I watched this wonderful video about touching the golf balls until they failed. This is a team-up video on YouTubers Destin Sandlin (Smarter Everyday) and Mark Rober. In the video, Destin and Mark want how bad it is to hit the golf ball. No matter how hard you can reach, or even how hard the best golfer in the universe can hit it. They want to find the hit that is very difficult to destroy the ball. SPOILER ALERT-they destroyed the golf ball.
But here's the cool part. If you hit a ball like a normal person, the ball gets compressed in contact with the golf club. During this compression, the ball plays an important role as a spring. Yes, it gets compressed for a short time-but then it returns to its original position. This is called elastic compression. All springs in introductory physics are (perhaps) in this category of elastic compression (or expanding). In fact, this is about Hooke's Law. This is a model for force forced by a spring which states that spring strength is proportional to the amount that the spring is compressed or stretched. As an equation, it looks like:
In this statement F s is the spring leading force, s k is the spring constant-a measure of the stiffness of a spring. You often see a negative sign in this equation. Some people place it there to emphasize that the force is in the opposite direction of the stretch. But let me know to be clear. Everyone does not follow Hooke's Law-not really a law but more like a guideline (really a science model). There are several things and some situations where things are not not need to have a linear relationship between force and stretch.
But if you're tapping a golf ball too much, it does not return to the original state. Instead, it cuts so that it is deformed. It still has properties like spring, but it is not the same as before. This is different. This is called plastic deformation. As an example, imagine you have some clay. If you prevent it too hard, it will appear and even in a new shape. It will not do the same as before you touched it.
Of course, something can be both resilient and plastics; The classic example is the common paperclip.
In the video, Destin explained the elasticity compared to the plastic properties of a paperclip with a graph that looks like this.
It's a beautiful visual showing the main point-that if you push the paperclip too far, it's going to move to the elastic region. This means that it will not return to the same position when you remove the force, it will be different. It's quite a bit that every material is moving it to the plastic region at some point. But how do we make a graph like this in real life? Yes. That's what I do. I use a paperclip.
It looks basic, but it should do the trick. I have a paperclip with one end held stationary with some vice pliers. The other end of the paperclip is attached to a force probe and a rotary motion sensor. The force probe clearly measures the force-the rotary motion sensor actually measures the displacement. By knowing the radius of a wheel, I can convert the angular position to the linear position. The combination of two sensors will give me a force compared to the position graph. Here's what it looks like.
This is kind of confusing look at this data. Remember, this is force vs. position-it does not show time. If you use your imagination, however, you can illustrate what will happen. When slipping a little, the role paper moves to that part of an outline that I have enclosed as "elastic." Just go it over and over to this same line followed by the data. That's a normal spring. But when you're pushing it very hard, it drops into another region with a different position. Yes, it is deformed.
But the most important thing about this framework-the elastic region is not the area under the curve (the blue object in Destin's example). No The elastic part is only one line.
If you find the slope of any part of this data, which will give you an effective spring constant (k) for the paperclip. Notice that the slope during the plastics era is somewhat similar to the region's flexible slope. In fact, this paperclip will still have good leverage (elastic) but with different lengths.
Oh, what about a traditional spring of physics? Like the kind you use in physics lab. What happens when one of them reaches too far? Here is a similar plot of force compared to the position for a spring.
Notice that in this case, the spring has increased more more than that paperclip. In fact, it goes from about 10 centimeters long to nearly one meter. Even though it is not just about to enter the plastic region. Also, since spring "behaved" it is a little easier to find the spring constant. From the slope of the linear fit, this spring has a constant of around 8.6 Newtons per meter-even after getting slightly destroyed. Of course, this is great. You know students physics lab abuse of these springs (not necessarily the goal). But even after over-stretched, it can still be modeled on Hooke's Law.
What about that golf ball in the video from Destin and Mark? Nope. That thing is gone. Even the ball that remains intact does not actually act like this ball before the hit.
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