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# Vectors - Forces

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Three forces act through the point O in the directions shown in the figure in the attachment. The magnitudes of the forces are 15kN, 10kN and P. The resultant R acts at an angle of 10 degrees to Ox. Find the magnitudes of P and R.

https://brainmass.com/physics/scalar-and-vector-operations/directions-magnitudes-resultant-vectors-408266

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Three forces act through the point O in the directions shown in the figure below. The magnitudes of the forces are 15kN, 10kN and P. The resultant R acts at an angle of 10 degrees to Ox. Find the magnitudes of P and R.

y

Solution: Resolving 15 kN, 10 kN and P into x and y components and adding them to get the net x and y components of the three forces:

Fx = 15cos75O + 10cos30O + Pcos60O = 3.88 + 8.66 + 0.5P = 12.54 + 0.5P .......(1)

Fy = 15sin75O + 10sin30O - Psin60O = 14.49 + 5 + 0.87P = 19.49 - 0.87P .......(2)

Fx
Î± = 10O
R
Fy

Fy/Fx = tan Î±

(19.49 - 0.87P)/(12.54 + 0.5P) = tan10O = 0.176

19.49 - 0.87P = 2.2 + 0.088P

P = 18 kN

____________________________
Magnitude of R = âˆš(12.54 + 0.5P)2 + (19.49 - 0.87P)2

Substituting for P in the above, we get:
________________________________
R = âˆš(12.54 + 0.5x18)2 + (19.49 - 0.87x18)2 = 21.88 kN

R = 21.88 kN

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