Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Force Resultants

  1. Sep 14, 2018 #1
    I just wanna know the difference between those rules:

    1. R^2 = F1^2 * F2^2 + 2*F1*F2*COS(the angle between F1 and F2)

    2. The second is about the parallelogram rule, it says that the two vectors are added and their summation is the magnitude of the resultant.

    Which one is correct?
     
  2. jcsd
  3. Sep 14, 2018 #2

    tnich

    User Avatar
    Homework Helper

    If I correctly understand you, both are correct. You seem to have the sign wrong in the equation. ##R^2=F_1^2+F_2^2-2F_1F_2\cos(\theta)##
     
    Last edited: Sep 14, 2018
  4. Sep 14, 2018 #3

    tnich

    User Avatar
    Homework Helper

    Here is a diagram showing my understanding of the problem.
    upload_2018-9-14_10-44-25.png
     
  5. Sep 14, 2018 #4

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member
    2017 Award

    That would typically not be ”the angle between the forces”. The angle between two forces in the same direction would typically be zero, whereas your convention would be pi.
     
  6. Sep 14, 2018 #5

    tnich

    User Avatar
    Homework Helper

    I agree. I am trying to interpret what the OP has written.
     
  7. Sep 15, 2018 #6

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Rule 1 is the dot-product [law of cosines] (which is a metrical statement).
    Note that the angle-between-the-vectors (tails together, as in the parallelogram method of addition) is not the interior angle in the triangle (in the tail-to-tip method of addition).

    The parallelogram rule for adding vectors is true, independent of the metric.
    That tells you how to add two vectors... with the tails together, construct a parallelogram, and draw from the common tail to the opposite corner.
    That's the resultant vector.
    Getting the magnitude of the vector-sum is a different step [see rule 1].
     
  8. Sep 17, 2018 #7

    sophiecentaur

    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    That's the old "Cos Rule" which we all did at school. Using the Supplementary Angle (as with vectors, you just get a change of sign.
    Cos(x) = -Cos(π-x)
    :smile:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted