Vector Problem Homework: Finding Components and Resultant of Three Forces

[Amuro]

Homework Statement

There are three forces, each of magnitude 5.00 N applied to a particle at O in the directions shown in Fig. 1. List the components of the individual forces F₁, F₂, and F₃. Obtain the x and y components of the resultant of the three forces, R = F₁ + F₂ + F₃ and the magnitude of R and its direction by giving the angle to one of the axes.

F₁ vector is right on the x-axis and its direction is east.
F₂ vector is 30 degrees from +y. It is between north and west.
F₃ vector is 30 degrees from -y. It is between south and west.

Homework Equations

The Attempt at a Solution

For the F₃ vector, I did sine 30 = x/5 and I got 2.5. Then I used cosine and I got 4.33 for the other side. I did the same process for the F₂ vector.

So my components were:
F₃ (-2.5, -4.33)
F₂ (-2.5, 4.33)
F₁ (5, 0)

I add the component up to get R and I get 0 for the components and for the vector of R. Did I do something wrong? Or is this correct?

 

[Amuro]

Help anyone?

 

[tiny-tim]

Welcome to PF!

Hi Amuro! Welcome to PF!

I add the component up to get R and I get 0 for the components and for the vector of R. Did I do something wrong? Or is this correct?

No, that looks correct … the magnitude is 0, and the angle is irrelevant.

 

[Amuro]

Hi Amuro! Welcome to PF!


No, that looks correct … the magnitude is 0, and the angle is irrelevant.

Thank you.

 

[rwisz]

Your approach to finding the components of F1, F2, and F3 is correct. However, when adding the components to find the resultant, you must also consider the direction. In this case, since all three forces are acting in different directions, the components will not simply cancel out to give a resultant of 0.

To find the x and y components of the resultant, you can use the formula R_x = F1_x + F2_x + F3_x and R_y = F1_y + F2_y + F3_y. Plugging in the values from your calculations, we get R_x = 0 and R_y = 0, which means the resultant vector has no x or y component. This makes sense because the forces are acting in different directions and cancel each other out.

To find the magnitude and direction of the resultant, you can use the Pythagorean theorem and trigonometric functions. The magnitude of the resultant, R, is given by R = √(R_x^2 + R_y^2). Plugging in the values, we get R = √(0^2 + 0^2) = 0. This means that the magnitude of the resultant is also 0, which again makes sense since the forces are cancelling each other out.

To find the direction of the resultant, you can use the inverse tangent function, tan^-1(R_y/R_x). In this case, since both R_x and R_y are 0, the direction of the resultant cannot be determined.

In summary, your approach to finding the components of the forces is correct, but when adding them to find the resultant, you must also consider the direction. In this case, the resultant vector has no x or y component and a magnitude and direction of 0.