A stepladder of negligible weight is constructed as shown in Figure P12.57 where

Question

A stepladder of negligible weight is constructed as shown in Figure P12.57 wherex=2.30m. A painter of mass66.0kg stands on the ladder 3.00 m from the bottom.

Assuming the floor is frictionless, find the following. (Suggestion: Treat the ladder as a single object, but also each half of the ladder separately.) (a) the tension in the horizontal bar connecting the two halves of the ladder (b) the normal forces atAandB (atA) (atB) (c) the components of the reaction force at the single hingeCthat the left half of the ladder exerts on the right half (rightward component) (upward component) The answers for (a) and (b) are correct. I just need help finding (c). Please show your work and if possible round to four decimal places.

Explanation / Answer

(a)the tension is T = mg/2 where m = 66.0 kg and g = 9.8 m/s^2 (b)the normal forces at A and B are F_A = mg * (3/4) and F_B = mg * (4/3) (c)the components of the reaction force are R1 = mg * cosA and R2 = mg * sinA where A = tan^-1(4/4) = tan^-1(1)

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