Find the resultant of these two force vectors using the following methods.

[Brillntbrntt]

Homework Statement

Find the resultant of the following vectors using these methods: triangle method, parallelogram method and mathematical method.
Fa is a force vector with magnitude of 10.0N and makes an angle of 25.0 degrees with the x-axis. Fb is a force vector with a magnitude of 5.0N and makes an angle of 45.0 degrees with the x-axis. Specify both the magnitude and direction of the resultant vector.

I've tried doing this problem using the triangle, parallelogram, and mathematical methods and all of my results are coming out different each time.

The Attempt at a Solution

I've attached my drawings and processes by which I arrived to the solutions, but each time I'm getting a different number. The magnitudes I've gotten are 14.80N for the parallelogram, 15.39 N for the mathematical, and 5.6 for the triangle. Directions are P:10 degrees, M:30.31 degrees and T:37.6 degrees. Please help!

I apologize in advance if the image isn't clear.

 

[SteamKing]

Sorry, your images are much too small to determine what calculations you have made.

 

[Brillntbrntt]

I'm new to the forum and it will only allow me to upload one photo so I tried putting them altogether. Do you have any suggestions on how I can upload each one individually?

 

[Brillntbrntt]

I tried it again. Please see if they are clear now.

 

[Nickie]

Hello,

Thank you for sharing your work and concerns. It is not uncommon to get slightly different results when using different methods to find the resultant of force vectors. This is due to the fact that each method has its own assumptions and approximations, which can lead to slight variations in the final result.

In this case, it is important to note that the triangle and parallelogram methods assume that the force vectors are acting on a point or object at the same time, while the mathematical method calculates the resultant by considering the components of the vectors separately. Additionally, the triangle and parallelogram methods rely on graphical constructions, which can introduce some errors.

To ensure accuracy, it is recommended to use the mathematical method to find the resultant vector. This method involves breaking down the vectors into their x and y components, adding them separately, and then finding the magnitude and direction of the resultant vector using trigonometric functions.

In this problem, the x component of Fa would be 10.0N cos(25.0) = 9.15N, and the y component would be 10.0N sin(25.0) = 4.24N. Similarly, the x component of Fb would be 5.0N cos(45.0) = 3.54N, and the y component would be 5.0N sin(45.0) = 3.54N.

Adding these components separately, we get the resultant x component as 9.15N + 3.54N = 12.69N, and the resultant y component as 4.24N + 3.54N = 7.78N.

Using the Pythagorean theorem, the magnitude of the resultant vector would be √(12.69^2 + 7.78^2) = 14.80N. To find the direction, we can use the inverse tangent function, giving us an angle of 30.31 degrees.

In conclusion, it is important to carefully consider the assumptions and approximations made when using different methods to find the resultant of force vectors. The mathematical method is generally the most accurate, but it is always a good idea to check your work and use multiple methods to ensure consistency. I hope this helps clarify the situation. Good luck with your studies!