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I am quite confused as to what method should be used when finding resultant forces. Here are two examples of a question that asks to find the resultant force.

Example 1

One requires the parallelogram law to be used.

Example 2

The other requires finding the total in Fx and Fy.

So how do I identify which method I am supposed to use if its not stated during an exam? The questions seem very similar to each other. Is there specific details that I should bear in mind when it comes to the parallelogram law? Thank you in advance and sorry if this is a bit messy. It's my first time using this website.

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  • $\begingroup$ What is the difference between "parallelogram law" and "finding the total in Fx and Fy"? How would you do one or another? $\endgroup$ – VictorSeven Oct 15 '17 at 7:45
  • $\begingroup$ The two methods give identical answers. (That's rather the whole point) If it's not stated during an exam, you can use either method. $\endgroup$ – Chris Oct 15 '17 at 8:10
  • $\begingroup$ I agree with Chris. Note that on an exam, you should use whichever method is faster, because the exam is being timed. $\endgroup$ – David White Sep 4 '18 at 1:22
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There is practically no difference between the two methods. However, while using, there are some cases where one method will be more helpful than the other.

If you know the direction of the resultant force or vector, and the angles made by the given forces or vectors with the resultant, then you can use the second method. However, you don't have to resolve into the x- and the y- components. You can just resolve each force into their components along the direction of resultant, and add them up to give the magnitude of the resultant force. Be careful about signs. An example of this type of problem may be this:

Two persons on different sides of a river, pull a boat towards themselves by means of a string. The boat moves forward in a straight line. The forces make $\theta$ and $\phi $ with the direction of motion of the boat. Find the resultant force on the boat.

Here, you know the direction of the resultant force. Just resolve the two given forces into their cosine and add them to get the resultant force.

In case where you don't know the direction of resultant, you can use either method. In this case, you'll have to find the x- and the y-components, if you are using the second one. Both shall give the correct answer, and both are accepted.

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