2. Vector Addition:
Vector addition may be done several ways including, Graphical Method, Trigonometric Method, and Component Method. We will be reviewing only the Component Method, as that is the method which will be used in the course. Other methods are detailed in your textbook.
3. Vector Addition - Component
The component method will follow the procedure shown below:
Example - Vector Addition
Three ropes are tied to a small metal ring. At the end of each rope three students are pulling, each trying to move the ring in their direction. If we look down from above the students, the forces and directions they are applying the forces are as follows: (See diagram to the right)
Find the net (resultant) force (magnitude and direction) on the ring due to the three applied forces.
Choose origin, sketch coordinate system and
vectors (done above)
Resolve vectors into x & y
components (See Diagram)
Ax = 30 lb cos 37o = + 24.0 lbs ; Ay = 30 lb sin 37o = + 18.1 lb
Bx = 50 lb cos135o = - 35.4 lbs ; By = 50 lb sin135o = + 35.4 lb
Cx = 80 lb cos240o = - 40.0 lbs ; Cy = 80 lb sin240o = - 69.3 lb
Sum x & y components to find resultant
Rx and Ry forces.
Rx = 24.0 lbs - 35.4 lbs - 40.0 lbs = -51.4 lbs
Ry =18.1 lbs + 35.4 lbs - 69.3 lbs = -15.8 lbs
'Recombine' (add) Rx and Ry to determine final resultant vector.
Thus the resultant force on the ring is 53.8 pounds acting at an angle of 197.1 degrees.
Vector review problems