Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 6, Problem 28E
To determine
To find: How much work is done in accelerating a particle from rest to some final speed (W).
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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
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 6 Solutions
Essential University Physics (3rd Edition)
Ch. 6.2 - Two objects are each displaced the same distance,...Ch. 6.3 - Three forces have magnitudes in newtons that are...Ch. 6.4 - For each situation, tell whether the net work done...Ch. 6.5 - Prob. 6.4GICh. 6 - Give two examples of situations in which you might...Ch. 6 - If the scalar product of two nonzero vectors is...Ch. 6 - Must you do work to whirl a ball around on the end...Ch. 6 - If you pick up a suitcase and put it down, how...Ch. 6 - You want to raise a piano a given height using a...Ch. 6 - Does the gravitational force of the Sun do work on...
Ch. 6 - A pendulum bob swings back and forth on the end of...Ch. 6 - Does your cars kinetic energy change if you drive...Ch. 6 - A watt-second is a unit of what quantity? Relate...Ch. 6 - A truck is moving northward at 55 mi/h. Later, its...Ch. 6 - Is it possible for you to do work on an object...Ch. 6 - How much work do you do as you exert a 75-N force...Ch. 6 - If the coefficient of kinetic friction is 0.21,...Ch. 6 - A crane lifts a 650-kg beam vertically upward 23 m...Ch. 6 - The worlds highest waterfall, the Cherun-Meru in...Ch. 6 - A meteorite plunges to Earth, embedding itself 75...Ch. 6 - An elevator of mass m rises a vertical distance h...Ch. 6 - Show that the scalar product obeys the...Ch. 6 - Find the work done by a force F = 1.8 + 2.2 N as...Ch. 6 - To push a stalled car, you apply a 470-N force at...Ch. 6 - Find the total work done by the force shown in...Ch. 6 - How much work does it take to stretch a spring...Ch. 6 - Uncompressed, the spring for an automobile...Ch. 6 - You do 8.5 J of work to stretch a spring with k =...Ch. 6 - Spider silk is a remarkable elastic material. A...Ch. 6 - Whats the kinetic energy of a 2.4105-kg airplane...Ch. 6 - Prob. 28ECh. 6 - At what speed must a 950-kg subcompact car be...Ch. 6 - A 60-kg skateboarder comes over the top of a hill...Ch. 6 - After a tornado, a 0.50-g drinking straw was found...Ch. 6 - From what height would you have to drop a car for...Ch. 6 - A typical human diet is 2000 calories per day,...Ch. 6 - A horse plows a 200-m-long furrow in 5.0 min,...Ch. 6 - A typical car battery stores about 1 kWh of...Ch. 6 - A sprinter completes a 100-m dash in 10.6 s. doing...Ch. 6 - How much work can a 3.5-hp lawnmower engine do in...Ch. 6 - A 75-kg long-jumper takes 3.1 s to reach a prejump...Ch. 6 - Estimate your power output as you do deep knee...Ch. 6 - In midday sunshine, solar energy strikes Earth at...Ch. 6 - It takes about 20 kJ to melt an ice cube. A...Ch. 6 - Prob. 42ECh. 6 - You slide a box of books at constant speed up a 30...Ch. 6 - Two people push a stalled car at its front doors,...Ch. 6 - Youre at the gym, doing arm raises. With each rep....Ch. 6 - A locomotive does 7.9 1011 J of work in pulling a...Ch. 6 - You pull a box 23 in horizontally, using the rope...Ch. 6 - Prob. 48PCh. 6 - (a) Find the scalar product of the vectors a + b...Ch. 6 - Looking to cut costs, the airline you work for...Ch. 6 - How much work does a force F = 67 + 23 + 55k N do...Ch. 6 - A force F Facts in the x-direction, its magnitude...Ch. 6 - A certain amount of work is required to stretch...Ch. 6 - A force with magnitude F = a x acts in the...Ch. 6 - The force exerted by a rubber band is given...Ch. 6 - You put your little sister (mass m) on a swing...Ch. 6 - Two unknown elementary particles pass through a...Ch. 6 - A tractor tows a plane from its airport gate,...Ch. 6 - E. coli bacteria swim by means of flagella that...Ch. 6 - On February 15, 2013, an asteroid moving at 19...Ch. 6 - An elevator ascends from the ground floor to the...Ch. 6 - Youre asked to assess the reliability of a nuclear...Ch. 6 - A force pointing in the x-direction is given by F...Ch. 6 - A force pointing in the x-direction is given by F...Ch. 6 - Two vectors have equal magnitude, and their scalar...Ch. 6 - At what rate can a half-horsepower well pump...Ch. 6 - The rate at which the United States imports oil,...Ch. 6 - By measuring oxygen uptake, sports physiologists...Ch. 6 - Youre writing performance specifications for a new...Ch. 6 - A 1400-kg car ascends a mountain road at a steady...Ch. 6 - You do 2.2 kJ of work pushing a 78-kg trunk at...Ch. 6 - (a) Find the work done in lifting 1 L of blood...Ch. 6 - (a) What power is needed to push a 95-kg crate at...Ch. 6 - You mix flour into bread dough, exerting a 45-N...Ch. 6 - A machine does work at a rate given by P = ct2,...Ch. 6 - A typical bumblebee has mass 0.25 mg. It beats its...Ch. 6 - Youre trying to decide whether to buy an...Ch. 6 - Your friend does five reps with a barbell, on each...Ch. 6 - A machine delivers power at a decreasing rate P =...Ch. 6 - A locomotive accelerates a freight train of total...Ch. 6 - A force given by F = b/x acts in the x-direction,...Ch. 6 - Youre assisting a cardiologist in planning a...Ch. 6 - Youre an engineer for a company that makes...Ch. 6 - You push an object of mass m slowly, partway up a...Ch. 6 - A particle moves from the origin to the point x =...Ch. 6 - Repeat Problem 85 for the following cases: (a) the...Ch. 6 - The worlds fastest elevator, in Taiwans Taipei 101...Ch. 6 - An experimental measurement of the force required...Ch. 6 - Youre an expert witness in a medical malpractice...Ch. 6 - The energy in a batted baseball comes from the...Ch. 6 - The energy in a batted baseball comes from the...Ch. 6 - The energy in a batted baseball comes from the...Ch. 6 - The energy in a batted baseball comes from the...
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