﻿ Experiments: static and dynamic loads

# Experiments: static and dynamic loads

Your first experiments are based on a rubber band spring.
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This week’s experiments all use a chain of rubber bands. We’ll use it for weeks two and three too. Here’s what we’ll do. We hung our chain of rubber bands from a wooden beam like this. You might have a better idea. If you do, please share it with us and your fellow students via the discussion for this step. To make the chain itself, we’ll link rubber bands together using paper clips, like this. Next week, we’ll need two chains that are similar, so we got enough identical bands and identical small paper clips for both.
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The paper clips distribute the load evenly on both sides of the rubber bands. If instead we knotted the bands together, one side might be shorter and take loads sooner and confuse the measurements. Before we move on, take a few moments to consider why we might need to use more than one rubber band. The answer - it’s for measurement resolution. We’ll need to measure the stretch of the bands with a rule, which isn’t easy, but you can probably measure to about plus or minus a millimetre. So for good accuracy, we want a chain that extends about 100 millimetres when moderately loaded. We’d expect to join several bands to get that. More bands means more extension for the same load.
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For our setup, two of these rubber bands deflected about right when loaded with 40 washers. We’ll explain the washers later. To load the chain, we hooked a weight pan onto the bottom paper clip. For these experiments, we’ll need just one weight pan, but later we’ll need a matched pair, so now was a good time to make them both. We cut these two from the bottom of plastic milk bottles and added string handles.
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We’ll need some identical weights. These steel washers are ideal. We’ll need a rule or tape measure, too.
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Let’s see how the chain behaves under static conditions. Static means that the load is stationary. It’s in equilibrium. Much more on this later. We’ll start by seeing what happens when we load it up. These are the steps.
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Measure the initial length with just the weight holder connected. We got 144 millimetres. Then, load it with 40 washers and measure it again. We got 281 millimetres.
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Then we left it for five minutes and measured again. In our test, it extended to 285 millimetres, four millimetres more. That’s creep. It occurs with rubber and plastics at ordinary temperatures. It happens with metals, too, but generally at higher temperatures. For example, creep is important when designing turbine blades in jet engines. Now, back to our rubber bands. We’ll unload them and measure again. We got 148 millimetres. Remember that it was 144 millimetres when we first started. We’ll wait and measure it again. When we did this, we got 145 millimetres, close to the starting value but not quite the same. We might have some permanent stretch. Load deflection curve.
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Now we’ll load the chain up gradually and plot a chart of load versus length using a spreadsheet programme or graph paper. Notice how we unloaded the chain between each measurement to give less time under load for creep to occur. We did the tests twice, once with two bands for moderate loads - we’ll use this configuration in later experiments - then, with just one band so we could do the test over a wider range of loads. We managed 100 washers this way. With two bands, the pan came down to the floor before we’d finished. Here’s the plot of load versus length for the wide-range test. It’s definitely not a straight line. It’s non-linear. We’ll explain it more in the analysis video.
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Bounce. Here’s how the chain behaves under dynamic conditions. Like a bungee jumper, the weight pan changes its speed as the motion progresses, which means acceleration is important. It’s not in static equilibrium. That’s why it’s called dynamics. Dynamics is the second of the two parts of engineering mechanics. We’ll concentrate on statics in this MOOC, but we will introduce dynamics at the end. Here’s a leap of faith. Dynamics theory for an undamped linear spring says that if you drop the loaded pan from an unstretched height, the spring will extend twice as much as the static extension under the same load. Let’s tease this out. Here’s the height to the bottom of the unloaded pan.
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The chain is unstretched or stretched a little bit to straighten out the bands. Here’s the height to the bottom of the loaded pan under static conditions. Static stretch is the difference. If we now load the pan until its static stretch is half the distance from the unloaded pan to the tabletop, when we drop it from the unloaded height, it should just touch the surface of the table. We’ll try it. Notice it didn’t quite touch the tabletop. We’ll look at this in the analysis video. But what about quasi-statics? Quasi means similar but not quite the same.
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In our case, it is when there are accelerations, but they are small and we can neglect them - for example, when you load up the rig and gently lower the pan. These are times when you can still apply statics theory despite the presence of some acceleration.
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Now for the analysis.
Your first experiments are based on a rubber band spring. You’ll learn about creep, load-deflection curves and bounce.
You will also see how we split Engineering Mechanics into ‘Statics’ and ‘Dynamics’. Textbooks generally come in two separate volumes, one for each.
There are those who say that it’s all Dynamics really, and what we call statics is just Dynamics where the accelerations are all zero. But we think Statics and Dynamics are different enough to justify the split.
But are Statics and Dynamics so clearly differentiated from one another?
Notice that there are situations where accelerations definitely exist, but where we can ignore them for all practical purposes. As an extreme example, there are accelerations when the bands creep, but these miniscule accelerations don’t affect the forces significantly. This is what you might call quasi-static, that is, we know there are accelerations but we can still treat the situation as though it were static.
We hope you’ll try the experiments yourself – get hands-on experience. This one’s simple enough. Why not give it a go?

### Talking points

• Did you see how simple experiments can give you insights? After all, physical reality is physical reality, however you look at it.
• Did you work out why a chain of bands produces a larger deflection than a single band?
• What else did you notice in the video?
• Which of the experiments did you try and what did you find?

If you attempt the experiment, take a photo and upload it to our Through Engineers’ Eyes Padlet wall. You can include a link to your photo in the comments for this step (click on your post on the Padlet wall and then copy the web address).
If you don’t have access to a camera, we encourage you to still do the activity and write a description of your experiment on the Padlet wall.
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