Phasors
w=5+2i, u=2-2i, are two complex numbers written in component form.
a. Draw them in the imaginary plane.
b. find w and u in terms of their magnitude and phase.
c. Find the new imaginary number g=w*u, and demonstrate that the magnitude and phase of g is the same whether you multiply w*u in component form or simply multiply their magnitudes and phases together.

c = 3.0 x 10⁸ m/s;        b = v/c;           g (gamma) = 1/sqrt[1 – b²];    u = (u’ + v) / (1 + u’v/c²);

E_ph = hf = hc/l;           P = esAT⁴;     s = 5.67 x 10^-8 Watts / m² / K⁴

1. Relativistic Factor. Calculate the value of the relativistic factor g for an object traveling at v = 0.999c.

2. E = mc². If precisely 1.00 kilogram of mass could be converted completely into energy, for how long could this amount of energy keep a 100-Watt light bulb shining? (Assume the bulb can operate for a very long time.)

3. Velocity Addition. A relativistic craft traveling at 0.6c w/r/t to the Earth launches a probe, which travels at a velocity of 0.8c w/r/t the craft. What is the velocity of the probe w/r/t the Earth? (It’s not 1.4c.)

The cylinder in the figure(Figure 1) has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm2, it contains 0.0051 mol of gas, and the spring constant is 1500 N/m. At 21 ∘C the spring is neither compressed nor stretched.

How far is the spring compressed if the gas temperature is raised to 140 ∘C?

Muons are elementary particles that have a lifetime of 2 millionths of a second. Classically we should not be able to detect them because they have a very quick decay times, however, there are detectors which detect a great number of them. How is this possible?

A child's play rifle uses a spring to fire a 5.21-g soft plastic ball. The spring is compressed by 4.99 cm and has a spring constant of 7.94 N/m. When the rifle is fired, the ball moves 14.1 cm through the horizontal barrel of the rifle, and the barrel exerts a constant friction force of 0.032 7 N on the ball.

(a) With what speed does the ball leave the barrel of the rifle?

Make certain you have correctly converted all of the centimeter and gram quantities to MKS units. m/s

(b) At what point does the ball have maximum speed?

The maximum speed does not occur at the equilibrium point of the spring, because the friction force is also present throughout the motion. cm (from its original position)

(c) What is this maximum speed?

A charge of -2.410 μC μ C is located at (2.980 m m , 4.714 m m ), and a charge of 1.615 μC μ C is located at (-2.703 m m , 0).

Part A: Find the electric potential at the origin. V=?

Part B: There is one point on the line connecting these two charges where the potential is zero. Find this point. x,y=?

A raft is constructed of wood having a density of 6.00x102 kg/m3. Its surface area is 5.50 m2 and its volume is 0.55 m3. When the raft is placed in fresh water, to what depth h is the raft submerged by its weight? The density of fresh water is 1000 kg/m3. Hint: Use Newton’s second to sum the forces (Buoyancy and weight) that are in equilibrium.

The winning time for the 2005 annual race up 86 floors of the Empire state building was 10 min and 49 seconds. The winner's mass was 60 Kg.

A) if each floor was 3.7 m high, what was the winners change in gravitational potential energy?

B) If the efficiency in climbing stairs is 25%, what total energy did the winner expend during the race?

C)How many food Calories did the winner burn in the race

D) Of those calories, how may were converted to thermal energy?

E) What was the winner's metabolic power in watts during the race up the stairs?

You are arguing over a cell phone while trailing an unmarked police car by 26.0 m. Both your car and the police car are traveling at 102 km/h. Your argument diverts your attention from the police car for 2.50 s (long enough for you to look at the phone and yell, "I won't do that!"). At the beginning of that 2.50 s, the police officer begins emergency braking at 5.00 m/s².

(a) What is the separation between the two cars when your attention finally returns?
m

(b) Suppose that you take another 0.400 s to realize your danger and begin braking. If you too brake at 5.00 m/s², what is your speed when you hit the police car?
  km/h

A hydraulic lift in a garage has two pistons: a small one of cross-sectional area 4.50cm2 and a large one of cross-sectional area 220cm2 .

There are two parts to this question please give CORRECT answer.

Part A If this lift is designed to raise a 3400-kg car, what minimum force must be applied to the small piston?

Part B If the force is applied through compressed air, what must be the minimum air pressure applied to the small piston?

An empty tin can with height of 30cm and a diameter of 15cm is open at one end and closed at the other end. If the vertical can, with open end down, be slowly immersed in water, how far the water will rise inside the can when the closed end is 10 cm below the water surface?

1)An object experiences a force in the direction opposite its motion. This means

the work vector points in the negative direction

the scalar value of work is negative

the scalar vector of work could be either positive or negative, depending on which direction is chosen to be positive.

the work vector could point in either the positive or negative direction, depending on which direction is chosen to be positive.

2: A hand lifts a block vertically upward at constant velocity. The work done by gravity on the block ____ if the system consists of the block only. The work done by gravity on the block ____ if the system consists of the block and the earth. AND WHY?

is zero, is zero/is zero, is negative/is zero, is positive/is negative, is negative/is positive, is positive

3: A block of mass M is moves down a frictionless ramp of angle θ and height H. The block is pushed at the top of the ramp so that its initial speed is 4 m/s.

Consider system A to be only the block and system B to be the block and the earth together. Is the speed of the block at the bottom of the ramp in system A ______to the speed of the block at the bottom of the ramp in system B?

greater than, less than, or equal

Ice to Steam via Water Due this Friday, Dec 4 at 11:59 pm (EST) How much heat is required to change a 49.4 g ice cube from ice at -13.7°C to water at 50°C? (if necessary, use cice=2090 J/kg°C and csteam= 2010 J/kg°C) 2.82×104 J You are correct. Your receipt no. is 150-2609 Help: Receipt Previous Tries How much heat is required to change a 49.4 g ice cube from ice at -13.7°C to steam at 120°C?

An electron follows a helical path in a uniform magnetic field of magnitude 0.447 T. The pitch of the path is 4.88 μm, and the magnitude of the magnetic force on the electron is 1.64 × 10-15N. What is the electron's speed?

ASAP