Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 8, Problem 1CQ
To determine
Whether the larger change in momentum results in a larger change in the net force exerted.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
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[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]
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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)
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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
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(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
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Chapter 8 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 8.1 - Two objects have equal kinetic energies. How do...Ch. 8.1 - Your physical education teacher throws a baseball...Ch. 8.3 - Prob. 8.3QQCh. 8.4 - A table-tennis ball is thrown at a stationary...Ch. 8.6 - A baseball bat of uniform denisty is cut at the...Ch. 8.7 - Prob. 8.6QQCh. 8 - Prob. 1OQCh. 8 - A head-on, elastic collision occurs between two...Ch. 8 - Prob. 3OQCh. 8 - A 57.0-g tennis ball is traveling straight at a...
Ch. 8 - A 5-kg cart moving to the right with a speed of 6...Ch. 8 - A 2-kg object moving to the right with a speed of...Ch. 8 - The momentum of an object is increased by a factor...Ch. 8 - The kinetic energy of an object is increased by a...Ch. 8 - Prob. 9OQCh. 8 - Prob. 10OQCh. 8 - Prob. 11OQCh. 8 - Prob. 12OQCh. 8 - Prob. 13OQCh. 8 - A ball is suspended by a string that is tied to a...Ch. 8 - A massive tractor is rolling down a country road....Ch. 8 - Prob. 16OQCh. 8 - Prob. 17OQCh. 8 - Prob. 18OQCh. 8 - Prob. 1CQCh. 8 - Prob. 2CQCh. 8 - A bomb, initially at rest, explodes into several...Ch. 8 - Prob. 4CQCh. 8 - Prob. 5CQCh. 8 - A juggler juggles three balls in a continuous...Ch. 8 - Prob. 7CQCh. 8 - Prob. 8CQCh. 8 - Prob. 9CQCh. 8 - Prob. 10CQCh. 8 - Prob. 11CQCh. 8 - Prob. 12CQCh. 8 - An open box slides across a frictionless, icy...Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - A girl of mass mg is standing on a plank of mass...Ch. 8 - Two blocks of masses m and 3m are placed on a...Ch. 8 - Prob. 8PCh. 8 - A 3.00-kg steel ball strikes a wall with a speed...Ch. 8 - A tennis player receives a shot with the ball...Ch. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - In a slow-pitch softball game, a 0.200-kg softball...Ch. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Prob. 18PCh. 8 - Two blocks are free to slide along the...Ch. 8 - As shown in Figure P8.20, a bullet of mass m and...Ch. 8 - Prob. 21PCh. 8 - A tennis ball of mass mt is held just above a...Ch. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - An object of mass 3.00 kg, moving with an initial...Ch. 8 - Prob. 26PCh. 8 - Prob. 27PCh. 8 - Prob. 28PCh. 8 - A billiard ball moving at 5.00 m/s strikes a...Ch. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Prob. 32PCh. 8 - Prob. 33PCh. 8 - Prob. 34PCh. 8 - Prob. 35PCh. 8 - A water molecule consists of an oxygen atom with...Ch. 8 - Prob. 37PCh. 8 - Prob. 38PCh. 8 - A 2.00-kg particle has a velocity (2.00i3.00j)m/s,...Ch. 8 - Prob. 40PCh. 8 - Prob. 41PCh. 8 - Prob. 42PCh. 8 - Prob. 43PCh. 8 - Prob. 44PCh. 8 - Prob. 45PCh. 8 - A rocket has total mass Mi = 360 kg, including...Ch. 8 - A model rocket engine has an average thrust of...Ch. 8 - Two gliders are set in motion on a horizontal air...Ch. 8 - Prob. 49PCh. 8 - Prob. 50PCh. 8 - Prob. 51PCh. 8 - Prob. 52PCh. 8 - Prob. 53PCh. 8 - Prob. 54PCh. 8 - A small block of mass m1 = 0.500 kg is released...Ch. 8 - Prob. 56PCh. 8 - A 5.00-g bullet moving with an initial speed of v...Ch. 8 - Prob. 58PCh. 8 - Prob. 59PCh. 8 - A cannon is rigidly attached to a carriage, which...Ch. 8 - Prob. 61PCh. 8 - Prob. 62PCh. 8 - George of the Jungle, with mass m, swings on a...Ch. 8 - Sand from a stationary hopper falls onto a moving...Ch. 8 - Prob. 65P
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