How to Avoid Common Mistakes in Solving Forces Problems?

[FaraDazed]

Homework Statement

A particles is under the influence of two forces, 500N at 50° from north and 350N at 350° from north. Find the magnitude and direction of the resultant pull on the particle.

Homework Equations

?

The Attempt at a Solution

$x=500cos40-350cos80\\ x=322.25N\\ y=500sin40+350cos10\\ y=666.08N \\ \sqrt{322.25^2 + 666.08^2}=739.94N \\ arctan(322.25/666.08)=25.82° from north. \\$
I am a bit confused on when to use cos or sin. The above is how a classmate pursaded me to change it to but on my first go I had
$x=500cos40-350sin10 \\ y=500sin40+350cos10 \\$

 

[rude man]

Draw the vectors on an x-y plot (+y = North). It should be obvious from that.

 

[FaraDazed]

Draw the vectors on an x-y plot (+y = North). It should be obvious from that.

Thanks for your reply. I have already done that and the figure and direction obtained seem correct but I don't know for sure and if my method is correct.

EDIT: Sorry just realized my mistake. They are both the same but doing it a different way, my calculator was set on radians instead of degrees and that is why I was getting different figure to earlier sorry.

 

[Redbelly98]

..., my calculator was set on radians instead of degrees ...

A very common mistake. Remember to check the setting whenever you have an exam

 

[Nickie]

\sqrt{322.25^2 + 666.08^2}=739.94N \\
arctan(322.25/666.08)=25.82° from north. \\

As a scientist, it is important to always approach problem solving with a clear understanding of the fundamental principles and equations involved. In this case, the fundamental principle is Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In order to accurately solve forces problems, it is important to follow these steps:

1. Draw a clear and accurate diagram of the forces acting on the object, including the angles and directions of each force.

2. Decompose the forces into their x and y components using trigonometric functions (cos and sin). This step is necessary because forces acting at an angle to each other cannot be directly added or subtracted.

3. Sum the x and y components of the forces separately, using algebraic addition and subtraction.

4. Use the Pythagorean theorem to find the magnitude of the resultant force by taking the square root of the sum of the squared x and y components.

5. Use inverse trigonometric functions to find the direction of the resultant force by taking the arctan of the y component divided by the x component.

In this specific problem, it is important to note that the 350N force is acting in the opposite direction of the 40° angle, therefore it should be subtracted from the 500N force instead of added. This is why using cos for the x component and sin for the y component is the correct approach.

In summary, avoiding common mistakes in solving forces problems involves a thorough understanding of the fundamental principles and equations, as well as careful attention to detail and accuracy in the steps taken to solve the problem. By following these steps, one can avoid errors and confidently arrive at the correct solution.