Force Vector Problem: Find Magnitude & Direction of F3

In summary, the problem involves finding the magnitude and direction of a third force that is applied to an object, given two other forces and the requirement that the vector sum of all three forces is zero. The equations F1x + F2x + F3x = 0 and F1y + F2y + F3y = 0 can be used to determine the components of the third force, and then the magnitude and direction can be found using the Pythagorean theorem. The direction is specified as a positive angle relative to the negative x axis, which means measuring the angle from the -x direction.
  • #1
dwagz
3
0

Homework Statement



Three forces are applied to an object, as shown in the figure. Force F1 has a magnitude of 26.8 Newtons (N) and is directed 30.0° to the left of the +y axis. Force F2 has a magnitude of 15.2 N and points along the +x axis. A third force F3 is applied such that the vector sum of the three forces is 0 N. What are (a) the magnitude and (b) direction of this third force? Specify the direction as a positive angle relative to the negative x axis, as shown in the figure.

Picture: http://s236.photobucket.com/albums/ff132/airpenny123/?action=view&current=ch01p_46.gif

Homework Equations



F3X = F1X + F2X
F3Y = F1Y + F2Y

F3= √F3X^2 + F3Y^2


The Attempt at a Solution



F1X = (-26.8N)(.8660)
F1X = -23.21N

F2X = 15.2N

F3X = -23.21N + 15.2N = -8.01N

F1Y = (26.8N)(0.5)
F1Y = 13.4N

F2Y = 0

F3Y = 13.4N + 0 = 13.4N

I found the components of F3X = -8.01 and F3Y = 13.4. When I plug the components into: F3= √F3X^2 + F3Y^2, I get 15.6115 N, which apparently is wrong. I've been on this problem forever and I don't know what I'm doing wrong.

As for this part of the question: "Specify the direction as a positive angle relative to the negative x axis, as shown in the figure." I am completely lost...

Thanks for any help.
 
Last edited:
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  • #2
Welcome to PF :smile:

I see two problems.

Since the vector sum is zero, the equations should read

F1x + F2x + F3x = 0​

and similarly for the y-components.

Also, calculating the x-component of F1 does not involve cos(30).

As for this part of the question: "Specify the direction as a positive angle relative to the negative x axis, as shown in the figure." I am completely lost...

They just mean the angle from the -x direction.
 
  • #3
why is that my prof taught us to get first the force sumation in X and in Y and use phytagorean theorem and then get the direction ..
 
  • #4
Welcome to Physics Forums.
dgiordan said:
why is that my prof taught us to get first the force sumation in X and in Y and use phytagorean theorem and then get the direction ..
That is pretty much how you do this sort of problem, or anything that involves adding vectors. I'm not sure what specifically is confusing you about it?
 

FAQ: Force Vector Problem: Find Magnitude & Direction of F3

What is a force vector problem?

A force vector problem is a type of physics problem that involves finding the magnitude and direction of a specific force vector, typically denoted as F3. This type of problem is often encountered in mechanics and can involve various scenarios such as objects on inclined planes, pulley systems, or objects in free fall.

How do I find the magnitude of F3?

The magnitude of F3 can be found using the Pythagorean theorem, which states that the magnitude of a vector can be calculated by taking the square root of the sum of the squares of its components. In the case of F3, this would involve finding the square root of the sum of the squares of its x and y components.

How do I determine the direction of F3?

The direction of F3 can be determined using trigonometric functions such as sine, cosine, and tangent. These functions can be used to find the angle between F3 and a known reference axis, such as the x-axis. The direction of F3 can then be described using this angle and the appropriate trigonometric function.

What units are typically used for force vectors?

Force vectors are typically measured in units of Newtons (N) in the SI (International System of Units) system of measurement. However, other units such as pounds (lb) or dynes (dyn) may also be used in different contexts.

Are there any common mistakes to avoid when solving force vector problems?

One common mistake when solving force vector problems is to forget to account for the direction of the vector. Magnitude alone is not enough to fully describe a vector, so it is important to always include the direction in your solution. Another mistake is to mix up the x and y components, so it is important to carefully label and organize the given information before attempting to solve the problem.

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