Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_1

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The 50-kg homogeneous smooth sphere rests on the 30° incline A and bears against the smooth vertical wall B. Calculate the contact forces at A and B. Problem 3/1 (a) Contact force at the incline A () 1. Formula: From the equilibrium of forces in the vertical direction (-axis), the vertical component of the normal force at must balance the weight of the sphere. 2. Substitution: Substitute the given mass , gravity , and the angle of the incline . 3. Calculation: Solve for . Calculate weight: Calculate cosine: Perform division: 4. Result: ● Final Conclusion: The contact force exerted by the incline at point is acting perpendicular to the incline surface toward the center of the sphere. (b) Contact force at the vertical wall B () 1. Formula: From the equilibrium of forces in the horizontal direction (-axis), the horizontal component of the normal force at must balance the normal force from the vertical wall at . N A y A F = ∑ y 0⟹N cosθ− A mg=0 m=50 kgg= 9.81 m/s 2 θ=30 ∘ N cos30= A ∘ 50×9.81 N A W=50×9.81=490.5 N cos30≈ ∘ 0.8660 N = A ≈ 0.8660 490.5 566.38 N N ≈ A 566 N A566 N N B x A B F = ∑ x 0⟹N sinθ− A N = B 0 2. Substitution: Substitute the calculated value of and the angle . 3. Calculation: Solve for . Calculate sine: Perform multiplication: 4. Result: ● Final Conclusion: The contact force exerted by the vertical wall at point is acting horizontally toward the center of the sphere. ✨ Final Answer Summary (a) (b) Mecademy AI Sol