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 4, Problem 2P
(a) A car with a mass of 850 kg is moving to the right with a constant speed of 1.44 m/s. What is the total force on the car? (b) What is the total force on the car if it is moving to the left?
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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]
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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
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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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(b)…
Chapter 4 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 4.1 - Which of the following statements is most correct?...Ch. 4.4 - An object experiences no acceleration. Which of...Ch. 4.4 - You push an object, initially at rest, across a...Ch. 4.5 - Prob. 4.4QQCh. 4.6 - (i) If a fly collides with the windshield of a...Ch. 4.6 - Which of the following is the reaction force to...Ch. 4.7 - Consider the two situations shown in Figure 4.8,...Ch. 4 - Prob. 1OQCh. 4 - Prob. 2OQCh. 4 - Prob. 3OQ
Ch. 4 - Prob. 4OQCh. 4 - Prob. 5OQCh. 4 - Prob. 6OQCh. 4 - Prob. 1CQCh. 4 - If a car is traveling due westward with a constant...Ch. 4 - A person holds a ball in her hand. (a) Identify...Ch. 4 - Prob. 4CQCh. 4 - If you hold a horizontal metal bar several...Ch. 4 - Prob. 6CQCh. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Balancing carefully, three boys inch out onto a...Ch. 4 - Prob. 10CQCh. 4 - Prob. 11CQCh. 4 - Prob. 12CQCh. 4 - Prob. 13CQCh. 4 - Give reasons for the answers to each of the...Ch. 4 - Prob. 15CQCh. 4 - In Figure CQ4.16, the light, taut, unstretchable...Ch. 4 - Prob. 17CQCh. 4 - Prob. 18CQCh. 4 - Prob. 19CQCh. 4 - A force F applied to an object of mass m1 produces...Ch. 4 - (a) A car with a mass of 850 kg is moving to the...Ch. 4 - A toy rocket engine is securely fastened to a...Ch. 4 - Two forces, F1=(6i4j)N and F2=(3i+7j)N, act on a...Ch. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Two forces F1 and F2 act on a 5.00-kg object....Ch. 4 - A 3.00-kg object is moving in a plane, with its x...Ch. 4 - A woman weighs 120 lb. Determine (a) her weight in...Ch. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - You stand on the seat of a chair and then hop off....Ch. 4 - Prob. 17PCh. 4 - A block slides down a frictionless plane having an...Ch. 4 - Prob. 19PCh. 4 - A setup similar to the one shown in Figure P4.20...Ch. 4 - Prob. 21PCh. 4 - The systems shown in Figure P4.22 are in...Ch. 4 - A bag of cement weighing 325 N hangs in...Ch. 4 - Prob. 24PCh. 4 - In Example 4.6, we investigated the apparent...Ch. 4 - Figure P4.26 shows loads hanging from the ceiling...Ch. 4 - Prob. 27PCh. 4 - An object of mass m1 = 5.00 kg placed on a...Ch. 4 - An object of mass m = 1.00 kg is observed to have...Ch. 4 - Two objects are connected by a light string that...Ch. 4 - Prob. 31PCh. 4 - A car is stuck in the mud. A tow truck pulls on...Ch. 4 - Two blocks, each of mass m = 3.50 kg, are hung...Ch. 4 - Two blocks, each of mass m, are hung from the...Ch. 4 - In Figure P4.35, the man and the platform together...Ch. 4 - Two objects with masses of 3.00 kg and 5.00 kg are...Ch. 4 - A frictionless plane is 10.0 m long and inclined...Ch. 4 - Prob. 39PCh. 4 - An object of mass m1 hangs from a string that...Ch. 4 - A young woman buys an inexpensive used car for...Ch. 4 - A 1 000-kg car is pulling a 300-kg trailer....Ch. 4 - An object of mass M is held in place by an applied...Ch. 4 - Prob. 44PCh. 4 - An inventive child named Nick wants to reach an...Ch. 4 - In the situation described in Problem 45 and...Ch. 4 - Two blocks of mass 3.50 kg and 8.00 kg are...Ch. 4 - Prob. 48PCh. 4 - In Example 4.5, we pushed on two blocks on a...Ch. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Review. A block of mass m = 2.00 kg is released...Ch. 4 - A student is asked to measure the acceleration of...Ch. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - A car accelerates down a hill (Fig. P4.57), going...Ch. 4 - Prob. 58PCh. 4 - In Figure P4.53, the incline has mass M and is...
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