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It’s so simple, yet we can’t analyse it!

Suppose forces on an object aren't acting at a point, and you can't use sliding vectors or other tricks to convert them.
This is the most important week in the course– how to apply equilibrium in two dimensions, a powerful capability. So far, we’ve analysed forces that act at a point. Now we’ll analyse forces that act anywhere on a two-dimensional rigid body. That’s one you can represent on a sheet of paper. In this week’s design task, we’ll choose the bolts that connect the parts of a folding washing line like this one. Here’s an FBD we’ll use. It’s very different from the loudspeaker task in week 2. To see why, we’ll look at a simpler rigid body– this sheet of cardboard. We’ll hang a weight pan on the centreline. Last week, we saw how to find forces that act at a point, like this.
But what if the strings don’t meet in a point? We’ll try hanging the cardboard from two parallel lengths of string. Parallel lines never meet. Each string is 70 millimetres from the centreline. Because it’s symmetrical, the combined weight acts on the centreline of the sheet. What’s the tension in the string on your left? Did you get it? From equilibrium, the two strings share the total load. And because it’s symmetrical, the tension in each string is the same. So each string takes half the load. Recognising symmetry can make problems much simpler. But our washing line FBD isn’t symmetrical. To represent this, we’ll move the load on our cardboard off-centre so it’s not symmetrical anymore.
What can engineering intuition tell us about the tensions now? Well, together they equal the total weight, because of equilibrium. And the string on your left will take a bigger share of the load. But intuition can’t tell us what each tension is. Surprisingly, we’ll need to know about the twisting effect of a force for that. So we’ll start this week by learning about twist. Twist gives us an extra equilibrium equation. With this equation, we will be ready to apply equilibrium– that’s Newton’s first law– to any two-dimensional rigid object. You’ll need FBDs, of course, and they might be complicated. You’ll learn more about them later this week. All of this will be in two dimensions.
Luckily, many objects in engineering can be treated as 2D even though they might seem like 3D. You’ll see this in the design task. It’s time for the most important week in the course.

Suppose forces on an object aren’t acting at a point, and you can’t use sliding vectors or other tricks to convert them.

How can you apply equilibrium to find the forces you need for design?

We’re into the realm of the ‘rigid body’.

Sometimes you can find what you need from symmetry. But for most cases you’ll need something more. You’ll need to consider the twisting effects of forces.

This video introduces these concepts, and shows you why you need them for design.

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Through Engineers' Eyes - Introducing the Vision: Engineering Mechanics by Experiment, Analysis and Design

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