Find resultant and diagram direction:

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Ili kupata nguvu jumla (resultant force) na mwelekeo wake, tutavunja kila nguvu katika vijenzi vyake vya x na y, kisha tujumuishe vijenzi hivyo.

Nguvu 1: $F_1 = 700 \text{ KN}$ kwa $60^\circ$ kutoka mhimili chanya wa x.
Nguvu 2: $F_2 = 80 \text{ KN}$ kwa $70^\circ$ kutoka mhimili chanya wa y kuelekea mhimili hasi wa x. Hii inamaanisha $20^\circ$ kutoka mhimili hasi wa x, au $180^\circ - 20^\circ = 160^\circ$ kutoka mhimili chanya wa x.
Nguvu 3: $F_3 = 700 \text{ KN}$ kando ya mhimili hasi wa x. Hii inamaanisha $180^\circ$ kutoka mhimili chanya wa x.
Nguvu 4: $F_4 = 80 \text{ KN}$ kwa $60^\circ$ kutoka mhimili hasi wa y kuelekea mhimili hasi wa x. Hii inamaanisha $30^\circ$ kutoka mhimili hasi wa x, au $180^\circ + 30^\circ = 210^\circ$ kutoka mhimili chanya wa x.
Nguvu 5: $F_5 = 400 \text{ KN}$ kando ya mhimili hasi wa y. Hii inamaanisha $270^\circ$ kutoka mhimili chanya wa x.

Tafuta vijenzi vya x vya kila nguvu na ujumuishe.
$\sum F_x = F_{1x} + F_{2x} + F_{3x} + F_{4x} + F_{5x}$ $F_{1x} = 700 \cos(60^\circ) = 700 \times 0.5 = 350 \text{ KN}$ $F_{2x} = 80 \cos(160^\circ) = 80 \times (-0.9397) = -75.18 \text{ KN}$ $F_{3x} = 700 \cos(180^\circ) = 700 \times (-1) = -700 \text{ KN}$ $F_{4x} = 80 \cos(210^\circ) = 80 \times (-0.8660) = -69.28 \text{ KN}$ $F_{5x} = 400 \cos(270^\circ) = 400 \times 0 = 0 \text{ KN}$ $\sum F_x = 350 - 75.18 - 700 - 69.28 + 0 = -494.46 \text{ KN}$
Tafuta vijenzi vya y vya kila nguvu na ujumuishe.
$\sum F_y = F_{1y} + F_{2y} + F_{3y} + F_{4y} + F_{5y}$ $F_{1y} = 700 \sin(60^\circ) = 700 \times 0.8660 = 606.20 \text{ KN}$ $F_{2y} = 80 \sin(160^\circ) = 80 \times 0.3420 = 27.36 \text{ KN}$ $F_{3y} = 700 \sin(180^\circ) = 700 \times 0 = 0 \text{ KN}$ $F_{4y} = 80 \sin(210^\circ) = 80 \times (-0.5) = -40 \text{ KN}$ $F_{5y} = 400 \sin(270^\circ) = 400 \times (-1) = -400 \text{ KN}$ $\sum F_y = 606.20 + 27.36 + 0 - 40 - 400 = 193.56 \text{ KN}$
Kokotoa ukubwa wa nguvu jumla (resultant force).
$R = \sqrt{(\sum F_x)^2 + (\sum F_y)^2}$ $R = \sqrt{(-494.46)^2 + (193.56)^2}$ $R = \sqrt{244490.67 + 37466.56}$ $R = \sqrt{281957.23}$ $R = 531.00 \text{ KN}$
Kokotoa mwelekeo wa nguvu jumla.
Mwelekeo $\alpha$ kutoka mhimili hasi wa x unatolewa na:
$\tan \alpha = \frac{|\sum F_y|}{|\sum F_x|} = \frac{193.56}{494.46} = 0.3915$ $\alpha = \arctan(0.3915) = 21.37^\circ$
Kwa kuwa $\sum F_x$ ni hasi na $\sum F_y$ ni chanya, nguvu jumla iko katika roboduara ya pili. Hivyo, mwelekeo $\theta$ kutoka mhimili chanya wa x (kinyume cha saa) ni:
$\theta = 180^\circ - \alpha = 180^\circ - 21.37^\circ = 158.63^\circ$
Nguvu jumla ni: $\boxed{\text{531.00 KN}}$
Mwelekeo ni: $\boxed{158.63^\circ \text{ kutoka mhimili chanya wa x (kinyume cha saa)}}$

Find resultant and diagram direction:

Answer

Step-by-step solution

Tafuta vijenzi vya x vya kila nguvu na ujumuishe.

Tafuta vijenzi vya y vya kila nguvu na ujumuishe.

Kokotoa ukubwa wa nguvu jumla (resultant force).

Kokotoa mwelekeo wa nguvu jumla.

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