Physics for Scientists and Engineers
9th Edition
ISBN: 9781133947271
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 8, Problem 8.52AP
Jonathan is riding a bicycle and encounters a hill of height h. At the base of the hill, he is traveling at a speed vi. When he reaches the top of the hill, he is traveling at a speed vf. Jonathan and his bicycle together have a mass m. Ignore friction in the bicycle mechanism and between the bicycle tires and the road. (a) What is the total external work done on the system of Jonathan and the bicycle between the time he starts up the hill and the time he reaches the top? (b) What is the change in potential energy stored in Jonathan’s body during this process? (c) How much work does Jonathan do on the bicycle pedals within the Jonathan–bicycle–Earth system during this process?
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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)
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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
Physics for Scientists and Engineers
Ch. 8 - By what transfer mechanisms does energy enter and...Ch. 8 - Consider a block sliding over a horizontal surface...Ch. 8 - A rock of mass m is dropped to the ground from a...Ch. 8 - Three identical balls are thrown from the top of a...Ch. 8 - You are traveling along a freeway at 65 mi/h. Your...Ch. 8 - You hold a slingshot at arms length, pull the...Ch. 8 - Two children stand on a platform at the top of a...Ch. 8 - At the bottom of an air track tilted at angle , a...Ch. 8 - An athlete jumping vertically on a trampoline...Ch. 8 - Answer yes or no to each of the following...
Ch. 8 - In a laboratory model of cars skidding to a stop,...Ch. 8 - What average power is generated by a 70.0-kg...Ch. 8 - A ball of clay falls freely to the hard floor. It...Ch. 8 - A pile driver drives posts into the ground by...Ch. 8 - One person drops a ball from the top of a building...Ch. 8 - A car salesperson claims that a 300-hp engine is a...Ch. 8 - Prob. 8.3CQCh. 8 - Prob. 8.4CQCh. 8 - Prob. 8.5CQCh. 8 - Prob. 8.6CQCh. 8 - In the general conservation of energy equation,...Ch. 8 - Consider the energy transfers and transformations...Ch. 8 - A block is connected to a spring that is suspended...Ch. 8 - In Chapter 7, the work-kinetic energy theorem, W =...Ch. 8 - For each of the following systems and time...Ch. 8 - Prob. 8.2PCh. 8 - A block of mass 0.250 kg is placed on top of a...Ch. 8 - A 20.0-kg cannonball is fired from a cannon with...Ch. 8 - cal energy of the ballEarth sys-tem at the maximum...Ch. 8 - A block of mass m = 5.00 kg is released from point...Ch. 8 - Two objects are connected by a light string...Ch. 8 - Prob. 8.8PCh. 8 - A light, rigid rod is 77.0 cm long. Its top end is...Ch. 8 - At 11:00 a.m, on September 7, 2001, more than one...Ch. 8 - Prob. 8.11PCh. 8 - A sled of mass m is given a kick on a frozen pond....Ch. 8 - A sled of mass m is given a kick on a frozen pond....Ch. 8 - A crate of mass 10.0 kg is pulled up a rough...Ch. 8 - A block of mass m = 2.(K) kg is attached to a...Ch. 8 - A 40.0-kg box initially at rest is pushed 5.00 m...Ch. 8 - A smooth circular hoop with a radius of 0.500 m is...Ch. 8 - At time ti, the kinetic energy of a particle is...Ch. 8 - A boy in a wheelchair (total mass 47.0 kg) has...Ch. 8 - As shown in Figure P8.10, a green bead of mass 25...Ch. 8 - A toy cannon uses a spring to project a 5.30-g...Ch. 8 - The coefficient of friction between the block of...Ch. 8 - A 5.00-kg block is set into motion up an inclined...Ch. 8 - A 1.50-kg object is held 1.20 m above a relaxed...Ch. 8 - A 200-g block is pressed against a spring of force...Ch. 8 - An 80.0-kg skydiver jumps out of a balloon at an...Ch. 8 - Prob. 8.27PCh. 8 - Sewage at a certain pumping station is raised...Ch. 8 - An 820-N Marine in basic training climbs a 12.0-m...Ch. 8 - The electric motor of a model train accelerates...Ch. 8 - When an automobile moves with constant speed down...Ch. 8 - Prob. 8.32PCh. 8 - An energy-efficient lightbulb, taking in 28.0 W of...Ch. 8 - An electric scooter has a battery capable of...Ch. 8 - Make an order-of-magnitude estimate of the power a...Ch. 8 - An older-model car accelerates from 0 to speed v...Ch. 8 - For saving energy, bicycling and walking are far...Ch. 8 - A 650-kg elevator starts from rest. It moves...Ch. 8 - Prob. 8.39PCh. 8 - Energy is conventionally measured in Calories as...Ch. 8 - A loaded ore car has a mass of 950 kg and rolls on...Ch. 8 - Make an order-of-magnitude estimate of your power...Ch. 8 - A small block of mass m = 200 g is released from...Ch. 8 - Prob. 8.44APCh. 8 - Review. A boy starts at rest and slides down a...Ch. 8 - Review. As shown in Figure P8.26, a light string...Ch. 8 - A 4.00-kg particle moves along the x axis. Its...Ch. 8 - Why is the following situation impossible? A...Ch. 8 - A skateboarder with his board can be modeled as a...Ch. 8 - Heedless of danger, a child leaps onto a pile of...Ch. 8 - Jonathan is riding a bicycle and encounters a hill...Ch. 8 - Jonathan is riding a bicycle and encounters a hill...Ch. 8 - Consider the blockspringsurface system in part (B)...Ch. 8 - As it plows a parking lot, a snowplow pushes an...Ch. 8 - Prob. 8.55APCh. 8 - Prob. 8.56APCh. 8 - As the driver steps on the gas pedal, a car of...Ch. 8 - Review. Why is the following situation impossible?...Ch. 8 - A horizontal spring attached to a wall has a force...Ch. 8 - More than 2 300 years ago, the Greek teacher...Ch. 8 - A child's pogo stick (Fig. P8.61) stores energy in...Ch. 8 - A 1.00-kg object slides to the right on a surface...Ch. 8 - A 10.0-kg block is released from rest at point in...Ch. 8 - Prob. 8.64APCh. 8 - A block of mass 0.500 kg is pushed against a...Ch. 8 - Review. As a prank, someone has balanced a pumpkin...Ch. 8 - Review. The mass of a car is 1 500 kg. The shape...Ch. 8 - A pendulum, comprising a light string of length L...Ch. 8 - A block of mass M rests on a table. It is fastened...Ch. 8 - Review. 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