College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Chapter 20, Problem 11PE
The batteries of a submerged non-nuclear submarine supply 1000 A at full speed ahead. How long does it take to move
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 20 Solutions
College Physics
Ch. 20 - Can a wire carry a current and still be...Ch. 20 - Car batteries are rated in ampere-hours (A h )....Ch. 20 - If two different wires having identical...Ch. 20 - Why are two conducting paths from a voltage source...Ch. 20 - In cars, one battery terminal is connected to the...Ch. 20 - Why isn't a bird sitting on a high-voltage power...Ch. 20 - The IR drop across a resistor means that there is...Ch. 20 - How is the I R drop in a resistor similar to the...Ch. 20 - In which of the three semiconducting materials...Ch. 20 - Does the resistance of an object depend on the...
Ch. 20 - If aluminum and copper wires of the same length...Ch. 20 - Explain why R=R0(1 + a?T) for the temperature...Ch. 20 - Why do incandescent lightbulbs grow dim late in...Ch. 20 - The power dissipated in a resistor is given by P =...Ch. 20 - Give an example of a use of AC power other than in...Ch. 20 - Why do voltage, current, and power go through zero...Ch. 20 - You are riding in a train, gazing into the...Ch. 20 - Using an ohmmeter, a student measures the...Ch. 20 - What are the two major hazards of electricity?Ch. 20 - Why isn’t a short circuit a shock hazard?Ch. 20 - What determines the severity of a shock? Can you...Ch. 20 - An electrified needle is used to burn off warts,...Ch. 20 - Some surgery is performed with high-voltage...Ch. 20 - Some devices often used in bathrooms, such as...Ch. 20 - We are often advised to not flick electric...Ch. 20 - Before working on a power transmission line,...Ch. 20 - Why is the resistance of wet skin so much smaller...Ch. 20 - Could a person on intravenous infusion (an IV) be...Ch. 20 - In view of the small currents that cause shock...Ch. 20 - Note that in Figure 20.28, both the concentration...Ch. 20 - Define depolarization, repolarization, and the...Ch. 20 - Explain the properties of myelinated nerves in...Ch. 20 - What is the current in milliamperes produced by...Ch. 20 - A total of 600 C of charge passes through a...Ch. 20 - What is the current when a typical static charge...Ch. 20 - Find the current when 2.00 nC jumps between your...Ch. 20 - A large lightning bolt had a 20,000-A current and...Ch. 20 - The 200-A current through a spark plug moves 0.300...Ch. 20 - (a) A defibrillator sends a 6.00-A current through...Ch. 20 - During open-heart surgery, a defibrillator can be...Ch. 20 - (a) A defibrillator passes 12.0 A of current...Ch. 20 - A clock battery wears out after moving 10,000 C of...Ch. 20 - The batteries of a submerged non-nuclear submarine...Ch. 20 - Electron guns are used in X-ray tubes. The...Ch. 20 - A large cyclotron directs a beam of He ++ nuclei...Ch. 20 - Repeat the above example on Example 20.3, but for...Ch. 20 - Using the results of the above example on Example...Ch. 20 - A 14-gauge copper wire has a diameter of 1.628 mm....Ch. 20 - SPEAR, a storage ring about 72.0 m in diameter at...Ch. 20 - What current flows through the bulb of a 3.00-V...Ch. 20 - Calculate the effective resistance of a pocket...Ch. 20 - What is the effective resistance of a car’s...Ch. 20 - How many volts are supplied to operate an...Ch. 20 - (a) F ind the voltage drop in an extension cord...Ch. 20 - A power transmission line is hung from metal...Ch. 20 - What is the resistance of a 20.0-m-long piece of...Ch. 20 - The diameter of 0-gauge copper wire is 8.252 mm....Ch. 20 - If the 0.100-mm diameter tungsten filament in a...Ch. 20 - Find the ratio of the diameter of aluminum to...Ch. 20 - What current flows through a 2.54-cm-diameter rod...Ch. 20 - (a) To what temperature must you raise a copper...Ch. 20 - A resistor made of Nichrome wire is used in an...Ch. 20 - Of what material is a resistor made if its...Ch. 20 - An electronic device designed to operate at any...Ch. 20 - a) Of what material is a wire made, if it is 25.0...Ch. 20 - Assuming a constant temperature coefficient of...Ch. 20 - A wire is drawn through a die, stretching it to...Ch. 20 - A copper wire has a resistance of 0.500at 20.0°C,...Ch. 20 - (a) Digital medical thermometers determine...Ch. 20 - Integrated Concepts (a) Redo Exercise 20.25 taking...Ch. 20 - Unreasonable Results (a) To what temperature must...Ch. 20 - What is the power of a 1.00 102 MV lightning boit...Ch. 20 - What power is supplied to the starter motor of a...Ch. 20 - A charge of 4.00 C of charge passes through a...Ch. 20 - How many watts does a flashlight that has 6.00102C...Ch. 20 - Find the power dissipated in each of these...Ch. 20 - Verify that the units of a volt-ampere are watts,...Ch. 20 - Show that the units 1 V2/=1W , as implied by the...Ch. 20 - Show that the units 1 A 2 = 1W, as implied by the...Ch. 20 - Verify the energy unit equivalence that 1 kWh =...Ch. 20 - Electrons in an X-ray tube are accelerated through...Ch. 20 - An electric water heater consumes 5.00 kW for 2.00...Ch. 20 - With a 1200-W toaster, how much electrical energy...Ch. 20 - What would be the maximum cost of a CFL such that...Ch. 20 - Some makes of older cars have 6.00-V electrical...Ch. 20 - Alkaline batteries have the advantage of putting...Ch. 20 - A cauterizer, used to stop bleeding in surgery,...Ch. 20 - The average television is said to be on 6 hours...Ch. 20 - An old lightbulb draws only 50.0 W, rather than...Ch. 20 - -gauge copper wire has a diameter of 9.266 mm....Ch. 20 - Integrated Concepts Cold vaporizers pass a current...Ch. 20 - Integrated Concepts (a) What energy is dissipated...Ch. 20 - Integrated Concepts What current must be produced...Ch. 20 - Integrated Concepts How much time is needed for a...Ch. 20 - Integrated Concepts Hydroelectric generators (see...Ch. 20 - Integrated Concepts (a) Assuming 95.0% efficiency...Ch. 20 - Integrated Concepts A light-rail commuter train...Ch. 20 - Integrated Concepts (a) An aluminum power...Ch. 20 - Integrated Concepts (a) An immersion heater...Ch. 20 - Integrated Concepts (a) What is the cost of...Ch. 20 - Unreasonable Results (a) What current is needed to...Ch. 20 - Unreasonable Results (a) What current is needed to...Ch. 20 - Construct Your Own Problem Consider an electric...Ch. 20 - (a) What is the hot resistance of a 25-W light...Ch. 20 - Certain heavy industrial equipment uses AC power...Ch. 20 - A certain circuit breaker trips when the rms...Ch. 20 - Military aircraft use 400-Hz AC power, because it...Ch. 20 - A North American tourist takes his 25.0-W, 120-V...Ch. 20 - In this problem, you will verify statements made...Ch. 20 - A small office-building air conditioner operates...Ch. 20 - What is the peak power consumption of a 12G-V AC...Ch. 20 - What is the peak current through a 500-W room...Ch. 20 - Two different electrical devices have the same...Ch. 20 - Nichrome wire is used in some radiative heaters....Ch. 20 - Find the time after t = 0 when the instantaneous...Ch. 20 - (a) At what two times in the first period...Ch. 20 - (a) Haw much power is dissipated in a short...Ch. 20 - What voltage is involved in a 1.44-kW short...Ch. 20 - Find the current through a person and identify the...Ch. 20 - While taking a bath, a person touches the metal...Ch. 20 - Foolishly trying to fish a burning piece of bread...Ch. 20 - (a) During surgery, a current as small as 20.0 ?...Ch. 20 - (a) What is the resistance of a 220-V AC short...Ch. 20 - A heart defibrillator passes 10.0 A through a...Ch. 20 - Integrated Concepts A short circuit in a 120-V...Ch. 20 - Construct Your Own Problem Consider a person...Ch. 20 - Integrated Concepts Use the ECG in Figure 20.34 to...Ch. 20 - Integrated Concepts (a) Referring to Figure 20.34,...
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Ohm's law Explained; Author: ALL ABOUT ELECTRONICS;https://www.youtube.com/watch?v=PV8CMZZKrB4;License: Standard YouTube License, CC-BY