Ladder (11 m) that weighs 419 N is placed against a wall?

Question

(smooth & vertical). A person who weighs 356 N stands 3.1 m up the ladder. The foot of the ladder rests on the floor 8.47 m from the wall.

Calculate the force exerted by the wall (in N)?

Calculate the normal force exerted by the floor on the ladder (in N)?

Answer 1

All forces and moments acting on the ladder must be at equilibrium:

Moment at the base of ladder = 0

let x = horizontal distance of man from base

let y = vert height of ladder on wall

let P = Force from wall

so from similar triangles

x / 8.47 = 3.1/11
x= 2.387 m

y=(11^2 - 8.47^2)^(1/2)=7.02 m

so 419x(8.47/2) + 356 x 2.387 = Px7.02

P= 373.8 N



vert force of ladder at the base Fv=419+363=782 N