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Why a golf ball is compressed like a spring – until it breaks

I watched this great video about hitting golf balls until they fail. It's a team-up video featuring creators Destin Sandlin (Smarter Every Day) and Mark Rober. In the video Destin and Mark want to find out how hard you can beat a golf ball. Not how hard you could beat or even how hard the best golfer in the universe could beat it. They wanted to find the hit that was so hard that it destroyed the ball. SPOILER ALERT – You destroyed the golf ball.

But here is the cool part. If you hit a ball like a normal human being, the ball is compressed when it comes into contact with the golf club. During this compression, the ball essentially acts like a spring. Yes, it compresses for a very short time ̵

1; but then returns to its original position. This is called elastic compression. All springs in the introduction physics belong (probably) to this category of elastic compression (or stretching). That's what Hooke's law is all about. It is a model of the force exerted by a spring and states that the spring force is proportional to the amount by which the spring is compressed or stretched. As an equation, it looks like this:

Rhett Allain

In this expression F s is the force exerted by the spring, s is the amount of compression, and k is the spring constant – a measure of the stiffness of a spring. In this equation, a negative sign is often displayed. Some people put it there to emphasize that the force is in the opposite direction of the track. But let me be clear. Everything does not follow Hooke's law – it's not really a law, but rather a guideline (actually it's a scientific model). There are objects and situations in which the object need not have a linear relationship between force and strain.

However, if you compress a golf ball too much, it will not return to its original position. Instead, it is smashed to deform. It still has spring-like qualities, but it is not the same as before. It is different. This is called plastic deformation. For example, imagine you have some clay. If you squeeze it too tight, it deforms and has a new shape. It will not behave like before.

Of course, an object can be both elastic and plastic. The classic example is the common paper clip. Take one and pull it apart to look like this.

Rhett Allain

In the video Destin explains the elastic and plastic properties of a paperclip with a graphic that looks something like this.

Rhett Allain

This is a nice picture that shows the main point: if you press the paperclip too far, it will move to the elastic area. This means that it does not return to the same starting position when you remove the force, it will be different. Almost every material eventually makes this transition into the plastic area. But how about creating a diagram like this in real life? Yup. I will do that. I will even use a paper clip.

Rhett Allain

It looks easy, but it should do the trick. I have a paperclip, one end of which is held with a pair of pliers. The other end of the paper clip is attached to a force probe and a rotary motion sensor. The force probe obviously measures the force – the rotation sensor actually measures the displacement. If I know the radius of a wheel, I can convert the angular position to a linear position. The combination of these two sensors gives a force-position diagram. That's how it looks.

It is difficult to look at this data. Remember, this is power versus position – it does not show time. But if you use your imagination, you can imagine what happens. When the paper clip is squeezed a little, it moves into the part of the plot that I've circled as "elastic." It simply moves back and forth on the same line, keeping track of the data. This is a normal spring. But if you squeeze it too hard, it will return to a different end position in another region. Yes, it is deformed.

But the most important thing about this plot is that the elastic area is not the area under the curve (the blue stuff in Destin's example). No. The elastic part is just one line.

When you determine the slope of part of this data, you get the effective spring constant (k) for the paperclip. Note that the slope in the plastic region is quite similar to the slope in the elastic region. In fact, this paper clip is still good-natured (elastic) but with a different length.

Oh, what about a traditional physics spring? Like the kind you use in the physics lab. What happens if one of them is stretched too far? Here is a similar plot of force versus position for a spring.

Note that in this case the spring stretched much further than this paperclip. In fact, it goes from about 10 centimeters in length to almost a meter. Even then, it was barely in the plastic field. Since the spring has "behaved", it is also a bit easier to find the spring constant. Based on the slope of the linear fit, this spring has a constant of about 8.6 Newtons per meter – even after partial destruction. Really, that's great. You know that students in the physics lab are abusing these sources (not really on purpose). But even if they are overstretched, they can still be modeled using Hooke's law.

What about the golf ball in the video by Destin and Mark? Nope. The thing is gone. Even the ball that stays intact will not really behave like the ball before the hit.

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