Explain two reasons behind the commercial failure of Low Earth Orbit satellite mobile communications companies (such as Iridium).
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An object with total mass mtotal = 14.8 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.8 kg moves up and to the left at an angle of θ1 = 22° above the –x axis with a speed of v1 = 27.6 m/s. A second piece with mass m2 = 5.1 kg moves down and to the right an angle of θ2 = 27° to the right of the -y axis at a speed of v2 = 20.5 m/s.
What is the x-component of the velocity of the third piece?
What is the y-component of the velocity of the third piece?
What is the magnitude of the velocity of the center of mass of the pieces after the collision?
Calculate the increase in kinetic energy of the pieces during the explosion?
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A gas of nitrogen molecules is at a temperature of 1000K. In this case molecule has 3 translational, 2 rotational, and 2 vibrational degrees of freedom per molecule, i.e. a total of 7.
1.9. [1pt] Assuming the cycle operates as an engine, calculate the engine efficiency.
ANSWER
1.10. [1pt] If you are to build the most efficient engine using the highest and the lowest temperatures available from #9 how would the cycle look like on a PV-diagram [you need to indicate both cycles]
ANSWER
1.11 [1pt] What is the efficiency of the most efficient cycle in 1.10?
ANSWER
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Two charged particles attract each other with a force of magnitude F acting on each. If the charge of one is doubled and the distance separating the particles is also doubled, the force acting on each of the two particles has magnitude
(a) F/2
(b) F/4
(c) F
(d) 2F
(e) 4F
(f) None of the above.
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The electric field at a point in space is a measure of
(a) The total charge on an object at that point.
(b) The electric force on any charged object at that point.
(c) The charge-to-mass ratio of an object at that point.
(d) The electric force per unit mass on a point charge at that point.
(e) The electric force per unit charge on a point charge at that point.
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A charged insulator and an uncharged metal object near each other
(a) Exert no electric force on each other.
(b) Repel each other electrically.
(c) Attract each other electrically.
(d) Attract or repel, depending on whether the charge is positive or negative.
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The following hypothetical reaction shows a neutron (n) decaying into a proton (p+), an electron (e−), and an uncharged particle called an antineutrino
:

At first there is no charge, but then charge seems to be “created.” Does this reaction violate the law of charge conservation? Explain.
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Which of these statements comparing electric and gravitational forces is correct?
(a) The direction of the electric force exerted by one point particle on another is always the same as the direction of the gravitational force exerted by that particle on the other.
(b) The electric and gravitational forces exerted by two particles on each other are inversely proportional to the separation of the particles.
(c) The electric force exerted by one planet on another is typically stronger than the gravitational force exerted by that same planet on the other.
(d) None of the above
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In the figure, which best represents the field lines due to two point charges with opposite charges?

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Two point charges q and 2q lie on the x-axis. Which region(s) on the x-axis include a point where the electric field due to the two point charges is zero?
(a) To the right of 2q
(b) Between 2q and point P
(c) Between point P and q
(d) To the left of q
(e) Both (a) and (c)
(f) Both (b) and (d)

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A rod is negatively charged by rubbing it with fur. It is brought near another rod of unknown composition and charge. There is a repulsive force on each.
(a) Is the first rod an insulator or a conductor? Explain.
(b) What can you tell about the charge of the second rod?
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In each of six situations, a particle (mass m, charge q) is located at a point where the electric field has magnitude E. No other forces act on the particles. Rank them in order of the magnitude of the particle’s acceleration, from largest to smallest.

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Some forms of cancer can be treated using proton therapy in which proton beams are accelerated to high energies, then directed to collide into a tumor, killing the malignant cells. Suppose a proton accelerator is 4.0 m long and must accelerate protons from rest to a speed of 1.0 × 107 m/s. Ignore any relativistic effects (Chapter 26) and determine the magnitude of the average electric field that could accelerate these protons.
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A tiny charged pellet of mass m is suspended at rest between two horizontal, charged metallic plates. The lower plate has a positive charge and the upper plate has a negative charge. Which statement in the answers here is not true?

(a) The electric field between the plates points vertically upward.
(b) The pellet is negatively charged.
(c) The magnitude of the electric force on the pellet is equal to mg.
(d) The plates are at different potentials.
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Can someone please explain how to use ladder operators for the addition of angular momentum, it can be found in chapter 4 of Griffiths intro to quantum mechanics. Please provide some examples of this, you may use problems from chapter four of the book. Thank you.
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