A force field F moves a particle with mass m > 0 along a trajectory C in space parametrized by r(t) with a
A force field F moves a particle with mass m > 0 along a trajectory C in space parametrized by r(t) with a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![A force field F moves a particle with mass m > 0 along a trajectory C in space parametrized by r(t) with a <t<b
according to Newton's second law of motion
F(r(t)) = mr" (t).
Show that the work done by F in moving the particle along C from r(a) to r(b) is the change in the kinetic energy of
the particle:
1
F - dr = =m|r (b)f² – -
m|r' (a)[².
Hint: Use the product rule for dot products of vector-valued functions
[u(t) · v(t)] = u'(t) · v(t) + u(t) · v' (t).
dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32ac3e12-ae1c-4f9c-8855-d6c71d330ed6%2Ff8158424-c8b3-4ba0-b25a-4640f2fbc49f%2Ffqi60h_processed.png&w=3840&q=75)
Transcribed Image Text:A force field F moves a particle with mass m > 0 along a trajectory C in space parametrized by r(t) with a <t<b
according to Newton's second law of motion
F(r(t)) = mr" (t).
Show that the work done by F in moving the particle along C from r(a) to r(b) is the change in the kinetic energy of
the particle:
1
F - dr = =m|r (b)f² – -
m|r' (a)[².
Hint: Use the product rule for dot products of vector-valued functions
[u(t) · v(t)] = u'(t) · v(t) + u(t) · v' (t).
dt
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