A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall, making 60° with the wall. Its lower end rests on a rough floor. Find friction at the floor, taking g = 10 m/s². Image
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A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall, making 60° with the wall. Its lower end rests on a rough floor. Find friction at the floor, taking g = 10 m/s². Image

G1 Physics · Accepted Answer

Step 1: The wall is smooth, so it provides only horizontal normal Nʷ. The floor provides vertical normal Nᶠ and horizontal friction f. Step 2: Horizontal equilibrium: f = Nʷ. Vertical equilibrium: Nᶠ = mg = 200 N. Step 3: The rod makes 60° with vertical; its horizontal projection is Lsin60°, vertical projection Lcos60°. Step 4: Taking moments about the floor contact: Nʷ Lcos60° = mg(L/2)sin60°. Step 5: Nʷ = (mg/2) tan60° = (200/2)√3 = 100√3 N. Step 6: Hence f = Nʷ = 100√3 N. Final answer: 100√3…