Which Method is Correct for Solving Statics Physics Problems?

[frozen7]

I have two different ways to solve this question. The first method is using the method taught in textbook: Draw the parallelogram and bend F to a direction which is perpendicular to the resultant force, and use sine rule to find F.
The second method I use is by assuming the direction of the resultant force of 600N and 400N is parallel to F, hence the resultant force,900N is parallel to 400N and F also. Under this condition, F can only be the minimum. The answer I got from the second method is much smaller than the answer from first method.
Can anyone tell me which one is the correct method? Where did I get wrong??
Thanks in advance.

 

[haynewp]

The question wants you to minimize the force in the cable "F". So in order to do that, you would want to find the angle and magnitude of the resultant of forces given already (like it says to do) then make "F" parallel with this force (at the same angle). So first break apart the given forces into x and y components and find the resultant and its angle.

 

[piercas]

Both methods can be correct, but they are based on different assumptions and approaches. The first method, using the parallelogram and sine rule, is a more traditional and commonly taught approach in statics. It assumes that the forces are acting at different angles and requires more calculations.

The second method, assuming the resultant force is parallel to F, is a simplified approach that may not always be applicable. It assumes that the forces are acting in the same direction, which may not always be the case in real-life scenarios. This method may give a smaller answer because it is only considering the minimum force needed to create the resultant force.

To determine which method is correct, it is important to understand the scenario and the assumptions being made. If the forces are indeed acting at different angles, then the first method is more accurate. However, if the forces are acting in the same direction, then the second method may be more appropriate.

It is also possible that there is an error in the calculations for one of the methods. It would be helpful to double-check the calculations and make sure all assumptions are correct before determining the correct method. Additionally, it is always good practice to check the answer using both methods to ensure accuracy.

Overall, both methods can be correct, but it is important to consider the assumptions and approach being used in each method. It is also important to double-check calculations and make sure all assumptions are accurate before determining the correct method.