I watched this amazing video about hitting golf balls until they succeed. It's a team video with YouTubers Destin Sandlin (Wiser Every Day) and Mark Rober. In the video, Destin and Mark want to figure out how hard you can hit a golf ball. Not like the hard that you could intervene, or even how the best golfer in space could hit him. They wanted to find a hit that was so heavy that they destroyed the ball. SPOILER ALERT – Destroyed the Golf Ball
But here's the cool part. If you hit a ball like a normal person, the ball will be pressed in contact with the golf club. During this compression, the ball acts essentially as a spring. Yes, it is pressed for a very short time ̵
In this term F s is spring force, s is compression size and to ] is a spring constant – spring stiffness measure. You often see a negative sign in this equation. Some people have pointed it out to emphasize that the force is in the opposite direction of the section. But let me be clear. Everything doesn't match Hook's law – it's not really a law, but rather a guideline (in fact it's a scientific model). There are some objects and some situations in which the object does not have no must have a linear relationship between force and stretch
But if you compress the golf ball too much, it will not return to its original state. Instead, it breaks so that it deforms. It still has spring properties, but it's not the same as before. That's different. This is called plastic deformation. As an example, imagine you have some clay. If you press it too hard, it will deform and be in a new shape. It will not behave as it did before you pressed it
Of course, the item may be both elastic and plastic; a classic example is a conventional paperclip. Take one and pull it out so it looks like this:
In Destin, the elastic and plastic properties of a paper clip with a chart that looks something like this are explained.
This is a nice visual that shows the main point – that if you press the paper clip too far, it moves into the elastic area. That is, it will not be removed to the same starting position when you remove power, it will be different. Almost every material makes this transition to the plastics area at some point. But what about making a real-life chart? Yes. That's what I'm going to do. I will even use a paperclip
It looks like a basic one, but it should be a trick. I have a paper clip with one end stationary using some pliers. The other end of the paperclip is attached to a force transducer and a rotary motion sensor. The force probe will, of course, measure the force – the rotary motion sensor actually measures the shift. By knowing the wheel radius, I can convert the angular position to a linear position. The combination of these two sensors gives me a graph of the position of the force. Here's how it looks
It's a little complicated looking at this data. Remember this is a force vs. position – does not show time. However, if you use your imagination, you can imagine what will happen. As she squeezes just a little, the clip moves up into that part of the land I circled as "elastic". It just goes back and forth on the same line of retracing data. This is a normal spring. But then, when you press it too hard, it returns to another region with another final position. Yes, it is deformed
But a very important thing about this plot – the elastic area is not the area under the curve (blue things in the Destin example). The elastic part is just a line
If you have found the slope of any part of this data, you would have an effective spring constant (k) for the paper clip. Note that the slope of the plastic region is relatively similar to that of the elastic region. In fact, this paper clip will still be well behaved (elastic) but of different length.
Oh, what's the traditional source of physics? Like the kind you use in a physical lab. What happens when one of them is stretched too far? Here is a similar graph of force versus spring position.
Note that in this case the spring was stretched further much more than this paperclip. In fact, it is about 10 centimeters to almost a meter. Even then, it hardly got into the plastics industry. Also, because in the spring "kept" it's a little easier to find a spring constant. From the slope of the linear fit, this spring has a constant of about 8.6 Newtons per meter – even after partial destruction. Really, it's great. You know that students in the physical lab are abusing these sources (not for purpose). But even after they have stretched, it is still possible to model Hook's law.
What about the golf ball on Destin and Mark? Not. The thing is gone. Even a ball that remains intact will not really act like a ball that was before the hit.
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