Eng. Tarteel Awad Page 1 L1: VECTORS AND SCALARS Example (1): Represent graphically: (a) a force of 10 lb in a direction 30° north of east (b) a force of 15 lb in a direction 30 ° east of north. Choosing the unit of magnitude shown, the required vectors are as indicated above.
19
Embed
L1: VECTORS AND SCALARS · 2019-01-30 · Eng. Tarteel Awad Page 2 Example (2): An automobile travels 3 miles due north, then 5 miles northeast. Represent these displacements graphically
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Eng. Tarteel Awad Page 1
L1: VECTORS AND SCALARS
Example (1): Represent graphically:
(a) a force of 10 lb in a direction 30° north of east
(b) a force of 15 lb in a direction 30 ° east of north.
Choosing the unit of magnitude shown, the required vectors are as indicated above.
Eng. Tarteel Awad Page 2
Example (2): An automobile travels 3 miles due north, then 5 miles northeast.
Represent these displacements graphically and determine the resultant
displacement
a. graphically.
b. analytically.
Vector OP or A represents displacement of 3 mi due north.
Vector PQ or B represents displacement of 5 mi north east.
Vector OQ or C represents the resultant displacement or
sum of vectors A and B, i.e. C = A+B. This, is the triangle law of vector
addition.
The resultant vector OQ can also be obtained by constructing the diagonal of the
parallelogram OPQR having vectors OP =A and OR (equal to vector PQ or B) as
sides. This is the parallelogram law of vector addition.
(a) Graphical Determination of Resultant. Lay off the 1 mile unit on
vector OQ to find the magnitude 7.4 mi (approximately).
Angle EOQ=61.5°, using a protractor.
Then vector OQ has magnitude 7.4 mi and direction 61.5 °
north of east.
Eng. Tarteel Awad Page 3
(b) Analytical Determination of Resultant. From triangle OPQ, denoting
the magnitudes of A, B. C by A, B, C, we have by the law of cosines
Ex. Show that addition of vectors is commutative, i.e. A + B = B + A. See Fig. (b)
below.
OP + PQ = OQ or A + B = C,
Eng. Tarteel Awad Page 4
and OR + RQ = OQ or B + A = C.
Then A + B = B + A .
Eng. Tarteel Awad Page 5
E.x. Show that the addition of vectors is associative, i.e. A + (B+C) = (A+B) + C