A fan is designed to last for a certain time before it will have to be replaced (planned obsolescence). The fan only has one speed (at a maximum of 650 rpm), and it reaches the speed in 2.0 s (starting from rest). It takes the fan 7.0 s for the blade to stop once it is turned off. The manufacturer specifies that the fan will operate up to 1 billion rotations. Andre lives in a hot climate, works outside of the home from approximately 8:00 am to 5:00 pm, Monday through Friday, does not own an air conditioner, and can't sleep with the fan running. Estimate how many hot days ?hot Andre will be able to use the fan, rounded to the nearest day.

Solve the following ordinary differential equations by separating variables and integration.
1. y'sinx=ylny, the boundary condition (b.c.) is that the function passes through (y=e,x=pi/3)
2. y'+2xy2=0, b.c. (y=1;x=2)
3. y'-xy=x, b.c. (y=1;x=0)

atoms with angular momentum s=1 is sent through a Stern-Gerlach apparatus oriented in the z (represented as SGz) direction and only the mz = 0 atoms are allowed to go through other sides.

1. Calculate the output at SGx

2. suppose one state (I 1 -1 > )x emerges . What happens if these beams are sent through SGz

A negative charge of –40nC exerts an attractive force of 12N on a second charge that is 0.050m away. What is the second charge?

What is the difference between induction and charging by conduction?

A charge of uniform linear density 2.20 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 4.00 cm, outer radius = 9.00 cm). The net charge on the shell is zero. (a) What is the magnitude of the electric field at distance r = 13.0 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of the shell?

When you take a bath, how many kilograms of hot water (47.3 °C) must you mix with cold water (13.3 °C) so that the temperature of the bath is 36.0 °C? The total mass of water (hot plus cold) is 195 kg. Ignore any heat flow between the water and its external surroundings.

Coherent electromagnetic waves with wavelength λ=500nm pass through two identical slits. The width of each slit is aa, and the distance between the centers of the slits is d=9.00mm.

a.What is the smallest possible width aa of the slits if the m=3 maximum in the interference pattern is not present?

b.What is the next larger value of the slit width for which the m=3 maximum is absent?

If you were conducting the wire/compass experiment (Part A) near the equator instead of in Oregon, would it be necessary to use more or less wire current to cause the compass needle to deflect? (This is related to the dip angle) Explain why.

1. What occurs on Dec. 21, March 21, June 21, and Sept. 21? What specific names are given to these dates?
2. Distinguish between the milky way and The Milky Way.
3. Every star (including the sun) we see by eye or telescopes belongs to the MWG. What does this mean? What are the only things we observe not in our MWG?
4. About how many stars are in the MWG? About how many galaxies are there?
5. What do we conclude about the shape of our MWG based on the fact we see the narrow milky band of light on very dark nights?
6. Name some nearby galaxies.
7. Some comets return regularly; others never do. What’s different in their orbits?
8. Here is a tide chart for some place along the ocean shore. Fill in the missing times or dates on the eight _______ lines below.

DATE               TIDE and TIME                                   NEXT TIDE and TIME

June 1 Very high at 4:00 AM                       Very low at _______

                        Very high again at_______    Very low again at _______

.

.

_______ Mildly high at 9:30 AM                    Mildly low at _______

                        Mildly high again at _______            Mildly low again at _______

.

.

_______ Very high and very low tides return

Using a crowbar, a person can remove a nail by exerting little force, whereas pulling directly on the nail requires a large force to remove it (you probably can't). Why? Using a crowbar, a person can remove a nail by exerting little force, whereas pulling directly on the nail requires a large force to remove it (you probably can't). Why?

A.The applied force is at a large distance from the pivot, giving rise to a large torque.

B.The applied force is at a small distance from the pivot, giving rise to a large torque.

C.The applied force is at a large distance from the pivot, giving rise to a small torque.

D. Because the crowbar is heavy.

A 57.40-pF cylindrical capacitor carries a charge of 1.740 µC. The capacitor has a length of 1.400 ✕ 10⁻³ m.

(a) What is the potential difference across the capacitor?
V

(b) If the radial separation between the two cylinders is 6.380 ✕ 10⁻⁴ m, what are the inner and outer radii of the cylindrical conductors? (Use 8.854 ✕ 10⁻¹² C²/(N · m²) for the permittivity of free space. Give your answers to at least four decimal places.)

In the formula A(t)=A0e^kt, A is the amount of radioactive material remaining from an initial amount A0 at a given time t, and k is a negative constant determined by the nature of the material. A certain radioactive isotope decays at a rate of 0.175% annually. Determine the half-life of this isotope, to the nearest year.