Vector Analysis 600321
Review 3
(1) Evaluate the line integral C F dR where F = 3y i + 2x j + 4z k and C is the line
segment from (0, 0, 0) to (1, 1, 2).
Solution: The line segment is given by R = t i + t j + 2t k, 0 t 1. Then
1
F dR =
C
1
(3t i + 2t j +
Vector Analysis 600321, Test 2
(1) The motion of a particle in polar coordinates is given by r = 3, = t2 . Find the
velocity v and the acceleration a in terms of ur , u , and use this to determine the
magnitudes of v and a.
Solution: Using equations (2.50
Vector Analysis 600321
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
Review 2
The motion of a particle in polar coordinates is given by r = 2 + sin t, = t. Find
the decomposition of the velocity and acceleration at t = /6 in terms of ur , u .
Represent the decompos
Name:
Vector Analysis 600321, Test 1
(1) Three masses with weights 1g , 2g , 4g are placed at P1 (2, 2, 0), P2 (1, 2, 3) and
P3 (4, 1, 0), respectively. Where do you have to place a fourth mass with weight 5g
such that the center of mass of all four point
Vector Analysis 600321
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(2)
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(6)
Review 1
A rst particle is located at P1 (2, 1, 1) with mass m1 = 3g , a second particle
is located at P2 (0, 3, 0) with mass m2 = 2g , and a third particle is located at
P3 (5, 1, 1) with mass m3 = 5g . Find
Vector Analysis 600321
Homework 3, due April 30, 2002
1. Evaluate the line integral C F dR, where F = xy i + x2 j and C is the
triangle with vertices (0, 0), (1, 0), (0, 1) taken in the counterclockwise
sense.
1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
Solutio
Vector Analysis 600321
Homework 2, due March 26, 2002
1. A particle moves so that its position (r, ) in polar coordinates is given by r = t2 ,
= t.
Express its velocity v and its acceleration a in terms of ur and u . Find the points
on the spiral at whic
Vector Analysis 600321
Homework 1, due February 12, 2002
1. A molecule of methane, CH4 , is structured with the four hydrogen atoms at the
vertices A(1, 0, 0), B (0, 1, 0), C (0, 0, 1), D(1, 1, 1) of a regular tetrahedron and the
carbon atom at the centro