Question

Four force vectors each have the same magnitude f. What is the largest magnitude the resultant force vector may have when these forces are added? What is the smallest magnitude of the resultant? Make a graph of both situations.

a) Largest: 4f, Smallest: 0
b) Largest: 2f, Smallest: f
c) Largest: 3f, Smallest: f
d) Largest: f, Smallest: 0

Answer 1

The largest magnitude of the resultant force vector is 4f and the smallest magnitude is 0 when four force vectors of the same magnitude are added. This can be illustrated graphically.

Step-by-step explanation:

In order to find the largest and smallest magnitudes of the resultant force vector when four force vectors of the same magnitude f are added, let's examine the different scenarios. When the forces are added in the same direction, the resultant force will have the largest magnitude, which is equivalent to 4f. This is because all four forces are contributing to the overall magnitude. On the other hand, when the forces are added in opposite directions, the resultant force will have the smallest magnitude, which is equivalent to 0. This occurs because the forces cancel each other ou

Graphically, the scenarios can be represented as follows:

Largest Magnitude: 4f

Smallest Magnitude: 0