Life in the Universe (4th Edition)
4th Edition
ISBN: 9780134089089
Author: Jeffrey O. Bennett, Seth Shostak
Publisher: PEARSON
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Chapter 4, Problem 29TYU
We can learn a lot about Earth’s early history by studying the Moon.
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Portfolio Problem 4. Consider two identical springs, each with natural length
and spring constant k, attached to a horizontal frame at distance 2l apart. Their
free ends are attached to the same particle of mass m, which is hanging under
gravity. Let z denote the vertical displacement of the particle from the hori-
zontal frame, so that z < 0 when the particle is below the frame, as shown in
the figure. The particle has zero horizontal velocity, so that the motion is one
dimensional along z.
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(a) Show that the total force acting on the particle is
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(b) Find the potential energy U(x, y, z) of the system such that U
x = : 0.
= O when
(c) The particle is pulled down until the springs are each of length 3l, and then
released. Find the velocity of the particle when it crosses z = 0.
In the figure below, a semicircular conductor of radius R = 0.260 m is rotated about the axis AC at a constant rate of 130 rev/min. A uniform magnetic field of magnitude 1.22 T fills the entire region below the axis and is directed out of the page.
R
Pout
(a) Calculate the maximum value of the emf induced between the ends of the conductor.
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(b) What is the value of the average induced emf for each complete rotation?
0
v
(c) How would your answers to parts (a) and (b) change if the magnetic field were allowed to extend a distance R above the axis of rotation? (Select all that apply.)
The value in part (a) would increase.
The value in part (a) would remain the same.
The value in part (a) would decrease.
The value in part (b) would increase.
The value in part (b) would remain the same.
The value in part (b) would decrease.
×
(d) Sketch the emf versus time when the field is as drawn in the figure. Choose File No file chosen
This answer has not been graded yet.
(e) Sketch the emf…
Portfolio Problem 2. A particle of mass m slides in a straight line (say along i)
on a surface, with initial position x ©0 and initial velocity Vo > 0 at t = 0. The
=
particle is subject to a constant force F = -mai, with a > 0.
While sliding on the surface, the particle is also subject to a friction force
v
Ff
= -m fo
= −m fov,
with fo > 0, i.e., the friction force has constant magnitude mfo and is always
opposed to the motion. We also assume fo 0, and solve it to find v(t) and x(t).
How long does it take for the particle to come to a stop? How far does it travel?
(b) After coming to a stop, the particle starts sliding backwards with negative
velocity. Write the equation of motion in this case, and solve it to find the time
at which the particle returns to the original position, x = 0. Show that the final
speed at x 0 is smaller than Vo.
=
Express all your answers in terms of a, fo and Vo.
Chapter 4 Solutions
Life in the Universe (4th Edition)
Ch. 4 - Briefly describe three aspects of geology that are...Ch. 4 - What do we mean by the geological record? Why is...Ch. 4 - Describe the three basic types of rock and the...Ch. 4 - How are sedimentary strata made, and how do they...Ch. 4 - Describe the technique of radiometric dating, and...Ch. 4 - How do fossils form? Do most living organisms...Ch. 4 - Summarize the geological time scale. What are...Ch. 4 - Prob. 8RQCh. 4 - Briefly describe how outgassing led to the origin...Ch. 4 - What was the heavy bombardment, and what effect...
Ch. 4 - Briefly describe Earths core-mantle-crust...Ch. 4 - Briefly describe the conveyorlike action of plate...Ch. 4 - Describe how plate tectonics shapes important...Ch. 4 - What evidence do we have for the operation of...Ch. 4 - What are the three requirements for a planetary...Ch. 4 - Briefly describe the mechanism by which the...Ch. 4 - What has happened to most of the carbon dioxide...Ch. 4 - What are ice ages, and what may cause them? What...Ch. 4 - Briefly summarize the key ways in which geology is...Ch. 4 - How do we think the Moon formed, and what evidence...Ch. 4 - We can expect that if there are paleontologists a...Ch. 4 - Nearly all the rocks I found in the lava fields of...Ch. 4 - Prob. 23TYUCh. 4 - Although Earth contains its densest material in...Ch. 4 - If you had a time machine that dropped you off on...Ch. 4 - If there were no plate tectonics on Earth, our...Ch. 4 - Without the greenhouse effect, there probably...Ch. 4 - If nitrogen were a greenhouse gas, our planet...Ch. 4 - We can learn a lot about Earths early history by...Ch. 4 - Prob. 30TYUCh. 4 - A rocks type (igneous, metamorphic, or...Ch. 4 - To learn a rocks age, we must (a) determine its...Ch. 4 - Radiometric dating now allows us to determine...Ch. 4 - Earths oceans formed (a) during the late stages of...Ch. 4 - We learn about the heavy bombardment by studying...Ch. 4 - Earth has retained a lot of internal heat...Ch. 4 - Plate tectonics is best described as a process...Ch. 4 - Earth has far less atmospheric carbon dioxide than...Ch. 4 - If Earth had more greenhouse gases in its...Ch. 4 - Snowball Earth refers to (a) one of a series of...Ch. 4 - The Age of Earth. Some people still question...Ch. 4 - Dating Planetary Surfaces. We have discussed two...Ch. 4 - Earth Without Differentiation. Suppose Earth had...Ch. 4 - Earth Without Plate Tectonics. Suppose plate...Ch. 4 - Feedback Processes in the Atmosphere. As the Sun...Ch. 4 - Geological Time. Geological time scales are often...Ch. 4 - Dating Lunar Rocks. You are analyzing Moon rocks...Ch. 4 - Carbon-14 Dating. The half-life of carbon-14 is...Ch. 4 - Martian Meteorite. Some unusual meteorites thought...Ch. 4 - Internal vs. External Heating. In daylight, Earths...Ch. 4 - Plate Tectonics. Typical motions of one plate...Ch. 4 - More Plate Tectonics. Consider a seafloor...Ch. 4 - Plate Tectonics and Us. Based on what you learned...
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