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# Equilibrium in 2D - Ladder Problems

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Sections
Center of Mass & Simple Balance
Equilibrium with Multiple Objects
More 2D Equilibrium Problems
Equilibrium in 2D - Ladder Problems
Equilibrium with Multiple Supports
Torque & Equilibrium
Review: Center of Mass
Beam / Shelf Against a Wall

Concept #1: Equilibrium in 2D - Ladder Problems

Transcript

Hey guys! In this video, we're going to start solving equilibrium questions that are two-dimensional and IÕm going to give an example of a classic problem in equilibrium that is the latter problem. Let's check it out. So far we've solved equilibrium problems that were essentially one-dimensional, meaning all the forces acted in the same axis, either you had all the forces in the x-axis or all the forces in the y-axis, most of them in the y-axis. Even if you had something at an angle like this, let's say you had something like this, that's still essentially one-dimensional because the angles were the same when we wrote the torque equation and they cancel. In all the problems weÕve solved so far, sin_ in the torque equation never really mattered because it either canceled or it was just the sin90 which is 1. Now we're going to finally solve some problems where that's not the case. We're going to actually have to worry about the angle. More advanced problems as it says here will include problems in two dimensions in two axes. Some of them in some of these cases, we may need to decompose the forces. Some of them will be decomposed. Remember however the torques are scalars so we will never need to decompose them. We're going to decompose forces in problems, but we don't have to decompose torques because torques are scalar. They may be positive or negative but they are scalars. They don't have a vector direction. Let's check out this problem here.

Practice: A ladder of mass 20 kg (uniformly distributed) and length 6 m rests against a vertical wall while making an angle of Θ = 60° with the horizontal, as shown. A 50 kg girl climbs 2 m up the ladder. Calculate the magnitude of the total contact force at the bottom of the ladder (Remember: You will need to first calculate the magnitude of N,BOT and f,S).

Example #1: Minimum angle and friction for ladder

Transcript