Forces and Motion in Two Dimension Vector Representatives Resultant Vectors Equilibrium and Equilibrant

Vector Representatives An arrow  is the graphical representation of a vector. The arrow will have a specified length and direction. The arrow is drawn to scale to represent the magnitude (size) of the vector. vs Arrows will point in a specified direction of vector.

Resultant Vectors 2 equal vectors – same length and direction 2 unequal vectors – different directions By adding the two unequal vectors, a resultant vector will be found. The most common method of adding vectors is the graphical method of head-to-tail addition. The question often arises as to the importance of the order in which the vectors are added. – For instance, if five vectors are added - let's call them vectors A, B, C, D and E - then will a different resultant be obtained if a different order of addition is used.

Will A + B + C + D + E yield the same result as C + B + A + D + E or D + E + A + B + C? The order in which two or more vectors are added does not effect the outcome. Adding A + B + C + D + E yields the same result as adding C + B + A + D + E or D + E + A + B + C! The resultant, shown as the green vector, has the same magnitude and direction regardless of the order in which the five individual vectors are added.

Resultant Vectors in Action 1 st, the plane encounters a tailwind (push from behind) of 20 mi/hr. Effect: the tailwind and the plane speed provide a resultant velocity of 120 mi/hr. 2nd, the plane encounters a headwind (push from the front) of 20 mi/hr. Effect: the headwind and the plane speed provide a resultant velocity of 80 mi/hr. 3rd, the plane encounters a crosswind (push from the side) of 20 mi/hr. Effect: the headwind and the plane speed provide a resultant velocity of 102 mi/hr

Equilibrium and Equilibrant When the sum of all forces (net force) is zero, objects are in equilibrium. When in equilibrium, all objects are motionless or moves with constant velocity. Equilibrium also occurs when the resultant of 3 or more forces equals a net force of zero. Vectors can be rearranged AS LONG AS you keep their direction or angle or length the same! Equilibrant is the force OPPOSITE the resultant force. R Equilibrant

Quick Pair Share Share one item learned from this set of notes with your neighbor. Write in your notes what they learned and vise versa. Use a Venn Diagram to compare Linear motion to 2-D motion.