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.
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Huu hapa ni ufumbuzi wa swali la 8: Tunatumia kanuni za trigonometry kutenganisha nguvu katika vijenzi vyake vya wima na mlalo. Kijenzi cha mlalo (F_x) = F (ikiwa ni pembe na mlalo) au F (ikiwa ni pembe na wima). Kijenzi cha wima (F_y) = F (ikiwa ni pembe na mlalo) au F (ikiwa ni pembe na wima). a) Nguvu F = 100 \, N. Pembe ni 60^ kutoka wima. Step 1: Kokotoa kijenzi cha mlalo. Kijenzi cha mlalo (F_x) = 100 60^ F_x = 100 × 0.8660 F_x = 86.60 \, N Step 2: Kokotoa kijenzi cha wima. Kijenzi cha wima (F_y) = 100 60^ F_y = 100 × 0.5000 F_y = 50.00 \, N Vijenzi vya (a) ni: Mlalo = 86.60 N, Wima = 50.00 N b) Nguvu F = 100 \, N. Pembe ni 85^ kutoka wima. Step 1: Kokotoa kijenzi cha mlalo. Kijenzi cha mlalo (F_x) = 100 85^ F_x = 100 × 0.9962 F_x = 99.62 \, N Step 2: Kokotoa kijenzi cha wima. Kijenzi cha wima (F_y) = 100 85^ F_y = 100 × 0.0872 F_y = 8.72 \, N Vijenzi vya (b) ni: Mlalo = 99.62 N, Wima = 8.72 N c) Nguvu F = 120 \, N. Pembe ni 40^ kutoka mlalo. Step 1: Kokotoa kijenzi cha mlalo. Kijenzi cha mlalo (F_x) = 120 40^ F_x = 120 × 0.7660 F_x = 91.92 \, N Step 2: Kokotoa kijenzi cha wima. Kijenzi cha wima (F_y) = 120 40^ F_y = 120 × 0.6428 F_y = 77.14 \, N Vijenzi vya (c) ni: Mlalo = 91.92 N, Wima = 77.14 N d) Nguvu F = 120 \, N. Pembe ni 10^ kutoka mlalo. Step 1: Kokotoa kijenzi cha mlalo. Kijenzi cha mlalo (F_x) = 120 10^ F_x = 120 × 0.9848 F_x = 118.18 \, N Step 2: Kokotoa kijenzi cha wima. Kijenzi cha wima (F_y) = 120 10^ F_y = 120 × 0.1736 F_y = 20.83 \, N Vijenzi vya (d) ni: Mlalo = 118.18 N, Wima = 20.83 N That's 2 down. 3 left today — send the next one.