Question

Two forces A and B are 6N at 36° to the +ve x axis and 7N along -ve xaxis . Find A +B and A - B by both geometrical and analytical by methods. (4:13M, 12:3

Answer 1

Geometrical method:
a) A + B: Place the tail of vector B at the head of vector A. The resultant vector (A + B) connects the tail of A to the head of B.
b) A - B: Place the tail of vector B at the tail of vector A. The resultant vector (A - B) connects the head of B to the head of A.

Analytical method:
a) A + B: Calculate the x-component of A and B. The x-component of the resultant (A + B) is (A * cos(36°) - B), and the y-component is (A * sin(36°)). Use the Pythagorean theorem to find the magnitude of (A + B).
b) A - B: Calculate the x-component of A and B. The x-component of the resultant (A - B) is (A * cos(36°) + B), and the y-component is (A * sin(36°)). Use the Pythagorean theorem to find the magnitude of (A - B).