FUNDAMENTALS OF PHYSICS V.1
11th Edition
ISBN: 9781119573913
Author: Halliday
Publisher: WILEY
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Chapter 9, Problem 97P
The three balls in the overhead view of Fig. 9-76 are identical. Balls 2 and 3 touch each other and are aligned perpendicular to the path of ball 1. The velocity of ball 1 has magnitude v0 = 10 m/s and is directed at the contact point of balls 1 and 2. After the collision, what are the (a) speed and (b) direction of the velocity of ball 2, the (c) speed and (d) direction of the velocity of ball 3, and the (e) speed and (f) direction of the velocity of ball 1? (Hint: With friction absent, each impulse is directed along the line connecting the centers of the colliding balls, normal to the colliding surfaces.)
Figure 9-76 Problem 97.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
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a)
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[2 marks]
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3
a
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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.
[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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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,
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[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
FUNDAMENTALS OF PHYSICS V.1
Ch. 9 - Figure 9-23 shows an overhead view of three...Ch. 9 - Figure 9-24 shows an overhead view of four...Ch. 9 - Consider a box that explodes into two pieces while...Ch. 9 - Figure 9-26 shows graphs of force magnitude versus...Ch. 9 - The free-body diagrams in Fig. 9-27 give, from...Ch. 9 - Figure 9-28 shows four groups of three or four...Ch. 9 - A block slides along a frictionless floor and into...Ch. 9 - Figure 9-30 shows a snapshot of block 1 as it...Ch. 9 - Two bodies have undergone an elastic...Ch. 9 - Figure 9-32: A block on a horizontal floor is...
Ch. 9 - Block 1 with mass m1 slides along an x axis across...Ch. 9 - Figure 9-34 shows four graphs of position versus...Ch. 9 - A 2.00 kg particle has the xy coordinates 1.20 m,...Ch. 9 - Figure 9-35 shows a three-particle system, with...Ch. 9 - Figure 9-36 shows a slab with dimensions d1 = 11.0...Ch. 9 - In Fig. 9-37, three uniform thin rods, each of...Ch. 9 - GO What are a the x coordinate and b the y...Ch. 9 - Figure 9-39 shows a cubical box that has been...Ch. 9 - ILW In the ammonia NH3 molecule of Fig. 9-40,...Ch. 9 - GO A uniform soda can of mass 0.140 kg is 12.0 cm...Ch. 9 - ILW A stone is dropped at t = 0. A second stone,...Ch. 9 - GO A 1000 kg automobile is at rest at a traffic...Ch. 9 - A big olive m = 0.50 kg lies at the origin of an...Ch. 9 - Prob. 12PCh. 9 - SSM A shell is shot with an initial velocity v0 of...Ch. 9 - In Figure 9-43, two particles are launched from...Ch. 9 - Figure 9-44 shows an arrangement with an air...Ch. 9 - GO Ricardo, of mass 80 kg, and Carmelita, who is...Ch. 9 - GO In Fig. 9-45a, a 4.5 kg dog stands on an 18 kg...Ch. 9 - A 0.70 kg ball moving horizontally at 5.0 m/s...Ch. 9 - ILW A 2100 kg truck traveling north at 41 km/h...Ch. 9 - GO At time t = 0, a ball is struck at ground level...Ch. 9 - A 0.30 kg softball has a velocity of 15 m/s at an...Ch. 9 - Figure 9-47 gives an overhead view of the path...Ch. 9 - Until his seventies, Henri LaMothe Fig. 9-48...Ch. 9 - In February 1955, a paratrooper fell 370 m from an...Ch. 9 - A 1.2 kg ball drops vertically onto a floor,...Ch. 9 - In a common but dangerous prank, a chair is pulled...Ch. 9 - SSM A force in the negative direction of an x axis...Ch. 9 - In tae-kwon-do, a hand is slammed down onto a...Ch. 9 - Suppose a gangster sprays Supermans chest with 3 g...Ch. 9 - Two average forces. A steady stream of 0.250 kg...Ch. 9 - Jumping up before the elevator hits. After the...Ch. 9 - A 5.0 kg toy car can move along an x axis; Fig....Ch. 9 - GO Figure 9-51 shows a 0.300 kg baseball just...Ch. 9 - Basilisk lizards can run across the top of a water...Ch. 9 - GO Figure 9-53 shows an approximate plot of force...Ch. 9 - A 0.25 kg puck is initially stationary on an ice...Ch. 9 - SSM A soccer player kicks a soccer ball of mass...Ch. 9 - In the overhead view of Fig. 9-54, a 300 g ball...Ch. 9 - SSM A 91 kg man lying on a surface of negligible...Ch. 9 - A space vehicle is traveling at 4300 km/h relative...Ch. 9 - Figure 9-55 shows a two-ended rocket that is...Ch. 9 - An object, with mass m and speed v relative to an...Ch. 9 - In the Olympiad of 708 B.C., some athletes...Ch. 9 - Prob. 44PCh. 9 - SSM WWW A 20.0 kg body is moving through space in...Ch. 9 - A 4.0 kg mess kit sliding on a frictionless...Ch. 9 - A vessel at rest at the origin of an xy coordinate...Ch. 9 - GO Particle A and particle B are held together...Ch. 9 - A bullet of mass 10 g strikes a ballistic pendulum...Ch. 9 - A 5.20 g bullet moving at 672 m/s strikes a 700 g...Ch. 9 - GO In Fig. 9-58, a 3.50 g bullet is fired...Ch. 9 - GO In Fig. 9-59, a 10 g bullet moving directly...Ch. 9 - Prob. 53PCh. 9 - A completely inelastic collision occurs between...Ch. 9 - ILW A 5.0 kg block with a speed of 3.0 m/s...Ch. 9 - In the before part of Fig. 9-60, car A mass 1100...Ch. 9 - Prob. 57PCh. 9 - In Fig. 9-62, block 2 mass 1.0 kg is at rest on a...Ch. 9 - ILW In Fig. 9-63, block 1 mass 2.0 kg is moving...Ch. 9 - Module 9-7 Elastic Collisions in One Dimension In...Ch. 9 - SSM A cart with mass 340 g moving on a...Ch. 9 - Two titanium spheres approach each other head-on...Ch. 9 - Block 1 of mass m1 slides along a frictionless...Ch. 9 - GO A steel ball of mass 0.500 kg is fastened to a...Ch. 9 - SSM A body of mass 2.0 kg makes an elastic...Ch. 9 - Block 1, with mass m1 and speed 4.0 m/s, slides...Ch. 9 - In Fig. 9-66, particle 1 of mass m1 = 0.30 kg...Ch. 9 - GO In Fig. 9-67, block 1 of mass m1 slides from...Ch. 9 - GO A small ball of mass m is aligned above a...Ch. 9 - GO In Fig. 9-69, puck 1 of mass m1 = 0.20 kg is...Ch. 9 - Prob. 71PCh. 9 - Ball B, moving in the positive direction of an x...Ch. 9 - After a completely inelastic collision, two...Ch. 9 - Two 2.0 kg bodies, A and B, collide. The...Ch. 9 - GO A projectile proton with a speed of 500 m/s...Ch. 9 - A 6090 kg space probe moving nose-first toward...Ch. 9 - SSM In Fig. 9-70, two long barges are moving in...Ch. 9 - Prob. 78PCh. 9 - SSM ILW A rocket that is in deep space and...Ch. 9 - An object is tracked by a radar station and...Ch. 9 - The last stage of a rocket, which is traveling at...Ch. 9 - Pancake collapse of a tall building. In the...Ch. 9 - Prob. 83PCh. 9 - Figure 9-73 shows an overhead view of two...Ch. 9 - Speed deamplifier. In Fig. 9-74, block 1 of mass...Ch. 9 - Speed amplifier. In Fig. 9-75, block 1 of mass m1...Ch. 9 - A ball having a mass of 150 g strikes a wall with...Ch. 9 - A spacecraft is separated into two parts by...Ch. 9 - SSM A 1400 kg car moving at 5.3 m/s is initially...Ch. 9 - ILW A certain radioactive parent nucleus...Ch. 9 - A 75 kg man rides on a 39 kg cart moving at a...Ch. 9 - Two blocks of masses 1.0 kg and 3.0 kg are...Ch. 9 - Prob. 93PCh. 9 - An old Chrysler with mass 2400 kg is moving along...Ch. 9 - SSM In the arrangement of Fig. 9-21, billiard ball...Ch. 9 - A rocket is moving away from the solar system at a...Ch. 9 - The three balls in the overhead view of Fig. 9-76...Ch. 9 - A 0.15 kg ball hits a wall with a velocity of 5.00...Ch. 9 - Prob. 99PCh. 9 - In a game of pool, the cue ball strikes another...Ch. 9 - Prob. 101PCh. 9 - In Fig. 9-79, an 80 kg man is on a ladder hanging...Ch. 9 - In Fig. 9 80, block 1 of mass m1 = 6.6 kg is at...Ch. 9 - Prob. 104PCh. 9 - SSM A 3.0 kg object moving at 8.0 m/s in the...Ch. 9 - A 2140 kg railroad flatcar, which can move with...Ch. 9 - SSM A 6100 kg rocket is set for vertical firing...Ch. 9 - A 500.0 kg module is attached to a 400.0 kg...Ch. 9 - SSM a How far is the center of mass of the...Ch. 9 - A 140 g ball with speed 7.8 m/s strikes a wall...Ch. 9 - SSM A rocket sled with a mass of 2900 kg moves at...Ch. 9 - SSM A pellet gun fires ten 2.0 g pellets per...Ch. 9 - A railroad car moves under a grain elevator at a...Ch. 9 - Figure 9-82 shows a uniform square plate of edge...Ch. 9 - SSM At time t = 0, force F1=(4.00i+5.00j) N acts...Ch. 9 - Two particles P and Q are released from rest 1.0 m...Ch. 9 - A collision occurs between a 2.00 kg particle...Ch. 9 - In the two-sphere arrangement of Fig. 9-20, assume...Ch. 9 - In Fig. 9-83, block 1 slides along an x axis on a...Ch. 9 - A body is traveling at 2.0 m/s along the positive...Ch. 9 - An electron undergoes a one-dimensional elastic...Ch. 9 - Prob. 122PCh. 9 - An unmanned space probe of mass m and speed v...Ch. 9 - A 0.550 kg ball falls directly down onto concrete,...Ch. 9 - An atomic nucleus at rest at the origin of an xy...Ch. 9 - Particle 1 of mass 200 g and speed 3.00 m/s...Ch. 9 - During a lunar mission, it is necessary to...Ch. 9 - Prob. 128P
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