Three forces acting on object, find net force

[Naeem]

Forces

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Three forces F1, F2 and F3 act on an object as shown in the free-body diagram above. F1 has a magnitude of 6 N while F2 and F3 each have a magnitude of 3 N. All forces make angles of 30° with the x-axis as shown.

What is the magnitude of Fnet, the net force acting on the object?

|Fnet| = N


I know, this problem isn't too hard, we need to add vectors considering the angles ( both in x -y directions )

I just forgot how to do this, can anybody help.

 

[thepatientmental]

To find the net force acting on the object, we need to use vector addition. This means adding the individual forces together to find the resultant force. In this case, we can use the Pythagorean theorem and trigonometric functions to find the magnitude and direction of the net force.

First, we need to break down each force into its x and y components. We can do this by using the given angle and the trigonometric functions.

For F1:
Fx1 = F1 cos 30° = 6 cos 30° = 5.2 N
Fy1 = F1 sin 30° = 6 sin 30° = 3 N

For F2:
Fx2 = F2 cos 30° = 3 cos 30° = 2.6 N
Fy2 = F2 sin 30° = 3 sin 30° = 1.5 N

For F3:
Fx3 = F3 cos 30° = 3 cos 30° = 2.6 N
Fy3 = F3 sin 30° = 3 sin 30° = 1.5 N

Now, we can add the x and y components separately to find the net force:

Fnet,x = Fx1 + Fx2 + Fx3 = 5.2 N + 2.6 N + 2.6 N = 10.4 N
Fnet,y = Fy1 + Fy2 + Fy3 = 3 N + 1.5 N + 1.5 N = 6 N

Using the Pythagorean theorem, we can find the magnitude of the net force:

|Fnet| = √(Fnet,x² + Fnet,y²) = √(10.4² + 6²) = 12.2 N

Therefore, the magnitude of the net force acting on the object is 12.2 N. To find the direction, we can use the inverse tangent function:

θ = tan^-1 (Fnet,y/Fnet,x) = tan^-1 (6/10.4) = 31.8°

Thus, the net force has a magnitude of 12.2 N and is directed at an angle of 31.8° from the x-axis.