1. a) Explain Einstein’s theories of special relativity and general relativity.

b) Include at least one piece of evidence in support of each theory.

topic: Ballustic Pendulum Lab.
why does the total momentum before the collision include only the momentum of the ball? why is the momentum of the pendulum included?

A 318 g object is attached to a spring and executes simple harmonic motion with a period of 0.270 s. If the total energy of the system is 6.29 J.

(a) Find the maximum speed of the object. (------m/s ?)

(b) Find the force constant of the spring. (--------N/m ?)

(c) Find the amplitude of the motion. (------- m ?)

Speedy Sue, driving at 32.0 m/s , enters a one-lane tunnel. She then observes a slow-moving van 175 m ahead traveling with velocity 5.00 m/s. Sue applies her brakes but can accelerate only at -2.00 m/s^2 because the road is wet. Will there be a collision?

A) Yes or No

B) If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sue's car and the van and enter zero for the time.

distance

______m

time

______s

discrete ordinates method for 1-D neutron transport

In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is 430 ly away, and that you want your 20,000 kg rocket to move so fast that you age only 24 years during the round trip.

A) How fast, as a fraction of c, must the rocket travel relative to earth?

B) How much energy is needed to accelerate the rocket to this speed?

C) Compare this amount of energy to the total energy E0 used by the United States in the year 2015, which was roughly 1.0×1020 J.

Each of the following objects has a radius of 0.199 m and a mass of 2.35 kg, and each rotates about an axis through its center (as in this table) with an angular speed of 38.1 rad/s. Find the magnitude of the angular momentum of each object.

(a) a hoop

(b) a solid cylinder

(c) a solid sphere

(d) a hollow spherical shell

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.67 m and 0.99 m, respectively. The respective rotational speeds are 449 rev/min and 4,149rev/min. Calculate the speeds of the tips of both rotors.

Compare these speeds with the speed of sound, 343 m/s.

A car travels downhill at 72 mile/hour, on level ground at 63 mile/hour, and uphill at only 56 mile/hour. The car takes 4 hours to travel from town A to town B. The return trip takes 4 hour and 40 mines. Find the distance between the two towns.

In a physics lab experiment, a compressed spring launches a 36 g metal ball at a 35 ∘ angle. Compressing the spring 20 cm causes the ball to hit the floor 2.0 m below the point at which it leaves the spring after traveling 5.9 m horizontally. Part A What is the spring constant? Express your answer to two significant figures and include the appropriate units.

Derive an expression for the magnitude of the acceleration of the system using Newton’s laws given the presence of kinetic friction

When a ball is launched from the ground at a 45° angle to the horizontal, it falls back to the ground 50 m from the launch point. If it is launched at the same speed directly upward, (a)how high does it get? (b)How much longer does it spend in the air

What's the different between force and motion in your own word

a) Monochromatic light of variable wavelength is incident normally on a thin sheet of plastic film in air. The reflected light is a maximum only for 487.9 nm and 683.0 nm in the visible spectrum. What is the minimum thickness of the film (n=1.58)?

t = _________ nm

b) A planoconvex lucite lens 3.6 cm in diameter is placed on a flat piece of glass as in the figure 34-18 in the textbook. When 600 −nm light is incident normally, 47 bright rings are observed, the last one right at the edge.

What is the radius of curvature of the lens surface?

R = ___________ m

What is the focal length of the lens?

f = ____________ m

The Rosetta space probe has a mass of 1200 kg. On November 12th 2014,Rosetta landed on Comet 67P/C-G which has a mass of M= 1×10 ^18 kg. The instant before landing was initiated, scientists found Rosetta’s relative (to the comet) position and velocity to be: r=〈3×10^3,0,5×10^3m v=〈−1×10^2,2×10^2,0〉m/s Calculate the (approximate) momentum and position of the space probe 100 seconds later. Start from a fundamental principle and show all steps in your work. Express your final answer as three-component vectors.