Question

Using the diagram shown, what is the magnitude of the resultant of these three forces?

I know the answer is 23.8 N I think because I looked it up but I have no idea how to actually solve.

Answer 1

Explanation:

The x component of the resultant force is the sum of the x components of the individual forces.

Fₓ = 65.0 cos 30° − 20.0 sin 20° − 30.0

Fₓ = 19.5

The y component of the resultant force is the sum of the y components of the individual forces.

Fᵧ = 65.0 sin 30° − 20.0 cos 20°

Fᵧ = 13.7

The magnitude is found with Pythagorean theorem:

F² = Fₓ² + Fᵧ²

F² = (19.5)² + (13.7)²

F = 23.8

Answer 2

The magnitude of the resulting force (Vector) is 23.8 N. The resulting vector can be calculated by the Pythagorean theorem.

How to calculate the resulting vector?

The resulting vector can be calculated by the addition of the X and Y component by the Pythagorean theorem,

First, calculate the horizontal or X-component,

$F_x = (65.0 \rm cos 30^o) - 20.0 \ sin 20^o - 30.0\\\\F_x = 19.5$

Now calculate the Vertical or Y-component,

$F_y ={\rm 65.0\ sin 30^o-20.0 \ cos 20^o}\\\\F_y = 13.7$

From the Pythagorean theorem:

$F =\sqrt { (19.5)^2 + (13.7)^2}\\\\F = 23.8$

Therefore, the magnitude of the resulting force (Vector) is 23.8 N.

Learn more about the resulting vector:

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