2. Suppose that in the U.S., the income velocity of money (V) is constant. Suppose, too, that every year, real GDP grows by 2.5 percent (%∆Y/year = 0.025) and the supply of money grows by 10 percent (%∆M/year = 0.10).

a. According to the Quantity Theory of Money, what would be the growth rate of nominal GDP = P×Y? Hint: %∆(X×Y)  %∆X + %∆Y.

b. In that case, what would be the inflation rate (i.e. %∆P/year)?

c. If the central bank wants the inflation rate to be 0%, what money supply growth rate (i.e. - %∆M per year) should it set?

Suppose that electrons are accelerated through a potential difference of 80 × 103 V. These collide with a metal slab and emit electromagnetic radiation.

a) Determine the kinetic energy of an individual electron. Express the answer in Joules and electron Volts (1.0 eV = 1.6 × 10−19 J.)

b) The electron collides with the metal and a photon is emitted. Determine the maximum frequency that is possible for the emitted photon.

An 8.5 nF capacitor is charged up by a 20 V battery. The battery is removed and replaced with a coil of wire. It then takes 7.3 x 10-5 s for this now LC circuit to undergo a full charging cycle. (a) Calculate the inductance of the coil

(b) Calculate the total energy of the circuit

(c) Calculate the charge on the capacitor after 1 x 10-5 s.

The velocity function of a particle moving along a line is given by the equation v(t) = t² - 2t -3. The particle has initial position s(0) = 4.

a. Find the displacement function

b. Find the displacement traveled between t = 2 and t = 4

c. Find when the particle is moving forwards and when it moves backwards

d. Find the total distance traveled between t = 2 and t = 4

e. Find the acceleration function, and use it to find the acceleration of the particle at t = 3

A block of mass 4m moves on a flat horizontal surface at speed v, and strikes another block of mass m, that is attached via a horizontal spring to another block of mass 2m. The two masses are stationary.  The spring constant is k. All collisions are completely inelastic and there is no friction anywhere.
What is the velocity of the center of mass when the spring is ¼ the way to max compression.

A. Chapter 19, Problem 09 The potential at location A is 405 V. A positively charged particle is released there from rest and arrives at location B with a speed vB. The potential at location C is 942 V, and when released from rest from this spot, the particle arrives at B with twice the speed it previously had, or 2 vB. Find the potential at B. Number ____ Units _____

B. Chapter 19, Problem 13 Two point charges, +3.40 μC and -7.80 μC, are separated by 3.50 m. What is the electric potential midway between them? Number ___ Units ___

C. Chapter 19, Problem 14 Two particles with charges +10e and -10e are initially very far apart (effectively an infinite distance apart). They are then fixed at positions that are 6.06 x 10-11 m apart. What is EPEfinal - EPEinitial, which is the change in the electric potential energy? Number ___ Units ___

An accelerating voltage of 2.54x10^3 V is applied to an electron gun, producing a beam of electrons originally traveling horizontally north in vacuum toward the center of a viewing screen 36.7 cm away.

(a) What is the magnitude of the deflection on the screen caused by the Earth's gravitational field? m

(b) What is the direction of the deflection on the screen caused by the Earth's gravitational field? up down east west

(c) What is the magnitude of the deflection on the screen caused by the vertical component of the Earth's magnetic field, taken as 20.0 µT down? mm

(d) What is the direction of the deflection on the screen caused by the vertical component of the Earth's magnetic field, taken as 20.0 µT down? north south east west

(e) Does an electron in this vertical magnetic field move as a projectile, with constant vector acceleration perpendicular to a constant northward component of velocity? Yes No (f) Is it a good approximation to assume it has this projectile motion? Yes No

Let V denote the number of units of a variable input (i.e., nitrogen fertilizer) that is used in combination with a fixed input (i.e., land).

Let TP denote the total amount of production of a crop (i.e., corn) that is obtained from using each input level.  

Point A is a point of inflection.

1. TP increases at a decreasing rate ____________.  (Points: 20)

a. from O to A

b. from A to C

c. beyond point O

d. beyond point C

2. MP equals zero at ____________.  (Points: 20)

a. point A

b. point B

c. point C

d. only A and C

e. every point on the TP curve

3. The point of diminishing marginal product is ____________.  (Points: 20)

a. point O

b. point A

c. point B

d. point C

4. TP is at maximum at ____________.  (Points: 20)

a. point O

b. point A

c. point B

d. point C

5. TP experiences negative marginal returns ____________.  (Points: 20)

a. from O to A

b. from O to B

c. from A to C

d. from B to C

e. beyond C

A 400 V dc shunt motor has a rated armature current of 76 A at a speed of 1000 rpm. The armature resistance of the motor is 0.4ohm, the field resistance is 100 ohm, and the rotational losses are 0.9 kW. The load of the motor is bidirectional. Calculate the following:

(a) No-load speed of the motor.

(b) Motor speed, where the armature current is 60 A during regenerative braking.

(c) Developed torque during regenerative braking.

(d) Back electromotive force, ea during regenerative braking.

(e) Power delivered by the source under normal motor operation.

(f) Terminal current under regenerative braking.

(g) Generated power during regenerative braking.

h) Total losses under regenerative braking.

(i) Power delivered to the source under regenerative braking.