Question

Two force vectors are oriented such that the angle between their directions is 40 degrees and they have the same magnitude. If their magnitudes are 7.79 newtons, then what is the magnitude of their sum?

Answer 1

Answer:

The magnitude of their sum is 14.64 N.

Explanation:

The magnitude of two forces are, $F_1=F_2=7.79\ N$

These two forces are oriented such that the angle between their directions is 40 degrees, $\theta=40^{\circ}$

We need to find the magnitude of their sum. The magnitude of the sum of two vectors is given by :

$F_{net}=\sqrt{F_1^2+F_2^2+2F_1F_2\ cos\theta}$

$F_{net}=\sqrt{7.79^2+7.79^2+2\times (7.79)^2\ cos(40)}$

$F_{net}=14.64\ N$

So, the magnitude of their sum is 14.64 N. Hence, this is the required solution.