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Mechanics tutorial_1.doc
1
1.
A surveying instrument for measuring distance and angle is located at C, point A is at an
elevation of 9.2
above the horizontal plane (xy plane). The instrument has to rotate about
the vertical axis through 41
from the x direction in order to align with A. The distance from
C to A is 5005m. Corresponding values for point B are 1.3
, 73.4
and 7037m. Determine
(a) the locations of points A and B in Cartesian coordinates relative to C,
(b) the distance from A to B,
(c) the distance from A to B projected onto the horizontal plane.
ans:
(a)
(3729, 3241, 800.2)m,(2010, 6742, 159.7)m
(b)
3952m
(c)
3900m
2.
Point C and D are located at (1,2,4)m and (2,1,1)m respectively. Determine the length of
CD and the angle COD, where O is the original of the coordinates.
ans:
4.36m, 69.12
3.
A vector is given by (2i+3j+1k)m. What is the component of this vector (a) in the ydirection
and (b) in the direction parallel to the line from A to B, where A is at point (1,1,0)m and B is
at (3,4,5)m?
ans:
3m, 2.92m
4.
What are the angles between the line joining the origin O and a point at (2,5,6)m and the
positive x, y and z axes?
ans:
75.6
, 128.3
, 41.9
5.
A point on a mechanism has a speed of 5m/s and a tangential acceleration of magnitude
2m/s
2
. If the magnitude of the total acceleration is 3.0m/s
2
, what is the radius of curvature of
the path traced by the point at this instant.
ans:
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This note was uploaded on 05/10/2009 for the course MXXM 2XX9 taught by Professor Gxxy during the Spring '09 term at City University of Hong Kong.
 Spring '09
 GXXY

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