College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 11, Problem 7P
A 75-kg sprinter accelerates from rest to a speed of 11.0 m/s in 5.0 s. (a) Calculate the mechanical work done by the sprinter during this time. (b) Calculate the average power the sprinter must generate. (c) If the sprinter converts food energy to mechanical energy with an efficiency of 25%, at what average rate is he burning Calories? (d) What happens to the other 75% of the food energy being used?
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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 11 Solutions
College Physics
Ch. 11.2 - Prob. 11.1QQCh. 11.4 - Prob. 11.2QQCh. 11.5 - Will an ice cube wrapped in a wool blanket remain...Ch. 11.5 - Two rods of the same length and diameter are made...Ch. 11.5 - Stars A and B have the same temperature, but star...Ch. 11 - Prob. 1WUECh. 11 - Physics Review An athlete lifts a 175-kg barbell...Ch. 11 - Prob. 3WUECh. 11 - Convert 3.50 103 cal to the equivalent number of...Ch. 11 - Prob. 5WUE
Ch. 11 - Prob. 6WUECh. 11 - A large room in a house holds 975 kg of dry air at...Ch. 11 - A wooden wall 4.00 cm thick made of pine with...Ch. 11 - A granite ball of radius 2.00 m and emissivity...Ch. 11 - Rub the palm of your hand on a metal surface for...Ch. 11 - In winter, why did the pioneers store an open...Ch. 11 - In warm climates that experience an occasional...Ch. 11 - Prob. 4CQCh. 11 - On a clear, cold night, why does frost tend to...Ch. 11 - The U.S. penny is now made of copper-coated zinc....Ch. 11 - Cups of water for coffee or tea can be warmed with...Ch. 11 - Prob. 8CQCh. 11 - A tile floor may feel uncomfortably cold to your...Ch. 11 - On a very hot day, its possible to cook an egg on...Ch. 11 - Concrete has a higher specific heat than does...Ch. 11 - You need to pick up a very hot cooking pot in your...Ch. 11 - A poker is a stiff, nonflammable rod used to push...Ch. 11 - Star A has twice the radius and twice the absolute...Ch. 11 - Prob. 15CQCh. 11 - The highest recorded waterfall in the world is...Ch. 11 - The temperature of a silver bar rises by 10.0C...Ch. 11 - Lake Erie contains roughly 4.00 1011 m3 of water....Ch. 11 - An aluminum rod is 20.0 cm long at 20.0C and has a...Ch. 11 - A 3.00-g copper coin at 25.0C drops 50.0 m to the...Ch. 11 - Prob. 6PCh. 11 - A 75-kg sprinter accelerates from rest to a speed...Ch. 11 - A sprinter of mass m accelerates uniformly from...Ch. 11 - Prob. 9PCh. 11 - Prob. 10PCh. 11 - Prob. 11PCh. 11 - A 1.5-kg copper block is given an initial speed of...Ch. 11 - A certain steel railroad rails 13 yd in length and...Ch. 11 - Prob. 14PCh. 11 - What mass of water at 25.0C must be allowed to...Ch. 11 - Lead pellets, each of mass 1.00 g, are heated to...Ch. 11 - Prob. 17PCh. 11 - In a showdown on the streets of Laredo, the good...Ch. 11 - Prob. 19PCh. 11 - A 1.50-kg iron horseshoe initially at 600C is...Ch. 11 - A student drops two metallic objects into a 120-g...Ch. 11 - When a driver brakes an automobile, the friction...Ch. 11 - Equal 0.400-kg masses of lead and tin at 60.0C are...Ch. 11 - Prob. 24PCh. 11 - A 75-g ice cube al 0C is placed in 825 g of water...Ch. 11 - Prob. 26PCh. 11 - Prob. 27PCh. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - Prob. 30PCh. 11 - Prob. 31PCh. 11 - Prob. 32PCh. 11 - A high-end gas stove usually has at least one...Ch. 11 - Prob. 34PCh. 11 - Steam at 100.C is added to ice at 0C. (a) Find the...Ch. 11 - The excess internal energy of metabolism is...Ch. 11 - A 3.00-g lead bullet at 30.0C is fired at a speed...Ch. 11 - A glass windowpane in a home is 0.62 cm thick and...Ch. 11 - A pond with a flat bottom has a surface area of...Ch. 11 - The thermal conductivities of human tissues vary...Ch. 11 - A steam pipe is covered with 1.50-cm-thick...Ch. 11 - The average thermal conductivity of the walls...Ch. 11 - Consider two cooking pots of the same dimensions,...Ch. 11 - A thermopane window consists of two glass panes,...Ch. 11 - A copper rod and an aluminum rod of equal diameter...Ch. 11 - A Styrofoam box has a surface area of 0.80 m and a...Ch. 11 - A rectangular glass window pane on a house has a...Ch. 11 - Prob. 48PCh. 11 - Measurements on two stars indicate that Star X has...Ch. 11 - The filament of a 75-W light bulb is at a...Ch. 11 - The bottom of a copper kettle has a 10.0-cm radius...Ch. 11 - A family comes home from a long vacation with...Ch. 11 - A 0.040.-kg ice cube floats in 0.200 kg of water...Ch. 11 - The surface area of an unclothed person is 1.50...Ch. 11 - A 200-g block of copper at a temperature of 90C is...Ch. 11 - Prob. 56APCh. 11 - A student measures the following data in a...Ch. 11 - Prob. 58APCh. 11 - A class of 10 students; taking an exam has a power...Ch. 11 - A class of 10 students taking an exam has a power...Ch. 11 - A bar of gold (Au) is in thermal contact with a...Ch. 11 - An iron plate is held against an iron, wheel so...Ch. 11 - Prob. 63APCh. 11 - Three liquids are at temperatures of 10C, 20C, and...Ch. 11 - Prob. 65APCh. 11 - A wood stove is used to heat a single room. The...Ch. 11 - Prob. 67APCh. 11 - Prob. 68APCh. 11 - The surface of the Sun has a temperature of about...Ch. 11 - The evaporation of perspiration is the primary...Ch. 11 - Prob. 71APCh. 11 - An ice-cube tray is filled with 75.0 g of water....Ch. 11 - An aluminum rod and an iron rod are joined end to...
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