Answer to Question #215292 in Physics for Sera

Question

A uniform ladder weighing 100N leans against a smooth vertical wall with its lower end resting on a rough floor, the ladder making an angle of 70o with the horizontal. Find (a) the force exerted by the wall on the ladder and (b) the force exerted by the floor at the lower end of the ladder.

Answer 1

(a)

$$\sum F_x=F_{fr}-F_{wall}=0,$$ $$F_{wall}=F_{fr}.$$ $$\sum \tau=0,$$ $$\tau_{wall}=\tau_{ladder},$$ $$F_{wall}Lcos\theta=\dfrac{L}{2}W_{wall}sin\theta,$$ $$F_{wall}=0.5W_{wall}tan\theta=0.5\cdot100\ N\cdot tan70^{\circ}=137\ N.$$

(b)

$$\sum F_y=F_{floor}-W_{ladder}=0,$$ $$F_{floor}=W_{ladder}=100\ N.$$