Lessons 47–48 · 2 lessons · A. A. Rahimqoriyev, M. A. To‘xtaxo‘jayeva. Geometry, Grade 8 (textbook for general secondary schools), revised 3rd edition. Yangiyo‘l Poligraf Servis, Tashkent, 2014
48
Physical and geometric interpretations of vectors
Textbook: p. 148
GoalKnow the physical meaning of vectors: sums of forces, displacement and vector quantities.
New words
resultant force · teng ta’sir etuvchi kuchdisplacement vector · siljish vektorivector quantity · vektor kattalikresolving a force · kuchni yoyish
Explanation
It is convenient to draw a force as an arrow: the arrow points the way the force acts, and its length is taken in proportion to how large the force is. The resultant of two forces acting at one point is the sum of their vectors: →c = →a + →b. Conversely, writing a force as the sum of two forces in two given directions is called resolving the force. In translational motion all points of a body shift the same distance in the same direction, so the displacement is given by a vector. Quantities such as velocity and force are determined by direction as well as modulus, and we call them vector quantities; for example, the modulus of a velocity is measured in m/s and that of a force in newtons (N).
Worked examples
Forces of 30 N and 40 N along one line in the same direction have resultant 70 N; in opposite directions the resultant is 40 − 30 = 10 N.
Perpendicular forces of 6 N and 8 N have a resultant equal to the rectangle’s diagonal: √(36 + 64) = 10 N.
Class activity
“Two children, one cart”: on paper draw two forces pulling a cart as arrows and construct the resultant with the parallelogram rule (no need to pull a real cart).
Practice
1
Perpendicular forces of 12 N and 5 N have a resultant of how many N?
13
2
Forces of 25 N and 9 N act along one line in opposite directions. What is the resultant in N?
16
3
A child walks 3 m east, then 4 m north. What is the modulus of the displacement vector (m)?
5
4
Why are the velocity vectors of two cars not equal even if their speeds are equal but they move in opposite directions?
Equal vectors must have the same direction too, and here the directions are opposite.