College Physics
OER 2016 Edition
ISBN: 9781947172173
Author: OpenStax
Publisher: OpenStax College
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Textbook Question
Chapter 3, Problem 10PE
Find the magnitudes of velocity vAand vBin figure 3.57
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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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0
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(a) Show that the total force acting on the particle is
X
F-mg k-2kz 1
(1.
l
k.
(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.
1.77
v
(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 3 Solutions
College Physics
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