a comma.

The density of helium is 7 times smaller than air. For any gas, the speed of sound is given by v= (Pressure/Gas Density) ^1/2. If the pressure is kept the same, what is the speed of sound in helium?

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