This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
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 KN kwa 60^ kutoka mhimili chanya wa x. Nguvu 2: F_2 = 80 KN kwa 70^ kutoka mhimili chanya wa y kuelekea mhimili hasi wa x. Hii inamaanisha 20^ kutoka mhimili hasi wa x, au 180^ - 20^ = 160^ kutoka mhimili chanya wa x. Nguvu 3: F_3 = 700 KN kando ya mhimili hasi wa x. Hii inamaanisha 180^ kutoka mhimili chanya wa x. Nguvu 4: F_4 = 80 KN kwa 60^ kutoka mhimili hasi wa y kuelekea mhimili hasi wa x. Hii inamaanisha 30^ kutoka mhimili hasi wa x, au 180^ + 30^ = 210^ kutoka mhimili chanya wa x. Nguvu 5: F_5 = 400 KN kando ya mhimili hasi wa y. Hii inamaanisha 270^ kutoka mhimili chanya wa x. Step 1: Tafuta vijenzi vya x vya kila nguvu na ujumuishe. F_x = F_1x + F_2x + F_3x + F_4x + F_5x F_1x = 700 (60^) = 700 × 0.5 = 350 KN F_2x = 80 (160^) = 80 × (-0.9397) = -75.18 KN F_3x = 700 (180^) = 700 × (-1) = -700 KN F_4x = 80 (210^) = 80 × (-0.8660) = -69.28 KN F_5x = 400 (270^) = 400 × 0 = 0 KN F_x = 350 - 75.18 - 700 - 69.28 + 0 = -494.46 KN Step 2: Tafuta vijenzi vya y vya kila nguvu na ujumuishe. F_y = F_1y + F_2y + F_3y + F_4y + F_5y F_1y = 700 (60^) = 700 × 0.8660 = 606.20 KN F_2y = 80 (160^) = 80 × 0.3420 = 27.36 KN F_3y = 700 (180^) = 700 × 0 = 0 KN F_4y = 80 (210^) = 80 × (-0.5) = -40 KN F_5y = 400 (270^) = 400 × (-1) = -400 KN F_y = 606.20 + 27.36 + 0 - 40 - 400 = 193.56 KN Step 3: Kokotoa ukubwa wa nguvu jumla (resultant force). R = sqrt(( F_x)^2 + ( F_y)^2) R = sqrt((-494.46)^2 + (193.56)^2) R = sqrt(244490.67 + 37466.56) R = sqrt(281957.23) R = 531.00 KN Step 4: Kokotoa mwelekeo wa nguvu jumla. Mwelekeo kutoka mhimili hasi wa x unatolewa na: = (| F_y|)/(| F_x|) = (193.56)/(494.46) = 0.3915 = (0.3915) = 21.37^ Kwa kuwa F_x ni hasi na F_y ni chanya, nguvu jumla iko katika roboduara ya pili. Hivyo, mwelekeo kutoka mhimili chanya wa x (kinyume cha saa) ni: = 180^ - = 180^ - 21.37^ = 158.63^ Nguvu jumla ni: 531.00 KN Mwelekeo ni: 158.63^ kutoka mhimili chanya wa x (kinyume cha saa) Tuma swali linalofuata 📸