Resolving Vectors Resolving vectors is the opposite of finding the resultant.
A vector is resolved into two component vectors. This is generally used to redefine a single vector into two perpendicular vectors. Based on Pythagoras’Theorem and SOHCAHTOA:
The component vectors are equal to the magnitude of the original vector multiplied by sin and cos , as illustrated in Fig 2.11.
SAMPLE PROBLEM 2C
A man pulls on a rope with a force of 25 N at an angle of 16.26 to the horizontal, as shown in the diagram. Calculate the vertical and horizontal component of the force.
16.26 25 N
y Rsin x Rcos
Fig 2.11: Illustration of resolving vectors
R
Fig 2.12: Illustration of a man pulling a rope
SAMPLE ANSWER 2C Using SOHCAHTOA: sin
cos
Opposite HypotenuseQOpposite 25(sin 16.26) 7
Adjacent HypotenuseQAdjacent 25(cos 16.26) 24
The 25 N force on the rope can be resolved into 7 N in the vertical and 24 N in the horizontal.
25 N 25(si
25(cos16.26) 16.26
Fig 2.13: Illustration of a man pulling a rope, with force resolved 25(sin16.26 (sin16.26)
DEMONSTRATION 2.1 Find the resultant of two vectors
Apparatus Three Newton balances, string, paper and pencil, ruler and protractor
Procedure Join the three balances together with string.
