University Physics Volume 1
18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: OpenStax - Rice University
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Chapter 9, Problem 39P
A 4.5 kg puffer fish expands to
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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 9 Solutions
University Physics Volume 1
Ch. 9 - Check Your Understanding The U.S. Air Force uses...Ch. 9 - Check Your Understanding What if we had assumed...Ch. 9 - Check Your Understanding Suppose the second,...Ch. 9 - Check Your Understanding Would the ball’s change...Ch. 9 - Check Your Understanding Even if there were some...Ch. 9 - Check Your Understanding The changes of momentum...Ch. 9 - Check Your Understanding There is a second...Ch. 9 - Check Your Understanding Suppose there had been no...Ch. 9 - Check Your Understanding Suppose the initial...Ch. 9 - Check Your Understanding Notice that the mass of...
Ch. 9 - Check Your Understanding Suppose we included the...Ch. 9 - Check Your Understanding Suppose you have a...Ch. 9 - Check Your Understanding How would the firework...Ch. 9 - Check Your Understanding What is the physical...Ch. 9 - An object that has a small mass and an object that...Ch. 9 - An object that has a small mass and an object that...Ch. 9 - Is it possible for a small force to produce a...Ch. 9 - Why is a 10-m fall onto concrete far more...Ch. 9 - What external force is responsible for changing...Ch. 9 - A piece of putty and a tennis ball with the same...Ch. 9 - Under what circumstances is momentum conserved?Ch. 9 - Can momentum be conserved for a system if there...Ch. 9 - Explain in terms of momentum and Newton’s laws how...Ch. 9 - Can objects in a system have momentum while the...Ch. 9 - A sprinter accelerates out of the starting blocks....Ch. 9 - A rocket in deep space (zero gravity) accelerates...Ch. 9 - Two objects of equal mass are moving with equal...Ch. 9 - Describe a system for which momentum is conserved...Ch. 9 - Momentum for a system can be conserved in one...Ch. 9 - Suppose a fireworks shell explodes, breaking into...Ch. 9 - It is possible for the velocity of a rocket to be...Ch. 9 - An elephant and a hunter are having a...Ch. 9 - A skater of mass 40 kg is carrying a box of mass 5...Ch. 9 - A car of mass 2000 kg is moving with a constant...Ch. 9 - The mass of Earth is 5.971024kg and its orbital...Ch. 9 - If a rainstorm drops 1 cm of rain over an area of...Ch. 9 - What is the average momentum of an avalanche that...Ch. 9 - What is the average momentum of a 70.0-kg sprinter...Ch. 9 - A 75.0-kg person is riding in a car moving at 20.0...Ch. 9 - One hazard of space travel is debris left by...Ch. 9 - A cruise ship with a mass of 1.00107kg strikes a...Ch. 9 - Calculate the final speed of a 110-kg rugby player...Ch. 9 - Water from a fire hose is directed horizontally...Ch. 9 - A 0.450-kg hammer is moving horizontally at 7.00...Ch. 9 - Prob. 31PCh. 9 - The x-component of a force on a 46-g golf ball by...Ch. 9 - A hockey puck of mass 150 g is sliding due east on...Ch. 9 - A ball of mass 250 g is thrown with an initial...Ch. 9 - Prob. 35PCh. 9 - Two identical pucks collide elastically on an air...Ch. 9 - The figure below shows a bullet of mass 200 g...Ch. 9 - A 20-kg child is coasting at 3.3 m/s over flat...Ch. 9 - A 4.5 kg puffer fish expands to 40 of its mass by...Ch. 9 - Explain why a cannon recoils when it fires a...Ch. 9 - Two figure skaters are coasting in the same...Ch. 9 - A 2000-kg railway freight car coasts at 4.4 m/s...Ch. 9 - A 5.50-kg bowling ball moving at 9.00 m/s collides...Ch. 9 - Ernest Rutherford (the first New Zealander to be...Ch. 9 - A 90.0-kg ice hockey player hits a 0.150-kg puck,...Ch. 9 - A 100-g firecracker is launched vertically into...Ch. 9 - In an elastic collision, a 400-kg bumper car...Ch. 9 - Repeat the preceding problem if the mass of the...Ch. 9 - An alpha particle (4He) undergoes an elastic...Ch. 9 - You are standing on a very slippery icy surface...Ch. 9 - A 35-kg child rides a relatively massless sled...Ch. 9 - A boy sleds down a hill and onto a frictionless...Ch. 9 - Prob. 53PCh. 9 - A billiard ball, labeled 1, moving horizontally...Ch. 9 - A projectile of mass 2.0 kg is fired in the air at...Ch. 9 - Two asteroids collide and stick together. The...Ch. 9 - Prob. 57PCh. 9 - A proton traveling at 3.0106m/s scatters...Ch. 9 - Prob. 59PCh. 9 - A family is skating. The father (75 kg) skates at...Ch. 9 - Prob. 61PCh. 9 - Two cars of the same mass approach an extremely...Ch. 9 - Three point masses are placed at the corners of a...Ch. 9 - Two particles of masses m1 and m2 separated by a...Ch. 9 - Two particles of masses m1 and m2 separated by a...Ch. 9 - Two particles of masses m1 and m2 , move uniformly...Ch. 9 - Two particles of masses m1 and m2 move uniformly...Ch. 9 - Find the center of mass of a one-meter long rod,...Ch. 9 - Find the center of mass of a rod of length L whose...Ch. 9 - Find the center of mass of a rectangular block of...Ch. 9 - Find the center of mass of a rectangular material...Ch. 9 - A cube of side a is cut out of another cube of...Ch. 9 - Find the center of mass of a cone of uniform...Ch. 9 - Find the center of mass of a thin wire of mass in...Ch. 9 - Find the center of mass of a uniform thin...Ch. 9 - Find the center of mass of a sphere of mass M and...Ch. 9 - (a) A 5.00-kg squid initially at rest ejects 0.250...Ch. 9 - A rocket takes off from Earth and reaches a speed...Ch. 9 - Repeat the preceding problem but for a rocket that...Ch. 9 - How much fuel would be needed for a 1000-kg rocket...Ch. 9 - What exhaust speed is required to accelerate a...Ch. 9 - Unreasonable Results Squids have been reported to...Ch. 9 - Two 70-kg canoers paddle in a single, 50-kg canoe....Ch. 9 - Which has a larger magnitude of momentum: a...Ch. 9 - A driver applies the brakes and reduces the speed...Ch. 9 - You friend claims that momentum is mass multiplied...Ch. 9 - Dropping a glass on a cement floor is more likely...Ch. 9 - Your 1500-kg sports car accelerates from 0 to 30...Ch. 9 - A ball of mass m is dropped. What is the formula...Ch. 9 - Repeat the preceding problem, but including a drag...Ch. 9 - A 5.0-g egg falls from a 90-cm-high counter onto...Ch. 9 - A car crashes into a large tree that does not...Ch. 9 - Two hockey players approach each other head on,...Ch. 9 - You are coasting on your 10-kg bicycle at 15 m/s...Ch. 9 - A load of gravel is dumped straight down into a...Ch. 9 - Two carts on a straight track collide head on. The...Ch. 9 - A 100-kg astronaut finds himself separated from...Ch. 9 - Derive the equations giving the final speeds for...Ch. 9 - Repeat the preceding problem for the case when the...Ch. 9 - A child sleds down a hill and collides at 5.6 m/s...Ch. 9 - For the preceding problem, find the final speed of...Ch. 9 - A 90-kg football player jumps vertically into the...Ch. 9 - Three skydivers are plummeting earthward. They are...Ch. 9 - Two billiard balls are at rest and touching each...Ch. 9 - Prob. 105APCh. 9 - Prob. 106APCh. 9 - Repeat the preceding problem if the balls collide...Ch. 9 - Repeat the preceding problem if the balls collide...Ch. 9 - Where is the center of mass of a semicircular wire...Ch. 9 - Where is the center of mass of a slice of pizza...Ch. 9 - If 1 of the Earth’s mass were transferred to the...Ch. 9 - You friend wonders how a rocket continues to climb...Ch. 9 - To increase the acceleration of a rocket, should...Ch. 9 - A 65-kg person jumps from the first floor window...Ch. 9 - Two projectiles of mass m1 and m2 , are fired at...Ch. 9 - Two identical objects (such as billiard balls)...Ch. 9 - A ramp of mass M is at rest on a horizontal...Ch. 9 - Find the center of mass of the structure given in...
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