A wheel 2.25 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.30 rad/s². The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3

1. Consider a charge of -1 nC at (-1,0) m, and a charge of +1 nC at (1,0). Calculate the electric potential everywhere in the plane.

2. For the same geometry as in the first problem, calculate the electric field everywhere, using -?V =E. In 2 dimensions, ?V= (?subxV, ?subyV) = ?subxV x^ + ?suby Vy^

Starting from the statement that decay rate is proportional to the number of nuclei in a sample, derive the exponential equation that relates the number of nuclei in a sample to the initial number and the elapsed time. Define all variables used. [3 marks] c) A 1 megaton nuclear bomb produces 0.45 kg of an isotope of 90Sr and the fallout spreads uniformly over an area of 110 km2 . 90Sr decays with a half-life of 29 years. Determine the ground area that holds an amount of radioactivity equal to 9.2 x104 Bq. Define variables used.

ESPECIALLY NEED ANS TO C THANKS

Two masses are connected by a light string, which passes over a frictionless pulley as shown in fig .3 on a the chalkboard. The inclined plane is rough. When m1=10kg , m2 = 3.0 kg and theta = 60degrees, the 10 kg mass moves down the inclined plane and accelerates down the nclined pane at a rate of 2.0m/s^2. Find a) the tension in the string. b)the coefficient of kinetic friction between the 10 kg mass and the inclined plane.

(6) Moons of Mars.
In 1727, Jonathan Swift wrote Gulliver's Travels in which he described two moons orbiting Mars. About 150 years later, the American astronomer Asaph Hall used a large telescope to discover two moons of Mars and they were named Phobos ("fear") and Diemos ("terror"). Their motions were surprisingly close to Jonathan Swift's description. The orbital period of Phobos is 8 hours and that of Diemos about 30 hours.

(2 pts.) (a) Using the information given above and one of Kepler's laws (which one?), explain which moon, Phobos or Diemos, is farther from Mars.

(2 pts.) (b) Describe the motions of Phobos and Diemos as seen by an inhabitant of Mars at, say, 40° north martian latitude.

(Note: Phobos and Diemos both orbit Mars close to Mars' equatorial plane and in the same (counterclockwise) direction that Mars spins. Mars' spin period is close to 24 hours. Drawing diagrams would probably help).

PLEASE EXPLAIN YOUR ANSWERS CLEARLY

Two powerful speakers, separated by 15.00 m, stand on the floor in front of the stage in a large amphitheater. An aisle perpendicular to the stage is directly in front of one of the speakers and extends 50.00 m to an exit door at the back of the amphitheater. The speed of sound in air is 344 m/s.

a) If the speakers produce in-phase, coherent 440.0 Hz tones, at how many points along the aisle is the sound minimal?

b) What is the distance between the farthest such point and the door at the back of the aisle?

c) Suppose the coherent sound emitted from both speakers is a linear superposition of a 440.0 Hz tone and another tone with frequency f. What is the smallest value of f so that minimal sound is heard at any point where the 440.0Hz sound is minimal?

d) At how many additional points in the aisle is the 440.0 HzHz tone present but the second tone is minimal?

e) What is the distance from the closest of these points to the speaker at the front of the aisle?

A 500 lines per mm diffraction grating is illuminated by light of wavelength 640 nm.

1. What is the maximum diffraction order seen? Express your answer as an integer.

2. What is the angle of each diffraction order starting from zero diffraction order to the maximum visible diffraction order? Enter your answers in degrees in ascending order separated by commas.

hOlaf is standing on a sheet of ice that covers the football stadium parking lot in Buffalo, New York; there is negligible friction between his feet and the ice. A friend throws Olaf a ball of mass 0.400 kg that is traveling horizontally at 11.1 m/s . Olaf's mass is 74.7 kg

A) If Olaf catches the ball, with what speed vf do Olaf and the ball move afterward? Express your answer numerically in meters per second.

B) If the ball hits Olaf and bounces off his chest horizontally at 7.80 m/s in the opposite direction, what is his speed vf after the collision? Express your answer numerically in meters per second.

Problem 2. A nuclear power plant produces radioactive waste as a byproduct. One such byproduct is an
isotope of the noble gas Krypton, 36Kr85, which decays via ?- decay with half-life T1/2 = 10.8 yrs. Each decay
releases a ?- particle with energy = 0.240 MeV (on average). This energy is converted into thermal energy as
the particle interacts with the surrounding particles.

SHORT QUESTIONS. 2 pts each.
Identify the following attributes of the daughter product that results from decay of 36Kr85.
A. What is the value of N? (i.e., number of neutrons)
B. What is the value of A? (i.e., mass number)
C. What the name of the element?

PROBLEMS. Show work for parts D and E .

D. (3 pts) Radioactive waste must be safely stored until it is no longer dangerous. At one nuclear plant, waste
containing 1.25 x 10^26 atoms of Kr-85 is placed in a container for storage. How many ?- decays will occur
inside the container during the first year of storage?

E. (3 pts) Averaged over that year, what is the (average) rate of heat production (Watts) inside the container, as
a result of ?- decay of Kr-85?

what is the Scientific reason behind " why stars have star shaped"!!

A block of mass m is moving to the right at 0.25m/s, while another block of mass 2m is moving to the left at 0.10m/s. Both blocks are on a frictionless and horizontal surface. After their head on elastic collision, what is the velocity of each block?

In a synchrotron, charged particles are accelerated as they travel around in circles; in a linear accelerator they move in a straight line. What are some of the advantages and disadvantages of each?

Discuss how levitation can be achieved by using super conductors.

A water faucet in a house is h=8 m below the water surface in the local water tower. The radius of the orifice in the fully opened faucet is r=0.01 m. We assume non-viscous flow in this problem.

a) How long does it take to fill a 20 liter bucket with water using this faucet?