At the center of a 50-mm-diameter circular ice rink, a 76 kg skater traveling north at 2.7 m/s collides with and holds onto a 61 kg skater who had been heading west at 3.8 m/s .

How long will it take them to glide to the edge of the rink?

Express your answer using two significant figures.

Where will they reach it? Give your answer as an angle north of west.

A radioactive sample has a certain number N of unstable nuclei that are emitting 4.5 MeV gamma rays with a half-life of 1.5 hours. If the rate of radioactive heating of the sample due to these decays is 13 watts, how many unstable nuclei are initially in the sample?

AND

A muon at rest decays into an electron, an anti-electron neutrino, and a muon neutrino. After the decay, the electron has a total energy of 52.85 MeV and the anti-electron neutrino has an energy of 20 MeV. What is the energy of the muon neutrino (in MeV, closest answer)?

AND

*Suppose that a particle of mass m is confined to a region of width a. Its energy in the ground state must be of order (the particle is non-relativistic)–

(1) \bar{h} ^2/(ma^2 ). (2) 2 eV. (3) \bar{h} /a. (4) \bar{h} ^2 *am. (5) \bar{h} ^2/(ma).

*(don't truly comprehend this last one specially-thanks.)

A solenoid wound with 2020 turns/m is supplied with current that varies in time according to I = (4 A)sin(120πt), where t is in s. A small coaxial circular coil of 40 turns and radius r = 4.1 cm is located inside the solenoid near its center. (a) Derive an expression that describes the manner in which the emf in the small coil varies in time. (Use the following as necessary: t.) (b) At what average rate is energy transformed into internal energy in the small coil if the windings have a total resistance of 8.00 Ω?

1. What is the moment of inertia of a solid iron sphere 20 inches in diameter about an axis passing through the sphere half way from its center to the surface (you will have to look up its density)? If the sphere rolls down an incline plane that makes an angle 20 degrees with the horizontal, what will be its acceleration?

b. Derive the formula for acceleration of a circular disk that rolls down an inclined plane that makes an angle θ with the horizontal. (draw a diagram and say in words what you are doing)

20 kg of steam at 100⁰C is  passed into a mixture of 30 kg of ice and 100 kg of

water at 0⁰C . Find the resulting temperature if the water equivalent of the

vessel is 10 kg.

Show that  Brewster angle does not exist for TE  polarized light.

. WHERE is TE transverse electric

• Two singly ionized atoms move into a magnetic fields of magnitude 0.100 T pointing into the page. Each has a speed of 1.00 X 106 m/s. The nucleus of the first atom contains one proton and has a mass of 1.67 X 10-27 kg, while the nucleus of the second atom contains a proton and a neutron and has a mass of 3.34 X 10-27 kg. Atoms with the same number of protons in the nucleus but different masses are called isotopes. The two isotopes here are hydrogen and deuterium. Find their distance of separation when they strike a photographic plate.

A 0.5 kg ball is dropped from a window. An archer shoots a 0.05 kg arrow to intercept the ball. When the ball is impaled it is traveling at -2 m/s in the y direction, and the arrow is traveling at 35 m/s at an angle of 20 degrees. What is the velocity of the pair after the collision in vector notation, magnitude, and direction? What is the impulse of the arrow?

1. Consider an object on a spring of k=200 N/m whose position is given by x=(5.00 cm)cos(9.90 rad/s). Find: (a) the maximum speed of the object and when this maximum speed first occurs after t=0, (b) the maximum of the acceleration of the object and when the maximum of the magnitude of the acceleration first occurs after t=0, (49.5cm/s 490 cm.s^2), (c) the amplitude and period of motion, (d) the position of the block at t=1.0s, (d) the maximum kinetic energy and potential energy of the spring block system.

Sassbot and Block Ness Monster play roller derby for the Reservoir Dolls, a roller derby team in Madison, Wisconsin. In a particular bout against the Unholy Rollers, another Madison team, Sassbot is playing the position of jammer: she must pass members of the Unholy Rollers in order to score points. Block Ness Monster is playing as a blocker: she must help Sassbot while also stopping the Unholy Rollers’ jammer. During a crucial moment in the bout, Monster sees that Sass, a few feet in front of her, is about to get hit by Skullz B. Kraken, a member of the Unholy Rollers. Monster reaches Sass quickly and pushes her forward, attempting to give Sass a boost of speed so she is out of the Skullz’s reach. Monster pushes Sass straight forward, delivering the push at Sass’s center of mass, her lower back, so that Sass does not experience any rotation due to the push. Neither Monster nor Sass are using their wheels to brake immediately before, during, or after the push, so the outside forces on them are negligible. Monster’s mass is 82 kg. Sass’s mass is 55 kg. Monster’s speed before the push is 2 m·s−1, and Sass’s speed before the push is 0.75 m·s−1. Monster and Sass have found, in previous practice, that the average coefficient of restitution of this sort of push between them is 0.8. The coefficient of restitution is defined as the ratio of the difference in two objects’ velocities after the collision to that of the difference in the objects’ velocities before the collision. e = v2,f − v1,fv2,i − v1,i At the moment Monster finishes her push, Skullz is 0.75 m to the left and 1.1 m in front of Sass. Skullz is moving laterally (to the right) at a speed of 2.15 m·s−1 in her attempt to hit Sass. Sass is moving directly forward after Monster’s push. Will Sass get hit by Skullz or will she get past her in time?

How long will it take Sass to travel forward past Skullz’s position?

from the laue condition explain why we can observe maximal peaks in the amplitude of the diffracted wave

In an attempt to save someone in a vertically falling car Spider-Man spins a web catching the 2000 kg car. The webbing has a spring constant of 22,000 N/m and the car is caught at t = 0 at a distance 0.500 m above equilibrium while it is still falling at a speed of -10.0 m/s. After this, the car goes into vertical SHM.

Wo = 3.32Hz

f = .528Hz

Period (T) = 1.89s

Find:

a) the amplitude

b) the phase angle

c) the time it takes the car to get to its lowest point (? = −?).

Draw an example of, and compare the differences between the three types of static equilibrium

Which of the following is ALWAYS true.

a) An object experiencing a constant negative acceleration has a decreasing momentum.

b) If an object has a constant acceleration, its kinetic energy is changing at a constant rate.

c) If an object has a zero net force acting on it, its kinetic energy is constant.

d) If an object's kinetic energy is constant, there is no net force acting on it.

e) If an object's kinetic energy is increasing there is a positive net force on it.

A bullet (m = 10 g) flies horizontally with an initial speed of v = 500 m/s and then embeds itself in a block of wood (m = 400 g) that is at rest on a flat surface. The surface has a coefficient of kinetic friction μk = 0.4. After the impact, how far does the block of wood slide?

(a) 40 m (b) 800 m (c) 8 m (d) 80 m (e) 20 m