EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 8220100546310
Author: Jewett
Publisher: CENGAGE L
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Chapter 9, Problem 9.95CP
On a horizontal air track, a glider of mass m carries a Γ-shaped post. The post supports a small dense sphere, also of mass m, hanging just above the top of the glider on a cord of length L. The glider and sphere are initially at rest with the cord vertical. A constant horizontal force of magnitude F is applied to the glider, moving it through displacement x1; then the force is removed. During the time interval when the force is applied, the sphere moves through a displacement with horizontal component x2. (a) Find the horizontal component of the velocity of the center of mass of the glider–sphere system when the force is removed. (b) After the force is removed, the glider continues to move on the track and the sphere swings back and forth, both without friction. Find an expression for the largest angle the cord makes with the vertical.
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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
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
Ch. 9 - Two objects have equal kinetic energies. How do...Ch. 9 - Your physical education teacher throws a baseball...Ch. 9 - Two objects are at rest on a frictionless surface....Ch. 9 - Rank an automobile dashboard, seat belt, and air...Ch. 9 - In a perfectly inelastic one-dimensional collision...Ch. 9 - A table-tennis ball is thrown at a stationary...Ch. 9 - A baseball bat of uniform density is cut at the...Ch. 9 - A cruise ship is moving at constant speed through...Ch. 9 - You are standing on a saucer-shaped sled at rest...Ch. 9 - Prob. 9.2OQ
Ch. 9 - A massive tractor is rolling down a country road....Ch. 9 - A 2-kg object moving to the right with a speed of...Ch. 9 - A 5-kg cart moving to the right with a speed of 6...Ch. 9 - A 57.0-g tennis ball is traveling straight at a...Ch. 9 - The momentum of an object is increased by a factor...Ch. 9 - The kinetic energy of an object is increased by a...Ch. 9 - If two particles have equal momenta, are their...Ch. 9 - If two particles have equal kinetic energies, are...Ch. 9 - A 10.0-g bullet is fired into a 200-g block of...Ch. 9 - Two particles of different mass start from rest....Ch. 9 - Two particles of different mass start from rest....Ch. 9 - A basketball is tossed up into the air, falls...Ch. 9 - A 3-kg object moving to the right on a...Ch. 9 - A ball is suspended by a string that is tied to a...Ch. 9 - A car of mass m traveling at speed v crashes into...Ch. 9 - A head-on, elastic collision occurs between two...Ch. 9 - An airbag in an automobile inflates when a...Ch. 9 - In golf, novice players are often advised to be...Ch. 9 - An open box slides across a frictionless, icy...Ch. 9 - While in motion, a pitched baseball carries...Ch. 9 - Prob. 9.5CQCh. 9 - A sharpshooter fires a rifle while standing with...Ch. 9 - Two students hold a large bed sheet vertically...Ch. 9 - A juggler juggles three balls in a continuous...Ch. 9 - (a) Does the center of mass of a rocket in free...Ch. 9 - On the subject of the following positions, state...Ch. 9 - Prob. 9.11CQCh. 9 - Prob. 9.12CQCh. 9 - A bomb, initially at rest, explodes into several...Ch. 9 - A particle of mass m moves with momentum of...Ch. 9 - An object has a kinetic energy of 275 J and a...Ch. 9 - At one instant, a 17.5-kg sled is moving over a...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 45.0-kg girl is standing on a 150-kg plank. Both...Ch. 9 - A girl of mass mg is standing on a plank of mass...Ch. 9 - A 65.0-kg boy and his 40.0-kg sister, both wearing...Ch. 9 - In research in cardiology and exercise physiology,...Ch. 9 - When you jump straight up as high as you can, what...Ch. 9 - Two blocks of masses m and 3m are placed on a...Ch. 9 - A man claims that he can hold onto a 12.0-kg child...Ch. 9 - An estimated force-time curve for a baseball...Ch. 9 - Review. After a 0.300-kg rubber ball is dropped...Ch. 9 - A glider of mass m is free to slide along a...Ch. 9 - In a slow-pitch softball game, a 0.200-kg softball...Ch. 9 - The front 1.20 m of a 1 400-kg car Ls designed as...Ch. 9 - A tennis player receives a shot with the ball...Ch. 9 - The magnitude of the net force exerted in the x...Ch. 9 - Review. A force platform is a tool used to analyze...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 10.0-g bullet is fired into a stationary block...Ch. 9 - A car of mass m moving at a speed v1 collides and...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 neutron in a nuclear reactor makes an elastic,...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 - As shown in Figure P9.30, a bullet of mass m and...Ch. 9 - A 12.0-g wad of sticky clay is hurled horizontally...Ch. 9 - A wad of sticky clay of mass m is hurled...Ch. 9 - Prob. 9.33PCh. 9 - (a) Three carts of masses m1 = 4.00 kg, m2 = 10.0...Ch. 9 - A 0.300-kg puck, initially at rest on a...Ch. 9 - Prob. 9.36PCh. 9 - An object of mass 3.00 kg, moving with an initial...Ch. 9 - Two shuffleboard disks of equal mass, one orange...Ch. 9 - Two shuffleboard disks of equal mass, one orange...Ch. 9 - A proton, moving with a velocity of vii, collides...Ch. 9 - A billiard ball moving at 5.00 m/s strikes a...Ch. 9 - A 90.0-kg fullback running east with a speed of...Ch. 9 - An unstable atomic nucleus of mass 17.0 10-27 kg...Ch. 9 - The mass of the blue puck in Figure P9.44 is 20.0%...Ch. 9 - Prob. 9.45PCh. 9 - The mass of the Earth is 5.97 1024 kg, and the...Ch. 9 - Explorers in the jungle find an ancient monument...Ch. 9 - A uniform piece of sheet metal is shaped as shown...Ch. 9 - A rod of length 30.0 cm has linear density (mass...Ch. 9 - A water molecule consists of an oxygen atom with...Ch. 9 - A 2.00-kg particle has a velocity (2.00. 3.00)...Ch. 9 - Consider a system of two particles in the xy...Ch. 9 - Romeo (77.0 kg) entertains Juliet (55.0 kg) by...Ch. 9 - The vector position of a 3.50-g particle moving in...Ch. 9 - A ball of mass 0.200 kg with a velocity of 1.50...Ch. 9 - Prob. 9.56PCh. 9 - A particle is suspended from a post on top of a...Ch. 9 - A 60.0-kg person bends his knees and then jumps...Ch. 9 - Figure P9.59a shows an overhead view of the...Ch. 9 - A model rocket engine has an average thrust of...Ch. 9 - A garden hose is held as shown in Figure P9.32....Ch. 9 - Review. The first stage of a Saturn V space...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 - Prob. 9.65APCh. 9 - An amateur skater of mass M is trapped in the...Ch. 9 - A 3.00-kg steel ball strikes a wall with a speed...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 particles with masses m and 3m are moving...Ch. 9 - Pursued by ferocious wolves, you are in a sleigh...Ch. 9 - Two gliders are set in motion on a horizontal air...Ch. 9 - Why is the following situation impossible? An...Ch. 9 - Two blocks of masses m1 = 2.00 kg and m2 = 4.00 kg...Ch. 9 - Prob. 9.78APCh. 9 - A 0.400-kg blue bead slides on a frictionless,...Ch. 9 - A small block of mass mt = 0.500 kg is released...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 - A 75.0-kg firefighter slides down a pole while a...Ch. 9 - George of the Jungle, will mass m, swings on a...Ch. 9 - Review. A student performs a ballistic pendulum...Ch. 9 - Review. A light spring of force constant 3.85 N/m...Ch. 9 - Prob. 9.88APCh. 9 - A 5.00-g bullet moving with an initial speed of i...Ch. 9 - Review. There are (one can say) three coequal...Ch. 9 - A 2.00-g particle moving at 8.00 m/s makes a...Ch. 9 - Prob. 9.92CPCh. 9 - Two particles with masses m and 3m are moving...Ch. 9 - Sand from a stationary hopper falls onto a moving...Ch. 9 - On a horizontal air track, a glider of mass m...Ch. 9 - Review. A chain of length L and total mass M is...
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