Answer to Question #215295 in Physics for Sera

Question

The weight of a uniform ladder 13 feet long is 150 N. It is placed against a smooth wall so that its lower end is at a distance of 5 feet from the wall. A man weighing 490 N stands on the ladder at a point 3 feet from the upper end. (a) Find the force which the ladder exerts against the wall and (b) find the horizontal and vertical components of the force exerted by the ladder on the floor.

Answer 1

$3\ feet=0.9144\ m$

$5\ feet=1.524 \ m$

$13 \ feet=3.9624\ m$

$\cos\phi=1.524/3.9624=0.3846$

(a)

$\sum \tau=0\to N_{w}\cdot3.6576-150\cdot(3.9624/2)\cdot0.3846-$

$-490\cdot(3.9624-0.9144)\cdot0.3846=0\to N_{w}=188.3\ (N)$

(b)

$N_{ver}=150+490=640\ (N)$

$N_{hor}=N_w=188.3\ (N)$