College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Textbook Question
Chapter 6, Problem 32P
A 75.0-kg ice skater moving at 10.0 m/s crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 5.00 m/s. Suppose the average force a skater can experience without breaking a bone is 4 500 N. If the impact time is 0.100 s, does a bone break?
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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 6 Solutions
College Physics
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A...Ch. 6 - Consider the ballistic pendulum device discussed...Ch. 6 - A car of mass m moving at a speed v1 collides and...Ch. 6 - In a Broadway performance, an 80.0-kg actor swings...Ch. 6 - Two shuffleboard disks of equal mass, one orange...Ch. 6 - A 0.030-kg bullet is fired vertically at 200 m/s...Ch. 6 - An bullet of mass m = 8.00 g is fired into a block...Ch. 6 - A 12.0-g bullet is fired horizontally into a 100-g...Ch. 6 - A 1200-kg car traveling initially with a speed of...Ch. 6 - A boy of mass mb and his girlfriend of mass mg,...Ch. 6 - A space probe, initially at rest, undergoes an...Ch. 6 - A 25.0-g object moving to the right at 20.0 cm/s...Ch. 6 - A billiard ball rolling across a table at 1.50 m/s...Ch. 6 - A 90.0-kg fullback running cast with a speed of...Ch. 6 - Identical twins, each with mass 55.0 kg, are on...Ch. 6 - A 2.00 1O3-kg car moving cast at 10.0 m/s...Ch. 6 - Two automobiles of equal mass approach an...Ch. 6 - A billiard ball moving at 5.00 m/s strikes a...Ch. 6 - In research in cardiology and exercise physiology,...Ch. 6 - Most of us know intuitively that in a head-on...Ch. 6 - Consider a frictionless track as shown in Figure...Ch. 6 - A 2.0-g particle moving at 8.0 m/s makes a...Ch. 6 - A bullet of mass m and speed v passes completely...Ch. 6 - Two objects of masses m1 = 0.56 kg m2 = 0.88 kg...Ch. 6 - A 0.400-kg blue bead slides on a frictionless,...Ch. 6 - A 730-N man stands in the middle of a frozen pond...Ch. 6 - An unstable nucleus of muss 1.7 1026 kg,...Ch. 6 - Two blocks of masses m1 and m2 approach each other...Ch. 6 - Two blocks of masses m1 = 2.00 kg and m2 = 4.00 kg...Ch. 6 - A block with mass m1 = 0.500 kg is released from...Ch. 6 - Two objects of masses m and 3m are moving toward...Ch. 6 - A small block of mass m1 = 0.500 kg is released...Ch. 6 - A cue ball traveling at 4.00 m/s makes a glancing,...Ch. 6 - A cannon is rigidly attached to a carriage, which...Ch. 6 - Prob. 68APCh. 6 - A neutron in a reactor makes an elastic head-on...Ch. 6 - Two blocks collide on a frictionless surface....Ch. 6 - (a) A car traveling due east strikes a car...Ch. 6 - A 60-kg soccer player jumps vertically upwards and...Ch. 6 - A tennis ball of mass 57.0 g is held just above a...Ch. 6 - A 20.0-kg toboggan with 70.0-kg driver is sliding...Ch. 6 - Measuring the speed of a bullet. 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