Consider the following four force vectors: F1 = 50 newtons, due east F2 = 10 newtons, due east F3 = 40 newtons, due west F4 = 30 newtons, due west Which two vectors add together to give a resultant with the smallest magnitude, and which two vectors add to give a resultant with the largest magnitude? In each case specify the magnitude and direction of the

F3 + F4 has the highest magnitude = 70 newtons west

and F1 + F3 has the lowest magnitude = 10 newtons east

Explanation:

F1 = 50 newtons, due east

F2 = 10 newtons, due east

F3 = 40 newtons, due west

F4 = 30 newtons, due west

Let us consider East as negative and west as positive, so

F1 = - 50 newtons

F2 = - 10 newtons

F3 = 40 newtons

F4 = 30 newtons

F3 + F4 = 40 + 30 = 70 newtons

F1 + F2 = - 50 - 10 = - 60 newtons

F1 + F3 = - 50 + 40 = 10 newtons

F1 + F4 = - 50 + 30 = - 20 newtons

F2 + F3 = - 10 + 40 = - 30 newtons

F2 + F4 = - 10 + 30 = 20 newtons

It can be seen that F3 + F4 has the highest magnitude = 70 newtons west

and F1 + F3 has the lowest magnitude = 10 newtons east