5 Essential Concepts in Engineering Dynamics
OK, I get it….you’ve finished high school, or maybe even a first degree, but you’re really not sure yet what you want “to be when you grow up”. Maybe you’re on a gap year trip or spending a little too much time on Insta and TikTok. Or perhaps you’re hanging out at the beach all day, and playing the latest video games and Intertops casino bonus games all night.
Need a little direction? Well, I’m here to give it to you.
Engineering Dynamics! Fascinating subject, fascinating studies and fascinating career – all rolled up into one. And I’m here to turn you on to it! What is Engineering Dynamics, you ask? Well, here we go…..
One of the many important subjects you have to learn as an engineer is Dynamics – or the physics behind moving objects. Static objects are all well and good, but if you want to go on to make bigger and better things, like planes, trains, and automobiles, you’re going to have to take into account the additional effects that acceleration has on your system. And it all starts with…
1. Newton’s Laws
Good ol’ Newton! Inventor of calculus, classical mechanics, and gravity- to the bane of rocket scientists everywhere. If you remember your high school physics, you might remember that Newton’s three laws are:
- An object at rest stays at rest, unless another force acts upon it. An object in motion stays in motion, unless bla bla bla.
- The net force upon an object is equivalent to the mass of the object multiplied by its acceleration. In other words, F = ma.
- Every action has an equal and opposite reaction.
All of these are vital for understanding dynamics, but that second one in particular is worth some extra discussion. If you’re taking engineering, up until Dynamics you’ve likely been dealing with either static systems (no motion at all) or systems with constant velocity (no acceleration).
In these situations, the net force on your object equals zero, and our calculations become infinitely easier. But we all have to grow up eventually, so get ready for pages of work for just getting to the equations you need to solve for the parameters you’re actually looking for now that you have to take into account acceleration.
2. Relative Systems
This is actually a concept that’s both a lot simpler and a lot harder than it actually is. Going through the tedious proofs for the equations that end up getting derived is a long, arduous affair, but the concept itself is rather straightforward. Instead of having a static XYZ axis (like you usually do in math class), your entire axial system moves too.
Think about it like this: You want to measure the distance a car has moved along a road. You set your house as the origin, and track how far the car has moved. Simple and easy. However, if you attach your origin (your coordinate system) to the car itself, it doesn’t seem like the car has moved at all! In fact, it seems like the road is what’s moving instead!
The question is, why would I ever want to do that?
Well, imagine now that a stripper is spinning on a pole, on top of the car, and you want to calculate the linear velocity of her tig biddies. You can save yourself a lot of work by placing your origin at the car, so that you can ignore the linear distance and velocity of the car itself.
3. Conservation of Momentum
Momentum, simply put, is “mass in motion”. The idea is that once an object has built up speed, it’s not so easy to get it to stop. An ideal system conserves momentum- think of a bowling ball barreling into the pins. The bowling ball has built up momentum, and once it collides with the pins, some of that momentum gets transferred to the pins- and since the pins are so light, they go flying.
Let’s return to our example: The popo is now coming down the street, and our stripper wants to bail because she’s carrying. She decides to make a break for it by jumping off the car. So here’s the question: How fast is the stripper moving in the horizontal direction the moment after she jumps (assuming she jumps straight up)?
Well, the instant after she jumps, she’ll actually be traveling at the exact same speed as the car. She and the car were traveling as one at first, and that momentum is conserved after she jumps. The only reason she’ll slow down after the jump is because of friction and air resistance.
4. Conservation of Energy
You’ve probably heard of the phrase, “Energy is neither created nor destroyed- only changed”. This is basically true in every extent that matters here.
But let’s start with a fundamental question: What IS energy? In short, energy is an object’s ability to do work, and work is a measure of the force applied over a distance. Pushing an object one meter horizontally requires less work than pushing an object one meter up a hill. When energy is conserved, the total work comes out to zero, because the amount of work that can be done by the system hasn’t changed.
Now let’s look at our example again: Our stripper has jumped off the car, and is plummeting towards the asphalt. If we assume she lands chest first, and that her tiddies function as ideal springs, how compressed will her tiddies be when she lands on the ground?
So, when she’s in the air, at the peak of her jump (before she has begun falling), she has only one source of energy: Gravitational Potential Energy. However, as she falls, that Potential Energy gets converted into Kinetic Energy, and she’ll be falling fastest the moment before she touches the ground. Then, once she splats, that kinetic energy is converted into spring energy. This comes out to a simple and clean equation:
Potential Energy = Kinentic Energy = Spring Energy
mgh = 0.5mv^2 = 0.5kx^2
Then we isolate for x (the change in spring size) to find out how compressed dem tiddies get!
5. Non-Sliding Wheels
Now let’s move away from those other concepts, and talk about one that’s not so intuitive: The humble wheel. The mechanics of how wheels work aren’t extremely complex, but require a lot of understanding of theory.
Let’s compare it to a simple system: A block is pushed across the ground. There’s going to be the force of the push, and the force of friction in opposition to it. If the pushing force is greater than the maximum static friction between the ground and the floor, the block will accelerate- otherwise, it will travel at a constant speed. Regardless, energy is not conserved because of friction.
However, a rolling wheel that’s pushed will rotate in addition to sliding, and because friction has to be opposite to the direction of movement, then the friction will be pointed opposite to the direction of the sliding block.
So if the wheel is rotating clockwise, the friction will be pointed to the right. This is because the rotation creates a moment, that pushes against the ground, and the friction has to be opposite to that force. So technically, when we’re rolling a wheel, we want the friction to be as large as possible, because the friction helps drive the wheel forward!
We also CAN assume that energy is conserved. This is because the point of contact between the ground and wheel technically has zero velocity relative to one another (remember relative systems?). Therefore, the friction is doing zero work, and therefore we can say that energy is being conserved. Pretty cool, right?
I think so, at least.