Static Equilibrium Problem 50˚ A B C D E F G

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Class Problem: Three cylinders, each weighing 8N, are stacked in a box as shown. Determine: The force exerted by cylinder B onto cylinder A. The forces exerted onto cylinder B by the vertical and horizontal surfaces at D and E. Since part a is asking for B onto A, we need to draw the FBD that shows B exerting a force on A 50˚ A B C D E F G x y 𝐹 𝑥 = 𝐹 𝐵 ∙ 𝑐𝑜𝑠 50° − 𝐹 𝐶 ∙cos⁡(50°)=0 A 8N 𝐹 𝑦 = 𝐹 𝐵 ∙sin⁡(50°)+ 𝐹 𝐶 ∙sin⁡(50°)−8𝑁=0 2x2 system of equations 𝐹 𝐵 50˚ 50˚ 𝐹 𝐶 𝐹 𝐵 =5.22𝑁 𝐹 𝐶 =5.22𝑁 x y 𝐹 𝐴 =5.22𝑁 Can you make a conclusion about the force of A on B based on what you determined the force of B is on A? They are the same FB = FA 50˚ B 8N 𝐹 𝑥 =−5.22𝑁∙ 𝑐𝑜𝑠 50° + 𝐹 𝐷 =0 𝐹 𝐷 =3.36𝑁 𝐹 𝐷 𝐹 𝑦 =−5.22𝑁∙ 𝑠𝑖𝑛 50° + 𝐹 𝐸 −8𝑁=0 𝐹 𝐸 =12.0𝑁 𝐹 𝐸