EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 9780100460300
Author: SERWAY
Publisher: YUZU
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Textbook Question
Chapter 7, Problem 7.8CQ
If only one external force acts on a particle, does it necessarily change the particle’s (a) kinetic energy? (b) Its velocity?
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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 7 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
Ch. 7 - Prob. 7.1QQCh. 7 - Figure 7.4 shows four situations in which a force...Ch. 7 - Which of the following statements is true about...Ch. 7 - A dart is inserted into a spring-loaded dart gun...Ch. 7 - A dart is inserted into a spring-loaded dart gun...Ch. 7 - Choose the correct answer. The gravitational...Ch. 7 - A ball is connected to a light spring suspended...Ch. 7 - What does the slope of a graph of U(x) versus x...Ch. 7 - Alex and John are loading identical cabinets onto...Ch. 7 - If the net work done by external forces on a...
Ch. 7 - A worker pushes a wheelbarrow with a horizontal...Ch. 7 - A cart is set rolling across a level table, at the...Ch. 7 - Prob. 7.5OQCh. 7 - Is the work required to be done by an external...Ch. 7 - A bloc k, of mass m is dropped from the fourth...Ch. 7 - An a simple pendulum swings back and forth, the...Ch. 7 - Bullet 2 has twice the mass of bullet 1. Both are...Ch. 7 - Figure OQ7.10 shows a light extended spring...Ch. 7 - If the speed of a particle is doubled, what...Ch. 7 - Prob. 7.12OQCh. 7 - Prob. 7.13OQCh. 7 - A certain spring that obeys Hookes law is...Ch. 7 - A cart is set rolling across a level table, al the...Ch. 7 - An ice cube has been given a push and slides...Ch. 7 - Can a normal force do work? If not, why not? If...Ch. 7 - Object 1 pushes on object 2 as the objects move...Ch. 7 - A student has the idea that the total work done on...Ch. 7 - (a) For what values of the angle between two...Ch. 7 - Prob. 7.5CQCh. 7 - Discuss the work done by a pitcher throwing a...Ch. 7 - Prob. 7.7CQCh. 7 - If only one external force acts on a particle,...Ch. 7 - Prob. 7.9CQCh. 7 - Prob. 7.10CQCh. 7 - A certain uniform spring has spring constant k....Ch. 7 - Prob. 7.12CQCh. 7 - Does the kinetic energy of an object depend on the...Ch. 7 - Cite two examples in which a force is exerted on...Ch. 7 - A shopper in a supermarket pushes a cart with a...Ch. 7 - A raindrop of mass 3.35 10-5 kg falls vertically...Ch. 7 - In 1990, Walter Arfeuille of Belgium lifted a...Ch. 7 - The record number of boat lifts, including the...Ch. 7 - A block of mass m = 2.50 kg is pushed a distance d...Ch. 7 - Spiderman, whose mass is 80.0 kg, is dangling on...Ch. 7 - Prob. 7.7PCh. 7 - Vector A has a magnitude of 5.00 units, and vector...Ch. 7 - Prob. 7.9PCh. 7 - Find the scalar product of the vectors in Figure...Ch. 7 - A force F = (6i 2j) N acts on a panicle that...Ch. 7 - Using the definition of the scalar product, find...Ch. 7 - Lei B = 5.00 m at 60.0. Let the vector C have the...Ch. 7 - The force acting on a panicle varies as shown in...Ch. 7 - A particle is subject to a force Fx that varies...Ch. 7 - In a control system, an accelerometer consists of...Ch. 7 - When a 4.00-kg object is hung vertically on a...Ch. 7 - Hookes law describes a certain light spring of...Ch. 7 - An archer pulls her bowstring back 0.400 m by...Ch. 7 - A light spring with spring constant 1 200 N/m is...Ch. 7 - A light spring with spring constant k1 is hung...Ch. 7 - Express the units of the force constant of a...Ch. 7 - A cafeteria tray dispenser supports a stack of...Ch. 7 - A light spring with force constant 3.85 N/m is...Ch. 7 - A small particle of mass m is pulled to the top of...Ch. 7 - The force acting on a particle is Fx = (8x 16),...Ch. 7 - When different loads hang on a spring, the spring...Ch. 7 - A 100-g bullet is fired from a rifle having a...Ch. 7 - A force F = (4xi + 3yj), where F is in newtons and...Ch. 7 - Review. The graph in Figure P7.20 specifies a...Ch. 7 - A 3.00-kg object has a velocity (6.00i - 2.00j)...Ch. 7 - Prob. 7.32PCh. 7 - A 0.600-kg particle has a speed of 2.00 m/s at...Ch. 7 - A 4.00-kg particle is subject to a net force that...Ch. 7 - A 2 100-kg pile driver is used to drive a steel...Ch. 7 - Review. In an electron microscope, there is an...Ch. 7 - Review. You can think of the workkinetic energy...Ch. 7 - Review. A 7.80-g bullet moving at 575 m/s strikes...Ch. 7 - Review. A 5.75-kg object passes through the origin...Ch. 7 - A 1 000-kg roller coaster car is initially at the...Ch. 7 - A 0.20-kg stone is held 1.3 m above the top edge...Ch. 7 - A 400-N child is in a swing that is attached to a...Ch. 7 - A 4.00-kg particle moves from the origin to...Ch. 7 - (a) Suppose a constant force acts on an object....Ch. 7 - A force acting on a particle moving in the xy...Ch. 7 - An object moves in the xy plane 111 Figure P7.43...Ch. 7 - Prob. 7.47PCh. 7 - Why is the following situation impossible? A...Ch. 7 - A potential energy function for a system in which...Ch. 7 - A single conservative force acting on a particle...Ch. 7 - A single conservative force acts on a 5.0-kg...Ch. 7 - For the potential energy curve shown in Figure...Ch. 7 - A right circular cone can theoretically be...Ch. 7 - The potential energy function for a system of...Ch. 7 - Prob. 7.55APCh. 7 - A particle moves along the xaxis from x = 12.8 m...Ch. 7 - Two identical steel balls, each of diameter 25.4...Ch. 7 - When an object is displaced by an amount x from...Ch. 7 - A 6 000-kg freight car rolls along rails with...Ch. 7 - Why is the following situation impossible? In a...Ch. 7 - Prob. 7.61APCh. 7 - The spring constant of an automotive suspension...Ch. 7 - An inclined plane of angle = 20.0 has a spring of...Ch. 7 - An inclined plane of angle has a spring of force...Ch. 7 - (a) Take U = 5 for a system with a particle at...Ch. 7 - A particle of mass m = 1.18 kg is attached between...Ch. 7 - Review. A light spring has unstressed length 15.5...
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