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 where x = 1.60 m. A painter of mass 71.0 kg 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.) the tension in the horizontal bar connecting the two halves of the ladder the normal forces at A and B the components of the reaction force at the single hinge C that the left half of the ladder exerts on the right half (rightward component) (upward component)

Explanation / Answer

A) height of ladder = sqrt(4^2-0.8^2) = 3.9192 m

consider ladder man system,

Taking torque about A,

Mg*x/2*3/4 = Bx

B = 71*9.8*3/8 = 260.9 N

A = Mg - B = 71*9.8 - 260.9 = 434.9 N

Let the tension be T. Balancing forces in horizontal on left ladder,

T + Cx = 0

Balancing forces in verical on left ladder,

A = Mg - Cy = 71*9.8 -Cy

Cy = 71*9.8 - A = 260.9 N

Balancing torque about the left bottom

Mg*(x/2)*3/4 + T*3.9192/2 - Cy 0.8 + Cx *3.9192 = 0

71*9.8*0.8*3/4 - T*3.9192/2 -0.8*260.9 = 0

T = [71*9.8*0.8*3/4 - 0.8*260.9]/[3.9192/2]

= 106.53 N

) Normal at A= 434.9 N

B = 260.9 N

C) Cxb = -Cx = 106.53 N

Cyb =-Cy = - 260.9 N

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