A simple microscope consists of two lenses. The object is just placed outside of the focal length of an objective lens with f = 5.00 mm. The focal length of the eyepiece is f = 30.00 mm. The microscope is being used to image an object with a size of .30 mm.

A) What is the angular size of the object when observed with the naked eye at 0.30 m (assume this is greater than the near point of the observer). Give your answer in radians.

B) How far from the lens should the object be placed so that the image from the objective will be 0.40 m from the objective lens?

C) How far from this image should the eyepiece be placed so as to make a virtual image .30 m from the eyepiece lens?

D) What is the approximate overall magnitude of the linear magnification of the microscope?

E) What is the overall angular magnification?

Neutron stars consist only of neutrons and have unbelievably high densities. A typical mass and radius for a neutron star might be 3.7 x 1028 kg and 1.3 x 103 m. (a) Find the density of such a star. (b) If a dime (V = 2.0 x 10-7 m3) were made from this material, how much would it weight (in pounds)?

During the power stroke in a four-stroke automobile engine, the pis-ton is forced down as the mixture of combustion products and air undergoes an adiabatic expansion. Assume (1) the engine is running at 2500 cycles/min; (2) the pressure immediately before the expansion is 20.0 atm; (3) the volumes of the mixture immediately before and after the expansion are 50.0 cm3and 400 cm3, respectively ; (4) the time interval for expansion is one-fourth that of the total cycle; and (5) the mixture behaves like an ideal gas with specific heat ratio 1.40. Find the average power generated during the power stroke.

A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally with a speed of 189 km/h (52.5 m/s ), how far in advance of the recipients (horizontal distance) must the goods be dropped? Suppose, instead, that the plane releases the supplies a horizontal distance of 425 m in advance of the mountain climbers. What vertical velocity (up or down) should the supplies be given so that they arrive precisely at the climbers' position?

There are plenty of references to this claim on the internet that tying knots in power cables will prevent a piece of equipment e.g. television or computer from a power surge.

How can this be debunked (or proven) using mathematics?

I stumbled across this which seems reasonable to me, but is there some way this can be proved?

The surge impedance of any line is the square root of its inductance divided by its capacitance, and electromagnetic waves travel most readily down a line where that surge impedance doesn't change. A point of changing impedance is a discontinuity that causes a partial reflection of the wave back towards its source. As an example, the end of the line is a surge impedance jump to infinity and the whole wave is reflected back (which means the wave voltage at the open end doubles!) This is also the reason why you want to use terminators on the ends of coaxial cables. Open-ended cables will reflect back the signal causing poorer picture quality and ghosting (and similar things happen for poorly made connections that have higher impedances than the surge impedance of the coax).

Knotting the line gives that part of it a higher inductance (think of the knot as a coil with a couple of turns). That means two surge impedance discontinuities (from line to knot, and from knot back to line). It seems to me (too lazy to resort to doing the math) that this is bound to reduce the magnitude (voltage and current) of a surge passing through the knot because some will be reflected back. However, I'd guess that the reduction would be small.

A 0.25 kg block slides down a ramp that is 0.6 m tall, 0.8 m long and has a diagonal length of 1.0 m. The block starts at rest and arrives at the bottom with a speed of 1.3m/s. a.) How much heat was created by friction? b.)What is the average frictional force acting on the block? At what rate is kinetic energy being dissipated into heat near the bottom of the ramp? c.)Instead of a block, a cart with a mass of 0.33 kg rolls without any frictional losses. It collides with a horizontally mounted spring at the bottom of the ramp. If the spring has a spring constant of 215 N/m, how far will it be compressed. d.)Draw energy bar graphs for the following four moments: a. the moment of release, b. halfway down the ramp, c. at the base of the ramp d. when the spring has reached maximum compression.

Constant amount of ideal gas is kept inside a cylinder by a piston. The piston is locked in to position, it is not allowed to move. The gas is then heated up. Compare the initial (i) and the final (f) physical quantities of the gas to each other.

(The fill in the blank options are greater than, less than, or equal too).

The volume Vf is ... Vi.

The temperature Tf is ... Ti.

The internal energy Uf is ... Ui.

The entropy Sf is ... Si.

The pressure pf is ... pi.

On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The acceleration due to gravity on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 18 m/s at an angle 45 ∘ above the horizontal. a)How much farther did the ball travel on the moon than it would have on earth? b)For how much more time was the ball in flight?

A person is pulling on a block with a force of 100N at an angle of 30 degrees with the horizontal (+x direction). If the mass of the block is 10kg and the coefficient of friction is uk=0.2, and the block undergoes a displacement of 15 m in the +x direction, what is the net work done on the block?

a.) -294 J

b.) 294 J

c.)1005 J

d.)1299 J

e.)1593 J

The balance wheel of a watch oscillates with angular amplitude 1.2π rad and period 0.70 s. Find (a) the maximum angular speed of the wheel, (b) the angular speed of the wheel at displacement 1.2π/2 rad, and (c) the magnitude of the angular acceleration at displacement 1.2π/4 rad.

Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.5×10⁴ m/s when at a distance of 2.8×10¹¹ m from the center of the sun, what is its speed when at a distance of 5.3×10¹⁰ m.

A 2.50-kg grinding wheel is in the form of a solid cylinder of radius 0.100 m.

1- What constant torque will bring it from rest to an angular speed of 1200 rev/min in 2.5 s?

2- Through what angle has it turned during that time?

3- Use equation W=τz(θ2−θ1)=τzΔθ to calculate the work done by the torque.

4- What is the grinding wheel’s kinetic energy when it is rotating at 1200 rev/min?

5- Compare your answer in part (D) to the result in part (C).

A group of students perform the same "Conservation of Mechanical Energy" experiment that you performed in lab by allowing a solid sphere and then a solid cylinder to roll down the ramp. Both objects were released from the same position at the top of the ramp. If the speed v_sphere of the solid sphere at the bottom of the ramp was  1.25 m/s, what would be the speed v_cylinder at the bottom of the ramp?

In this assignment , we will explore the life of Isaac Newton, please listen to the radio show from the BBC and do a little research about Isaac Newton.

1. Listen the first episode (Age of Ingenuity) of the following podcast show: Seven Ages of Science BBC Radio. (http://www.bbc.co.uk/programmes/b0380wf8/episodes/downloads)

You can also find this series from iTunes or any other podcast apps.

2. This first episode (The Age of ingenuity) describes the age of Isaac Newton. (I highly recommend you listen to all seven episodes. These are fun.) After you listen to the episode, please answer following questions.
   1. In this episode, they mentioned about a special telescope designed by Robert Hooke. What is the name of the telescope? Search online to find a picture of the telescope and attached to this paper. Explain how the telescope works.

2. How was the relationship between Robert Hooke and Isaac Newton? Were they good friends or enemies? Search online to find more stories about them and write here.

3. Isaac Newton is an interesting person. Find any interesting stories about Isaac Newton, you can use any resources such as online resources, DVDs, TV and books. Please write a story you found and reference the source of the story correctly.

Reference: ______________________________________________________

A bicycle wheel can be thought of simply as a central solid cylinder (the part that attaches to the axle) surrounded by a thin shell of mass (the rim and tire) located along the outer edge of the wheel. Compared to these parts of the wheel, the mass of the spokes is small enough to be neglected. A sample bicycle wheel has mass 2.0 kg, half of which is in the central cylinder. The other half is in the rim and tire. The central cylinder has a radius of 4.0 cm (note the unit!). The wheel has a radius of 40.0 cm.

a) What is the moment of inertia of the central cylinder?

b) What is the moment of inertia of the rim/tire? Hint: you should not be using the same equation you used in (a).

c) The moment of inertia of the entire wheel is just the sum of the individual moments of inertia of the parts. What is the moment of inertia of the wheel?

The wheel described above rolls down a ramp without slipping. It starts rolling on the ramp at a point where the ramp is 2.0 m above the ground. Any energy lost to frictional effects as the wheel rolls is negligible.

d) What gravitational potential energy (relative to the ground) does the wheel have at the top of the ramp?

e) What types (plural!) of mechanical energy does the wheel have when it reaches the ground?

f) How fast is the wheel moving at the bottom of the ramp? Hint: This is asking for the translational velocity of the wheel. You need to set up an energy conservation equation in which you can isolate the translational velocity as the only unknown quantity.

g) Assuming acceleration is constant, what is the average translational velocity of the wheel as it rolls down the ramp? Hint: since the wheel started from rest, the relationship between the average velocity and the velocity at the bottom of the ramp is quite simple; go back to your kinematics equations!