1 / 10

Vector Analysis

Vector Analysis. Physics – 11.1.1 Vectors. 5a. N. 5b. N. N. 6. 7. If this problem is to be solved mathematically we must establish two formulae. One in the vertical and one in the horizontal;. The key is knowing that the resultant force is 30N at 0 º. Hence; Resolving Horizontally;

stacyk
Download Presentation

Vector Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Vector Analysis Physics – 11.1.1 Vectors

  2. 5a N

  3. 5b N N

  4. 6

  5. 7 If this problem is to be solved mathematically we must establish two formulae. One in the vertical and one in the horizontal; The key is knowing that the resultant force is 30N at 0º. Hence; Resolving Horizontally; 30N = FCos + 60NCos(360-120) 30N = FCos + 60N x -0.5 30N = FCos - 30N 60N = FCos  Eq 1 Resolving Vertically; 0 = FSin + 60NSin(360-120) 0 = FSin + 60NSin(240) 0 = FSin + 60N x 3/2 0 = FSin -51.96N 51.96N = FSin Eq 2 30N So by dividing Eq 2 by Eq 1 FSin / FCos  = 51.95N/ 60N tan  = 0.866  = 40.89 F = 60N / cos  = 79.4N Or F = 51.96N / sin  = 78.96N

  6. 7 Alternative method using cosine and sine rule…. Make a triangle of vectors where we are trying to find length c and angle A; 30N b = 30N 120 A a = 60N c = F Sine Rule Use reciprocal version of above SinC / c = SinA / a (60N x Sin 120) / 79.4N) = SinA Sin-1 (60N x Sin 120) / 79.4N) =A A = 40.876 = 41  Cosine Rule c2 = a2 + b2 - 2abCosC c2 = 60N2 + 30N2 – 2x60Nx30N xCos120 c2 = 4500N2 +1800N2 c2 = 6300N c = 79.4N c = F = 79.4N

  7. hyp opp = hyp x sin adj = hyp x cos opp  adj Reasoning! When using a resolving triangle to solve this type of problem. We have to turn it on its side to make it fit the problem; This means that the formulae for resolving V & H are reversed for this situation as we are working out  and not (90-) So reverse angles.

  8. Wires example – Correct So by turning it on its side we can use the same formulae (which is confusing but correct) right side Left side

  9. WRONG ANSWER – does not take this into account!!!

  10. Can do by using (90- ) as angle; If we take the outside angle instead of the inner angle we can do this and use the triangle; (90-)

More Related