If you lean back in a chair, the two back legs act as a pivot. You can only lean so far back without falling over. Explain why in terms of your centre of mass and a turning force.
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Falling back in your chair is something that's happened to all of us, and there’s a simple explanation to why something so clumsy can sneak up on you. I’m Grady, and this is Practical Engineering. On today’s episode, we’re talking about static stability, or the study of objects at rest, and how far is too far to lean back in your chair.
One thing I love about engineering is that it gives us the tools to communicate concepts that we already know through intuition. It’s second nature to us that pushing on this block will cause it to fall down, or that tall, narrow objects aren’t very stable. Even cats can grasp this. Statics allows us to take our intuitions one step further and answer specific questions like how hard can I push this before it falls down, or how narrow can this be before it’s unbalanced. Engineers use the same methods to answer questions like how many trucks can this bridge support, and how heavy does a dam need to be to resist the pressure of all that water?
It all starts with Newton’s Second Law, which says that a net force on an object will cause it to accelerate. Well, we don’t want our roads, bridges, dams, and buildings to accelerate. In fact, the job description of a structural engineer is essentially just to make sure that acceleration doesn’t occur. So to keep things static, we need we need to balance our forces. Here’s a simple example of how this works. Imagine an object is floating in space… any object will do. How about a classic square? Applying a force to this object would cause it to accelerate. If you’re an aerospace engineer, your job is finished here, but in civil engineering terms, acceleration is bad news. So, we can add another force to make the net force acting on the object zero. We’ve achieved static equilibrium, which means we keep our job for another day.
Stay with me because now it gets fun. What if I take the two forces on this object and adjust them so they are not inline with one another. The sum of the two forces is still zero, but you intuitively know that this object is not going to be static. It’s going to spin. A rotational force is known as a moment or torque. If an engineer tells you they shared a moment with someone special, keep that alternate definition in mind. Here’s another intuition you already have: torque is the product of the force and its distance from the center of rotation. So a small force with a long lever arm is equivalent to a large force with a small lever arm. Static equilibrium requires not only that net forces be zero, but also that the moments be zero as well. And that’s really all there is to it. For an object to be at rest, you simply have to satisfy these two conditions. Static analysis involves adding up all of the forces and moments on an object and making sure they sum to zero.