EBK APPLIED PHYSICS
11th Edition
ISBN: 9780134241173
Author: GUNDERSEN
Publisher: YUZU
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Textbook Question
Chapter 6.2, Problem 6P
A 75.0-kg paint cart with rubber bumpers is rolling 0.965 m/s to the right and strikes a second cart of mass 85.0 kg moving 1.30 m/s to the left. After the collision, the heavier cart is traveling 0.823 m/s to the right. What is the velocity of the lighter cart after the collision?
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Question B3
Consider the following FLRW spacetime:
t2
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[2 marks]
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[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.
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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.
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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]
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Chapter 6 Solutions
EBK APPLIED PHYSICS
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