A 10-kg ladder 2.5m long rests against a frictionless wall with its base on the floor 80cm from the wall. How much force does the top of the ladder exert on the wall?

Question

A 10-kg ladder 2.5m long rests against a frictionless wall with its base on the floor 80cm from the wall.  How much force does the top of the ladder exert on the wall?

drwls · Answer

This question has been answered by Damon

http://www.jiskha.com/display.cgi?id=1303587287

The moment of the ladder about the floor support point is zero. The 98 N ladder weight acts downward 0.4 m from the wall.

The wall contact point is sqrt[2.5^2-0.8^2] = 2.37 m above the floor. The force F at the wall contact point is normal to the wall, because it is frictionless there.

Setting the total moment equal to zero,

98*0.4 = F*2.37
F = 16.54 N