why would someone be curious about Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI)? and how is it related to modern physics?   

Starting in Albany, you travel a distance 319 miles in a direction 22.3 degrees north of west. Then, from this new position, you travel another distance 360 miles in a direction 11.0 degrees north of east. In your final position, what is your displacement from Albany?

An unstable nucleus of mass 1.7 ✕ 10−26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 = 1.0 ✕ 10−27 kg, moves in the positive y-direction with speed v1 = 5.4 ✕ 106 m/s. Another particle, of mass m2 = 7.0 ✕ 10−27 kg, moves in the positive x-direction with speed v2 = 3.6 ✕ 106 m/s. Find the magnitude and direction of the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)

Suppose that an electron and a proton are placed at a distance of 1.2nm away from each other (about 10 times the radius of a hydrogen atom).

(a) How much is the Coulomb force between the electron and the proton?

(b) Under this Coulomb force alone, how much is the acceleration of the electron towards the proton (in m/s2 )? (Google for the missing information.)

(c) If the electron is instead placed on the edge of the supermassive black hole Sagittarius A* (about 22 million km away from the center), how much is the gravitational acceleration of electron towards the black hole (in m/s2 )? (Google for the missing information about Sagittarius A*.)

(d) For this electron, how does the gravitational influence of the black hole compare to the electric influence of the proton?

A billiard ball rolling across a table at 1.45 m/s makes a head-on elastic collision with an identical ball. Find the speed of each ball after the collision when each of the following occurs.

(a) The second ball is initially at rest.

(b) The second ball is moving toward the first at a speed of 1.10 m/s.

(c) The second ball is moving away from the first at a speed of 0.90 m/s.

Consider the steady, incompressible blood flow through the following vascular network: 100 µm diameter which is 80 mm in length to the first branching point, which can be estimated as a standard tee (flow through run), the branch off the tee turns 45 degrees and undergoes a constriction to 65 µm diameter and the flow through run continues for another 80 mm. The velocity of the blood into the 100 µm diameter vessel is 100 mm/s and 20% of the mass flow rate exits via the branch.

a) What are the velocities of both the run and branch?

b) What is the change in pressure from the inlet to the end of the run?

c) What length would the branch need to be to achieve the same pressure drop?

d) What assumptions did you make in completing this problem.

Two objects of masses m and 8m are moving toward each other along the x-axis with the same initial speed
v0 = 525 m/s.
The object with mass m is traveling to the left, and the object with mass 8m is traveling to the right. They undergo an elastic glancing collision such that m is moving downward after the collision at a right angle from its initial direction.

What is the final speeds of the two objects m and 8m?

What is the angle theta at which the object with mass 8m is scattered? ( counterclockwise from the x-axis)

Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.60 m . The merry‑go‑round is spinning at 22.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the 28.0 kg child moves to the center of the merry‑go‑round, what is the new angular velocity in revolutions per minute? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses.

final angular velocity: ________ rpm

why are systems with fixed restriction metering devices critical to charge

The pilot of an airplane executes a loop-the-loop maneuver in a vertical circle. The speed of the airplane is 250 mi/h, at the top of the loop and 450 mi/h at the bottom, and the radius of the circle is 1 150 ft. Note: His apparent weight is equal to the magnitude of the force exerted by the seat on his body.

(a) What is the pilot's apparent weight at the lowest point if his true weight is 160 lb?
lb

(b) What is the magnitude of his apparent weight at the highest point?
lb

(c) Describe how the pilot could experience weightlessness if both the radius and the speed can be varied.

A light source emits a photon during a time interval of 2.89 10-8 s. (a) Find the minimum uncertainty in the photon's energy. (b) Find the minimum frequency bandwidth of the light

An airplane’s propeller blades slow down to 2rev/s in 5s, making 200rev in the process. Assuming a constant acceleration, what was the blades’ angular speed before starting to slow down? Answer: 4680 rpm

Problem 6. In space, thermal equilibrium is achieved when incoming radiation (e.g. from the Sun) is balanced against outgoing radiation (e.g. from the surface of Earth). The equilibrium achieved is a dynamic one, because there is still a net flow of heat in and out of the system, and the Sun and Earth never reach the same temperature (thankfully) because much of the radiation leaves the system.

(a) The Sun provides a heat to the surface of Earth with an intensity (power per unit area) of about 1000 W/m2 . Compute the total power received. (Hint: The correct area to use is the cross-sectional area of the Earth, because that is the size of the ‘shadow’ of solar radiation that is absorbed.) (In reality, about 1400 W/m2 reaches Earth and about 30% is reflected.)

(b) Suppose the Earth is a perfect black-body absorber and emitter of radiation, and has a uniform surface temperature. (This is not a great assumption.) Find the equilibrium temperature T of the surface in Kelvin and in Celsius, where Earth radiates exactly as much power as it receives from the Sun. Is it anywhere close to Earth’s average surface temperature?

(c) In fact, Earth’s atmosphere is not transparent to the outgoing radiation, which makes the emissivity of Earth imperfect. The result is a delicate balance that preserves a life-friendly temperature. What emissivity e is required to achieve the current 15◦C average surface temperature? What emissivity e would cause the temperature to rise by 2◦C? This is a vastly oversimplified model of Earth’s climate. More accurate models include multiple coupled layers with independent temperatures and emissivities; these models can fairly accurately predict the surface temperature as a function of greenhouse gas emissions (which determine the emissivity of the atmosphere). The net effect of adding carbon dioxide to the atmosphere is to reduce the amount of infrared emission at a given temperature, lowering e and raising the temperature.

Problem 1. Calculate the average speed of nitrogen molecules (N2) in air at room temperature (∼ 300 K). Compare to the speed of sound, which is about 343 m/s at the same temperature. Speculate on why they might be similar.