Components 67664

The force R = 12 N is divided into two components, F1 and F2. Their directions make angles α = 30 °, β = 45 ° with the direction R. What are the components F1, F2?

Correct answer:

F1 =  6.2117 N
F2 =  8.7846 N

Step-by-step explanation:

R=12 N α=30  β=45   x=R cosβ=R cos45° =12 cos45° =12 0.707107=8.48528 y=R sinβ=R sin45° =12 sin45° =12 0.707107=8.48528  γ=α+β=30+45=75   x=F1+F2 cosγ y=0+F2 sinγ  F2=y/sinγ=y/sin75° =8.4853/sin75° =8.4853/0.965926=8.78461 N  F1=xF2 cosγ=xF2 cos75° =8.48538.7846 cos75° =8.48538.7846 0.258819=6.212=6.2117 N



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