In recent times the principle of the Michelson intereferometer is being used in an attempt to detect gravitational waves (LIGO experiment). A successful measurement requires an accuracy of 10-16cm. Assuming t hat the light is reflected only once in each arm and the wavelength of the laser is 632.8 nm, calculate the relative change of the intensity in the center of the image. (for simplicity assume that the intensity is zero for minimum and 1 for maximum of the interference patterns and that the alignment is such that intensity in the center of the screen is at 0.5).

Suppose you kept your accelerating voltage and coil current constant. How would your circular beam change if we were using a proton beam instead of an electron beam? Explain your reasoning.

Equipment used:

Thread, dense spherical mass like a marble or a bearing, perhaps about 0.5 – 1.0 cm in diameter. Otherwise, use a
mass that is approximately spherical, e.g., a tangerine or apple.

Method of obtaining g:

Measure the period of 4 lengths of thread from 75 cm to 1.50 cm. Be sure to measure the length from the support
point to the center of mass of the spherical mass at the bottom end of the thread. For each length of thread, pull
the string from the bottom mass out to about 10 degrees from the vertical, then let the pendulum oscillate back
and forth 20 times while measuring the time with a stopwatch. Determine the period, T, by dividing the elapsed
time by 20.

Plot the period squared versus the length of the pendulum. The resulting curve should be a straight line with a
period involving the acceleration of gravity. Put your data for the length of the pendulum and the period squared
into Excel. Use LINEST to find the best fit slope for the data and the error in the slope. Calculate the acceleration of
gravity and the estimated error of the measurement for g.

Please give an excel file here.

A block with a mass of 0.488 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What is the amplitude of the oscillation?

A block with a mass of 0.976 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What is the amplitude of the oscillation?

A block with a mass of 0.488 kg is attached to a spring of spring constant 856 N/m. It is sitting at equilibrium. You then pull the block down 5.10 cm from equilibrium and let go. What is the amplitude of the oscillation?

A block with a mass of 0.488 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 10.2 cm from equilibrium and let go. What is the amplitude of the oscillation?

A block with a mass of 0.488 kg is attached to a spring of spring constant 428 N/m. It is sitting at equilibrium. You then pull the block down 10.2 cm from equilibrium and let go. What is the frequency of the oscillation?

A music fan at a swimming pool is listening to a radio on a diving platform. The radio is playing at a constant frequency tone when this person, clutching the portable radio, jumps. Describe the observed frequency or pitch for the following three observers. Explain your reasoning.

a) The person holding the radio

b) A person left behind on the platform

c) A person below the platform floating on a rubber raft

A star with apparent visual magnitude mV = 3.5, absolute magnitude MB = 2.0 has parallax of 0.03 arcseconds. Does this star look red or blue in the sky? Estimate its spectral type.

Consider an optical fiber that has a 200-μm core diameter and a 240-μm cladding diameter. (a) Show that the size of the active area in a bundle with two rings is 1.13 mm2. (b) Show that the ratio of the active area to the total cross sectional area of the bundle is 53 %.

The coordinates of an object moving in the XY plane vary with time according to the equations  x = −7.43 sin ωt and y = 4.00 − 7.43 cos ωt,

where ω is a constant, x and y are in meters, and t is in seconds.

(a) Determine the components of the velocity of the object at t = 0. (Use the following as necessary: ω.)

(b)  Determine the components of the acceleration of the object at t = 0. (Use the following as necessary: ω.)

(c) Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t > 0. (Use the following as necessary: omega for ω and t.)

(d) Describe the path of the object in an XY plot.

A piano tuner hears a beat every 1.60 s when listening to a 272.0 Hz tuning fork and a single piano string. What are the two possible frequencies (in Hz) of the string? (Give your answers to at least one decimal place.)

f =          Hz (Smaller Value)

f =          Hz (Larger Value)

1. A block of mass m is sliding on a horizontal surface. The kinetic coefficient of friction between the block and the surface is µ_k. The drag force is linear with speed (F_D = −ℓv, where ℓ is a constant). The initial velocity of the block is v₀.

(e) Find x(t)

(f) Graph v(t)

(g) Graph x(t)

(h) Describe your solution in words.

A 200 gram of ice block falls from a height of 80 meters onto a bucket of 1 kg water in a copper bucket of mass 100 grams. The initial temperature of the ice is 0 and the bucket and water is 20 C. Assume that 60% of the potential energy of the ice block goes into heat!!!! What is the final temperature of the ice, water and bucket mixture?? If not all the ice melts, then what is the final mass of the remaining block of ice?

Use C_cu = .092 cal/g.C, C_water = 1 cal/g.C, L_fwater = 333.55 J/gram

answer choices

a) 4.02 C

b) 61.6 grams of ice block left

c) 45.5 grams of ice block left

d) 3.53 C

e) 3.50 C

One of the particle accelator technologies is cycotron. Please explain principle contruction, working and limitations of cycotron.

Try out some of the principles of light by comparing Polaris to the sun.

a. The intensity of sunlight at a satellite in earth orbit is 1360 W/m2. What is the magnitude of the electric and magnetic field ?

b. Astronomers estimate the distance to Polaris is 431 light years and its intrinsic luminosity (energy per second) is 2200 times that of the sun. Use proportional reasoning and your answer to part a to estimate the intensity and the magnitude of the electric field at the earth. You can give it in terms of A.U., factors of earth’s distance from our sun.

c. A planet in the “habitable zone” around Polaris should receive a light intensity similar to our planet. Again use proportional reasoning to estimate what distance might be a good one.

d. The color of a star depends on temperature of the outer regions of the star. The peak wavelength for polaris is 400 nm and for the sun is 500 nm. Another famous star, Betelgeuse, has its peak wavelength at 828 nm. What color light are these specific wavelengths, and what is the frequency of this light? Actually, we perceive the first two stars to be “white” and Betelgeuse to be distinctly “red”. Explain in your own words.