Physics for Scientists and Engineers, Volume 2
10th Edition
ISBN: 9781337553582
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 9, Problem 35AP
An amateur skater of mass M is trapped in the middle of an ice rink and is unable to return to the side where there is no ice. Every motion she makes causes her to slip on the ice and remain in the same spot. She decides to try to return to safety by throwing her gloves of mass m in the direction opposite the safe side. (a) She throws the gloves as hard as she can, and they leave her hand with a horizontal velocity
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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]
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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)
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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]
Chapter 9 Solutions
Physics for Scientists and Engineers, Volume 2
Ch. 9.1 - Two objects have equal kinetic energies. How do...Ch. 9.1 - Your physical education teacher throws a baseball...Ch. 9.3 - Two objects are at rest on a frictionless surface....Ch. 9.3 - Rank an automobile dashboard, seat belt, and air...Ch. 9.4 - In a perfectly inelastic one-dimensional collision...Ch. 9.4 - A table-tennis ball is thrown at a stationary...Ch. 9.6 - A baseball bat of uniform density is cut at the...Ch. 9.7 - A cruise ship is moving at constant speed through...Ch. 9 - A particle of mass m moves with momentum of...Ch. 9 - A 3.00-kg particle has a velocity of...
Ch. 9 - A baseball approaches home plate at a speed of...Ch. 9 - A 65.0-kg boy and his 40.0-kg sister, both wearing...Ch. 9 - Two blocks of masses m and 3m are placed on a...Ch. 9 - When you jump straight up as high as you can, what...Ch. 9 - A glider of mass m is free to slide along a...Ch. 9 - You and your brother argue often about how to...Ch. 9 - The front 1.20 m of a 1 400-kg car Ls designed as...Ch. 9 - The magnitude of the net force exerted in the x...Ch. 9 - Water falls without splashing at a rate of 0.250...Ch. 9 - A 1 200-kg car traveling initially at vCi = 25.0...Ch. 9 - A railroad car of mass 2.50 104 kg is moving with...Ch. 9 - Four railroad cars, each of mass 2.50 104 kg, are...Ch. 9 - A car of mass m moving at a speed v1 collides and...Ch. 9 - A 7.00-g bullet, when fired from a gun into a...Ch. 9 - A tennis ball of mass 57.0 g is held just above a...Ch. 9 - (a) Three carts of masses m1 = 4.00 kg, m2 = 10.0...Ch. 9 - You have been hired as an expert witness by an...Ch. 9 - Two shuffleboard disks of equal mass, one orange...Ch. 9 - Two shuffleboard disks of equal mass, one orange...Ch. 9 - A 90.0-kg fullback running east with a speed of...Ch. 9 - A proton, moving with a velocity of vii, collides...Ch. 9 - A uniform piece of sheet metal is shaped as shown...Ch. 9 - Explorers in the jungle find an ancient monument...Ch. 9 - A rod of length 30.0 cm has linear density (mass...Ch. 9 - Consider a system of two particles in the xy...Ch. 9 - The vector position of a 3.50-g particle moving in...Ch. 9 - You have been hired as an expert witness in an...Ch. 9 - Prob. 30PCh. 9 - A 60.0-kg person bends his knees and then jumps...Ch. 9 - A garden hose is held as shown in Figure P9.32....Ch. 9 - A rocket for use in deep space is to be capable of...Ch. 9 - A rocket has total mass Mi = 360 kg, including...Ch. 9 - An amateur skater of mass M is trapped in the...Ch. 9 - (a) Figure P9.36 shows three points in the...Ch. 9 - Review. A 60.0-kg person running at an initial...Ch. 9 - A cannon is rigidly attached to a carriage, which...Ch. 9 - A 1.25-kg wooden block rests on a table over a...Ch. 9 - A wooden block of mass M rests on a table over a...Ch. 9 - Two gliders are set in motion on a horizontal air...Ch. 9 - Pursued by ferocious wolves, you are in a sleigh...Ch. 9 - Review. A student performs a ballistic pendulum...Ch. 9 - Why is the following situation impossible? An...Ch. 9 - Review. A bullet of mass m = 8.00 g is fired into...Ch. 9 - Review. A bullet of mass m is fired into a block...Ch. 9 - A 0.500-kg sphere moving with a velocity expressed...Ch. 9 - Prob. 48APCh. 9 - Review. A light spring of force constant 3.85 N/m...Ch. 9 - Prob. 50APCh. 9 - Review. There are (one can say) three coequal...Ch. 9 - Sand from a stationary hopper falls onto a moving...Ch. 9 - Two particles with masses m and 3m are moving...Ch. 9 - On a horizontal air track, a glider of mass m...
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