Math Problem Statement
A uniform ladder of length 7m against a vertical wall. It makes an angle of 45 with the wall. The coefficients of friction between the ladder and the wall is 1/3 and between the ladder and the ground is 1/2. A girl whose weight is half that of the ladder slowly ascends the ladder. Find how far up along the ladder will she climb before the ladder begins to slip.
Solution
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Math Problem Analysis
Mathematical Concepts
Statics
Friction
Torque
Equilibrium
Trigonometry
Formulas
Horizontal equilibrium: N1 = μ2 * N2
Vertical equilibrium: N2 = W_L + W_G + μ1 * N1
Torque equation: W_L * 3.5 + W_G * x = N1 * 7 + μ1 * N1 * 7
Trigonometry: sin(45°) = cos(45°) = 1/√2
Theorems
Equilibrium conditions
Torque balance
Suitable Grade Level
University Level (Engineering/Physics)
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