Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 12, Problem 12.28P
Assume Young’s modulus for bone is 1.50 × 1010 N/m2. The bone breaks if stress greater than 1.50 × 108 N/m2 is imposed on it. (a) What is the maximum force that can be exerted on the femur bone in the leg if it has a minimum effective diameter of 2.50 cm? (b) If this much force is applied compressively, by how much does the 25.0-cm-long bone shorten?
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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
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Chapter 12 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Ch. 12 - Consider the object subject to the two forces of...Ch. 12 - Consider the object subject to the three forces in...Ch. 12 - A meterstick of uniform density is hung from a...Ch. 12 - For the three parts of this Quick Quiz, choose...Ch. 12 - The acceleration due to gravity becomes weaker by...Ch. 12 - A rod 7.0 in long is pivoted at a point 2.0 m from...Ch. 12 - Prob. 12.3OQCh. 12 - Two forces are acting on an object. Which of the...Ch. 12 - Prob. 12.5OQCh. 12 - A 20.0-kg horizontal plank 4.00 in long rests on...
Ch. 12 - Prob. 12.7OQCh. 12 - In analyzing the equilibrium of a flat, rigid...Ch. 12 - A certain wire, 3 m long, stretches by 1.2 mm when...Ch. 12 - The center of gravity of an ax is on the...Ch. 12 - A ladder stands on the ground, leaning against a...Ch. 12 - Prob. 12.2CQCh. 12 - (a) Give an example in which the net force acting...Ch. 12 - Prob. 12.4CQCh. 12 - Prob. 12.5CQCh. 12 - A girl has a large, docile dog she wishes to weigh...Ch. 12 - Prob. 12.7CQCh. 12 - What kind of deformation does a cube of Jell-O...Ch. 12 - What are the necessary conditions for equilibrium...Ch. 12 - Why is the following situation impossible? A...Ch. 12 - Prob. 12.3PCh. 12 - Prob. 12.4PCh. 12 - Your brother is opening a skateboard shop. He has...Ch. 12 - A circular pizza of radius R has a circular piece...Ch. 12 - Prob. 12.7PCh. 12 - Prob. 12.8PCh. 12 - Prob. 12.9PCh. 12 - Prob. 12.10PCh. 12 - A uniform beam of length 7.60 m and weight 4.50 ...Ch. 12 - A vaulter holds a 29.4-N pole in equilibrium by...Ch. 12 - A 15.0-in uniform ladder weighing 500 N rests...Ch. 12 - A uniform ladder of length L.and mass m1 rests...Ch. 12 - A flexible chain weighing 40.0 N hangs between two...Ch. 12 - A uniform beam of length L and mass m shown in...Ch. 12 - Figure P12.13 shows a claw hammer being used to...Ch. 12 - A 20.0-kg floodlight in a park is supported at the...Ch. 12 - Prob. 12.19PCh. 12 - Review. While Lost-a-Lot ponders his next move in...Ch. 12 - John is pushing his daughter Rachel in a...Ch. 12 - Prob. 12.22PCh. 12 - One end of a uniform 4.00-m-long rod of weight Fg...Ch. 12 - A 10.0-kg monkey climbs a uniform ladder with...Ch. 12 - A uniform plank of length 2.00 m and mass 30.0 kg...Ch. 12 - A steel wire of diameter 1 mm can support a...Ch. 12 - The deepest point in the ocean is in the Mariana...Ch. 12 - Assume Youngs modulus for bone is 1.50 1010 N/m2....Ch. 12 - A child slides across a floor in a pair of...Ch. 12 - Evaluate Youngs modulus for the material whose...Ch. 12 - Assume if the shear stress in steel exceeds about...Ch. 12 - When water freezes, it expands by about 9.00%....Ch. 12 - A 200-kg load is hung on a wire of length 4.00m,...Ch. 12 - A walkway suspended across a hotel lobby is...Ch. 12 - Review. A 2.00-m-long cylindrical steel wire with...Ch. 12 - Review. A 30.0-kg hammer, moving with speed 20.0...Ch. 12 - A bridge of length 50.0 m and mass 8.00 104 kg is...Ch. 12 - A uniform beam resting on two pivots has a length...Ch. 12 - Prob. 12.39APCh. 12 - The lintel of prestressed reinforced concrete in...Ch. 12 - Prob. 12.41APCh. 12 - When a person stands on tiptoe on one foot (a...Ch. 12 - A hungry bear weighing 700 N walks out on a beam...Ch. 12 - The following equations are obtained from a force...Ch. 12 - A uniform sign of weight Fg and width 2L hangs...Ch. 12 - A 1 200-N uniform boom at = 65 to the vertical is...Ch. 12 - Prob. 12.47APCh. 12 - Assume a person bends forward to lift a load with...Ch. 12 - A 10 000-N shark is supported by a rope attached...Ch. 12 - Why is the following situation impossible? A...Ch. 12 - A uniform beam of mass m is inclined at an angle ...Ch. 12 - Prob. 12.52APCh. 12 - When a circus performer performing on the rings...Ch. 12 - Figure P12.38 shows a light truss formed from...Ch. 12 - Prob. 12.55APCh. 12 - A stepladder of negligible weight is constructed...Ch. 12 - A stepladder of negligible weight is constructed...Ch. 12 - (a) Estimate the force with which a karate master...Ch. 12 - Two racquetballs, each having a mass of 170 g, are...Ch. 12 - Review. A wire of length L, Youngs modulus Y, and...Ch. 12 - Review. An aluminum wire is 0.850 m long and has a...Ch. 12 - Prob. 12.62APCh. 12 - A 500-N uniform rectangular sign 4.00 m wide and...Ch. 12 - A steel cable 3.00 cm2 in cross-sectional area has...Ch. 12 - A uniform pole is propped between the floor and...Ch. 12 - In the What If? section of Example 12.2, let d...Ch. 12 - Figure P12.67 shows a vertical force applied...Ch. 12 - A uniform rod of weight Fg and length L is...
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