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 and 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

Did you find an error or inaccuracy? Feel free to write us. Thank you!

Tips for related online calculators
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: