A 5. 00-m-long ladder, weighing 200 n, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1. 20 m away from the wall. The center of mass of the ladder is 2. 50 m from its base, and the coefficient of static friction between the ladder and the floor is 0. 200. How far up the ladder, measured along the ladder, can a 600-n person climb before the ladder begins to slip?.

A ladder is a piece of equipment consisting of repeated bars or steps (rungs) between two upright lengths of metal, wood, or rope, used for climbing up or down something.
Choosing the Right Ladder. Ladders are built from one of three basic materials; wood, fiberglass and metal (aluminum).
Ladder diagrams are specialized schematics commonly used to document industrial control logic systems. They are called “ladder” diagrams because they resemble a ladder, with two vertical rails (supply power) and as many “rungs” (horizontal lines) as there are control circuits to represent.
Maintain a 3-point contact (two hands and a foot, or two feet and a hand) when climbing/ descending a ladder. Stay near the middle of the ladder and face the ladder while climbing up/down. Use a barricade to keep traffic away from the ladder. Keep ladders free of any slippery materials.

0.488 m

If θ be the angle ladder makes with the plane

cos θ = 1.2 / 5

Tan θ = 4.04

Let the height a person of weight 600 N can climb be h from the ground .Distance from the base point where ladder touches the floor = h / tanθ

= h / 4.04

Total reaction force = total downward force

R = 200 + 600

800 N

Frictional force = μ R

= .2 x 800

= 160 N

Taking moment of force about the point on the ladder where it touches the floor and balancing them

200 x 1.2 x .5 + 600 x h / tanθ = μ R x 1.2 / tanθ ( reaction at the top point of ladder where it touches the wall is R₁ and

R₁ =μ R )

= 200 x 1.2 x .5 + 600 x h / tanθ = 160 x 1.2 / tanθ

120 - 600 h / 4.04 = 47.52

120 - 47.52 = 600 h / 4.04

72.48= 148.51 h

h = 0.488 m

=

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