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I was watching this awesome video about golf ball striking until they failed. It's a team video with YouTubers Destin Sandlin (Smarter Every Day) and Mark Rober. In the video, Destin and Mark want to understand how hard it is to hit a golf ball. Not how difficult you could hit, or even how much the best golfer in the universe could hit him. They wanted to find the blow so hard that he was destroying the balloon. SPOILER ALERT: They destroyed the golf ball.
But here is the cool part. If you hit a ball like a normal human, the ball is squeezed in contact with the golf club. During this compression, the ball acts essentially as a spring. Yes, it is compressed for a very short time, but then it returns to its original position. This is what is called elastic compression. All springs of introductory physics belong (probably) to this category of elastic compression (or stretching). In fact, it's Hooke's law. This is a model of the force exerted by a spring that says the spring force is proportional to the amount of spring compressed or stretched. Like an equation, it looks like this:
Rhett Allain
In this expression Fs is the force exerted by the spring, s is the amount of compression, and k is the constant spring – a measure of the rigidity of a spring. You will often see a negative sign in this equation. Some people say it to emphasize that the force is in the opposite direction of the stretch. But let me be clear. Everything does not follow Hooke's law – it's not really a law but rather a directive (it's actually a scientific model). There are objects and situations in which the object does not do not need to have a linear relationship between strength and stretch.
But if you compress too much a golf ball, it will not return to its original state. Instead, it is crushed and distorted. It still has spring properties, but it's just not like before. It's different. This is what is called plastic deformation. For example, imagine that you have clay. If you press it too hard, it will warp and take on a new shape. He will not behave as before.
Of course, an object can be both elastic and plastic; the classic example is the common trombone. Take one and separate it so that it looks like this.
Rhett Allain
In the video, Destin explains the elastic / plastic properties of a paper clip with the help of a graph looking like this.
Rhett Allain
It's a pretty visual that shows the main point: if you push the trombone too far, it will move into the elastic region. This means that it will not come back to the same starting position when you remove the force, it will be different. Almost all materials make this transition to the plastic region at some point. But why not create a graphic like this in real life? Yep. That's what I'm going to do. I will even use a paper clip.
Rhett Allain
This looks basic, but it should do the trick. I have a paper clip with one end blocked with the help of a vice clamp. The other end of the trombone is attached to a force sensor and a rotary motion sensor. The force sensor will obviously measure the force – the rotary motion sensor will actually measure the displacement. By knowing the radius of a wheel, I can convert an angular position to a linear position. The combination of these two sensors will give me a strength / position graph. Here is what it looks like.
It's a little tricky to look at this data. Remember this is the force against the position – it does not show the time. If you use your imagination, you can visualize what is happening. Once squeezed a little bit, the trombone moves into the part of the plot that I have surrounded as "elastic". It just goes back on that same line by tracing the data. It's a normal spring. But then, when you squeeze it too hard, it comes back to a different region with a different end position. Yes, it's distorted.
But what is very important in this plot, is that the elastic region is not the area under the curve (the blue thing in the example of Destiny). No, the elastic part is just a line.
If you find the slope of any of this data, it would give you the effective spring constant (k) of the paper clip. Note that the slope in the plastic region is quite similar to the slope of the elastic region. In fact, this trombone will always be well behaved (elastic) but with a different length.
Oh, what about a spring of traditional physics? Like the kind you use in the physics lab. What happens when one of these is overworked? Here is a similar graph of strength versus the position of a spring.
Note that in this case, the spring has been stretched a lot further than this trombone. In fact, it goes from about 10 centimeters to almost a meter. Even then he had barely entered the plastic area. In addition, since spring has "behaved", it is a little easier to find the spring constant. From the slope of the linear adjustment, this spring has a constant of about 8.6 Newton per meter, even after being partially destroyed. Really, it is awesome. You know that physics lab students are abusing these sources (not really on purpose). But even after being overwhelmed, they can still be modeled with Hooke's law.
What about this golf ball in Destin and Mark's video? Nope. This thing is gone. Even the ball that stays intact will not behave as it was before the shot.
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