suppose-a-force-given-as-F-1-24-N-and-F-2-50-N-act-through-points-AB-and-AC-where-OA-2i-3j-OB-5i-6j-and-OC-7i-8j-a-find-in-vector-notation-F-1-and-F-2-then-find-thier-result

Question Number 98208 by Rio Michael last updated on 12/Jun/20

suppose a force given as F_{1} = 24 N and F_{2} = 50 N act through

points A B and A C where O A = 2 i + 3 j, O B = 5 i + 6 j and

O C = 7 i + 8 j

(a) find in vector notation F_{1} and F_{2}

then find thier resultant .

Commented by mr W last updated on 12/Jun/20

A B = O B - O A = 3 i + 3 j

F_{1} =∣ F_{1} ∣ \times \frac{A B}{∣ A B ∣} = 12 \sqrt{2} (i + j)

A C = O C - O A = 5 i + 5 j

F_{2} =∣ F_{2} ∣ \times \frac{A B}{∣ A B ∣} = 25 \sqrt{2} (i + j)

F_{1} + F_{2} = (12 + 25) \sqrt{2} (i + j) = 37 \sqrt{2} (i + j)

∣ F_{1} + F_{2} ∣= 37 \sqrt{2} \sqrt{1^{2} + 1^{2}} = 74 K N

Commented by Rio Michael last updated on 12/Jun/20

thanks for that