I'm struggling a bit with angular momentum.

Consider the satellites of the planets orbiting their respective host planets while those planets orbit the Sun. Galileo's observation of Jupiter's "moons" were an inspiration to the development of universal laws of motion and gravity that could describe not only effects here on Earth, but throughout the universe as well. Jupiter's satellite Europa has oceans under its ice and may even host life. It orbits the planet on a nearly circular path with a radius of 670,900 km and completes its orbit every 3.55 Earth days. Use Newton's universal law of gravitation to find the mass of Jupiter. Knowing Jupiter's mass, and that it orbits the Sun on the average (it has an elliptical orbit with an eccentricity of 0.05) at 7.8×108 km from the Sun in 11.86 years, what is its angular momentum? Compare Jupiter's orbital angular momentum to the angular momentum of the rotating Sun, which is a spinning sphere of radius 695,700 km and mass 1.99×1030 kg that completes a turn in 25 days (with respect to distant stars).

Four resistors are connected to a battery as shown in the figure. The current in the battery is I, the battery emf is ? = 6.20 V, and the resistor values are R1 = R, R2 = 2R, R3 = 4R, R4 = 3R. Find the voltages across each resistor. R 1, R2 and R3 are in series. R4 is in parallel.

In a volcanic eruption, a 2.40 � 103 kg boulder is thrown vertically upward into the air. At its highest point, it suddenly explodes (due to trapped gases) into two fragments, one being three times the mass of the other. The lighter fragment starts out with only horizontal velocity and lands 253mdirectly north of the point of the explosion.

Part A:

Where will the other fragment land? Neglect any air resistance.

Express your answer using three significant figures.

A mass m1 on a horizontal shelf is attached by a thin string that passes over a frictionless pulley to a 2.4 kg mass (m2) that hangs over the side of the shelf 1.2 m above the ground. The system is released from rest at t = 0 and the 2.4 kg mass strikes the ground at t = 0.86 s. The system is now placed in its initial position and a 1.2 kg mass is placed on top of the block of mass m1. Released from rest, the 2.4 kg mass now strikes the ground in 1.3 seconds.

(a) Determine the mass m₁.

(b) Determine the coefficient of kinetic friction between m₁ and the shelf.

Part A

How many years are required for the amount of krypton-85 in a spent nuclear reactor fuel rod to be reduced by a factor of 1/8? The half-life of krypton-85 is 10.8 years.

Express your answer using three significant figures.

t1/8 = ______ years

Part B

How many years are required for the amount of krypton-85 in a spent nuclear reactor fuel rod to be reduced by a factor of 1/32?

Express your answer using three significant figures.

t1/32 = ______ years

Part C

How many years are required for the amount of krypton-85 in a spent nuclear reactor fuel rod to be reduced by a factor of 1/128?

Express your answer using three significant figures.

t1/128 = ______ years

Suppose you put positive charge on an insulated metal box (actually, remove electrons from the box). Since it is a conductor, the charges will rearrange.
- The greatest accumulation of charges will be

- The electric field inside the box will be

2. Suppose identical metal spheres are insulated from their surroundings and touching each other. A positive charge is brought near, but not touching sphere A, and held near to sphere A as the two spheres are separated. Now, the positive charge is removed. What charge will be left on sphere A and sphere B, respectively?

1. A planet orbits a star with a period of 275 days and semimajor axis of 3.4×10^11m. If this planet's eccentricity is zero, what is the mass of the star?

b. Another planet orbits this same star with a period of 453 days. If it's eccentricity is e= 0.43 then how fast is this planet moving at Perihelion? Aphelion?

c. What is the second planet’s Kinetic Energy at Aphelion if it has a mass of 5×10^26 kg? What is it’s potential energy at Aphelion?

a). A net charge of 10C is available and can be distributed in each case in
• a line describing a quarter circle of radius 10cm, • The surface of a sphere of radius .5 m
• A 5cm side bucket.
Calculate in each case the linear, surface and volumetric charge density.
In each case, in what length, area and volume is 1/4 content of the total charge?

b). A sphere of radius R has a volumetric charge density ρ = 3Q/4πR3. What is the total electric field flow that
flows through a surface S that encloses it.

1. A science fiction enthusiast has figured out how to make nanobots with a mass of onehuman cell (10⁻¹² kg). Each nanobot is capable of reproducing itself with any material it finds at a rate of 1 nanobot per hour.
   1. Assuming unlimited materials and starting with one nanobot, how many nanobotsdo we have after 10 days? What is the combined mass of those nanobots?
   2. What is the general function, in terms of time t in units of hours, that tells us how many nanobots we have? Assume that at t = 0, we have one nanobot.
   3. How long would it take to convert an average car into all nanobots starting witha single nanobot? How many nanobots would that be and what would their total mass be?
   4. How long would it take to convert the entire Earth into nanobots? Assume anEarth mass of 6 × 10²⁴ kg.
   5. How long would it take to convert the entire observable Universe into nanobots? Assume the mass of the observable Universe is 3 × 10⁵² kg and ignore travel time and energy considerations.

A firework of mass 0.25 kg is launched at an angle of 75 degrees above the horizontal, pointing due west. The initial speed of the firework is 69 m/s. At the top of its trajectory, it explodes into two pieces of equal mass. One of the pieces takes 2.1 s to fall to the ground, and lands on the ground a distance of 53 m due west from the launch position. Neglect air resistance. (a) Find the velocity of both pieces just after the explosion. (b) Where does the other piece land? (c) Sketch a picture of the resulting motion and convince yourself that it is plausible.

Calculate the magnitude and direction of both the equilibrant and the resultant of the following three vectors: 0.4N at 60°, 0.5N at 30°, and 0.2N at 330° .The object of this experiment is to demonstrate the vector property of forces and to gain experience in the addition of vector quantities.

Dock diving is a great form of athletic competition for dogs of all shapes and sizes. Sheba, the American Pit Bull Terrier, runs and jumps off the dock with an initial speed of 9.52 m/s at an angle of 27° with respect to the surface of the water. (Assume that the +x axis is in the direction of the run and the +y axis is up.)

(a) If Sheba begins at a height of 0.78 m above the surface of the water, through what horizontal distance does she travel before hitting the surface of the water?

(b) Write an expression for the velocity of Sheba, in component form, the instant before she hits the water. (Express your answer in vector form.)

(c) Determine the peak height above the water reached by Sheba during her jump.

An 7.42 kg block drops straight down from a height of 1.34 m, striking a platform spring having a force constant of 1.10 103 N/m. Find the maximum compression of the spring.

6.3: a factory worker pushes a 30 kg crate a distance of 4.5 m along a level floor at constant velocity by pushing horizontally on it. the coefficient of kinetic friction between the crate and the floor is 0.25.

Suppose the worker in exercise 6.3 pushes downward at an angleof 30⁰ below the horizontal

(a) what magnitude of forcemust the worker apply to move the crate at constatnt velocity?

(b)how mach work is done on the crate by this force when the crate ispushed a distance of 4.5m?

(c) how mach work is done onthe crate by friction during this displacment?

(d) how much work isdone on the crate by the normal force? by gravity?

(e) what is thetotal work done on the crate?

Select the following correct MC answer for the questions pertaining to the Photoelectric Experiment

1. The quantized nature of photon energy is confirmed by the photoelectric effect since

Select one:

a. only the right number of photons hitting the metal surface consecutively will cause electron ejection.

b. only a photon carrying the right amount energy will eject an electron from the metal surface.

c. only light of the highest intensity will be able to cause electron ejection.

d. any photon, regardless of the energy it carries, will be able to eject an electron.

2. In the photoelectric effect experiment we use a Hg lamp to shine a light on a metal surface encased inside a photocell. One of the things we observe is that the energy of electrons ejected from the metal surface is independent of the intensity of light that shines on that surface. In practice this means that

Select one:

a. if we don’t move the lamp at all the photoelectric effect cannot take place.

b. if we move the lamp further away from the photocell than the photocurrent (amount of ejected electrons) will increase.

c. if we move the lamp closer to the photocell nothing will happen to the photocurrent (amount of ejected electrons).

d. if we move the lamp closer to the photocell we will increase the photocurrent (amount of ejected electrons) without increasing individual electron’s energy.

3. In the photoelectric effect experiment we use a Hg lamp to shine a light on a metal surface encased inside a photocell. There are multiple filters mounted on the front of the photocell to help us separate the light from the lamp into single-wavelength beams. Which of the following statements is true?

Select one:

a. Knowing the wavelength of the incoming photons does not help us determine the energy of the ejected electrons.

b. Even if we had monochromatic light source, we would still need filters to separate its constituent wavelengths.

c. Without the filters the photoelectric effect cannot occur.

d. Without the filters the photoelectric effect will still happen, but we will have no way to determine which electron was ejected by which photon wavelength.

4. The sign (positive or negative) on the value of the work function gives us an indication of the direction of energy flow between the metal surface (the system) and the environment around it (the surroundings) during the photoelectric effect. The sign on the work function is interpreted from the point of view of the system (the metal surface). For example, if the work function is positive the energy is flowing into the system from the surroundings (i.e. the energy of the system is increasing). Which of the following statements is true?

Select one:

a. We expect the work function to be positive, because energy must be given to the system for an electron to be ejected.

b. We expect the work function to be positive, because energy must be released by the system for an electron to be ejected.

c. We expect the work function to be negative, because energy must be released by the system for an electron to be ejected.

d. We expect the work function to be negative, because energy must be given to the system for an electron to be ejected.