College Physics
1st Edition
ISBN: 9781938168048
Author: Paul Peter Urone, OpenStax, Roger Hinrichs
Publisher: OpenStax
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Textbook Question
Chapter 8, Problem 17CQ
Mixed-pair ice skaters performing in a show are standing motionless at arms length just before starting a routine. They reach out, clasp hands, and pull themselves together by only using their arms. Assuming there is no friction between the blades of their skates and the ice, what is their velocity after their bodies meet?
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ROTATIONAL DYNAMICS
Question 01
A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure
rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
down the same plane inclined at 30° to the horizontal
Which body gets the bottom first and what is its acceleration
b) What angle of inclination of the plane is needed to give the slower body the same
acceleration
Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
A car wheel has its angular velocity changing from 2rads to 30 rads
seconds. If the radius of the wheel is 400mm. calculate
ii)
The angular acceleration
iii)
The tangential linear acceleration of a point on the rim of the wheel
Question 04
in 20
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]
Chapter 8 Solutions
College Physics
Ch. 8 - An object that has a small mass and an object that...Ch. 8 - An object that has a small mass and an object that...Ch. 8 - Professional Application Football coaches advise...Ch. 8 - How can a small force impart the same momentum to...Ch. 8 - Professional Application Explain in terms of...Ch. 8 - While jumping on a trampoline, sometimes you land...Ch. 8 - Professional Application Tennis racquets have...Ch. 8 - Professional Application If you dive into water,...Ch. 8 - Under what circumstances is momentum conserved?Ch. 8 - Can momentum be conserved for a system if there...
Ch. 8 - Momentum for a system can be conserved in one...Ch. 8 - Professional Application Explain in terms of...Ch. 8 - Can objects in a system have momentum while the...Ch. 8 - Must the total energy of a system be conserved...Ch. 8 - What is an elastic collision?Ch. 8 - What is an inelastic collision? What is a...Ch. 8 - Mixed-pair ice skaters performing in a show are...Ch. 8 - A Small pickup truck that has a caliper shell...Ch. 8 - Figure 8.16 shows a cube at rest and a small...Ch. 8 - Professional Application Suppose a fireworks shell...Ch. 8 - Professional Application During a visit to the...Ch. 8 - Professional Application It is possible for the...Ch. 8 - (a) Calculate the momentum of a 2000-kg elephant...Ch. 8 - (a) What is the mass of a large ship that has a...Ch. 8 - (a) At what speed would a 2.00104 -kg airplane...Ch. 8 - (a) What is the momentum of a garbage truck that...Ch. 8 - A runaway train car that has a mass of 15,000 kg...Ch. 8 - The mass of Earth is 5.9721024 kg and its orbital...Ch. 8 - A bullet is accelerated down the barrel of a gun...Ch. 8 - Professional Application A car moving at 10 m/s...Ch. 8 - A person slaps her leg with her hand, bringing her...Ch. 8 - Professional Application A professional boxer hits...Ch. 8 - Professional Application Suppose a child drives a...Ch. 8 - Professional Application One hazard of space...Ch. 8 - Professional Application A 75.0-kg person is...Ch. 8 - Professional Application Military rifles have a...Ch. 8 - A cruise ship with a mass of 1.00107 kg strikes a...Ch. 8 - Calculate the final speed of a 110-kg rugby player...Ch. 8 - Water from a fire hose is directed horizontally...Ch. 8 - A 0.450-kg hammer is moving horizontally at 7.00...Ch. 8 - Starting with the definitions of momentum and...Ch. 8 - A ball with an initial velocity of 10 m/s moves at...Ch. 8 - When serving a tennis ball, a player hits the ball...Ch. 8 - A punter drops a ball from rest vertically 1 meter...Ch. 8 - Professional Application Train cars are coupled...Ch. 8 - Suppose a clay model of a koala bear has a mass of...Ch. 8 - Professional Application Consider the following...Ch. 8 - What is the velocity of a 900-kg car initially...Ch. 8 - A 1.80-kg falcon catches a 0.650-kg dove from...Ch. 8 - Two identical objects (such as billiard balls)...Ch. 8 - Professional Application Two manned satellites...Ch. 8 - A 70.0-kg ice hockey goalie, originally at rest,...Ch. 8 - A 0.240-kg billiard ball that is moving at 3.00...Ch. 8 - During an ice show, a 60.0-kg skater leaps into...Ch. 8 - Professional Application Using mass and speed data...Ch. 8 - A battleship that is 6.00*10' kg and is originally...Ch. 8 - Professional Application Two manned satellites...Ch. 8 - Professional Application A 30,000-kg freight car...Ch. 8 - Professional Application Space probes may be...Ch. 8 - A 0.0250-kg bullet is accelerated from rest to a...Ch. 8 - Professional Application One of the waste products...Ch. 8 - Professional Application The Moon's craters are...Ch. 8 - Professional Application Two football players...Ch. 8 - What is the speed of a garbage truck that is...Ch. 8 - During a circus act, an elderly performer thrills...Ch. 8 - (a) During an ice skating performance, an...Ch. 8 - Two identical pucks collide on an air hockey...Ch. 8 - Confirm that the results of the example Example...Ch. 8 - A 3000-kg cannon is mounted so that it can recoil...Ch. 8 - Professional Application A 5.50-kg bowling ball...Ch. 8 - Professional Application Ernest Rutherford (the...Ch. 8 - Professional Application Two cars collide at an...Ch. 8 - Starting with equations m1v1=m1v1cos1+m2v2cos2 and...Ch. 8 - Integrated Concepts A 90.0-kg ice hockey player...Ch. 8 - Professional Application Antiballistic missiles...Ch. 8 - Professional Application What is the acceleration...Ch. 8 - Professional Application Calculate the increase in...Ch. 8 - Professional Application Ion-propulsion rockets...Ch. 8 - Derive the equation for the vertical acceleration...Ch. 8 - Professional Application (a) Calculate the maximum...Ch. 8 - Given the following data for a fire...Ch. 8 - How much of a single-stage rocket that is 100,000...Ch. 8 - Professional Application (a) A 5.00-kg squid...Ch. 8 - Unreasonable Results Squids have been reported to...Ch. 8 - Construct Your Own Problem Consider an astronaut...Ch. 8 - Construct Your Own Problem Consider an artillery...
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