[#video: https://www.youtube.com/embed/Q7DDsCP6y8k&feature=youtu.be
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It's easier to follow the rules when you understand why they're there in the first place. In this case, the rule is "Wear your hard hat, fool." On a construction site, you are supposed to wear a hard hat just in case something falls on you. In the video above, you can see what happens when a one-pound nut and bolt fall 20 feet, and then 30 feet, onto a watermelon with a face drawn on it to resemble a head. The head is then protected with a hard hat. Maybe you can learn a lesson here.
Let's go through the physics of this situation. The video claims that the one-pound piece will have an impact force of about 2,000 pounds when it collides after falling 20 feet. I'll be honest, I am skeptical. It's really difficult to calculate the impact force for a couple of reasons. First, the impact force is typically not just one constant value&#;instead, it changes over the short time interval during the collision. Second, the impact force depends on the stopping distance. If the bolt hit a hard surface and stopped in a super short period of time, the impact force would be much larger than if it hit a soft surface (soft like a watermelon head). Sometimes it's just easier to consider the force over some impact distance. But still, a shorter impact distance means a shorter impact time.
Let's do it. How do you estimate the impact force? The falling bolt problem doesn't really depend on the time of the fall. (Well, we just don't really care about it.) If we focus on the falling distance and the stopping distance, this problem is a perfect situation in which to use the work-energy principle.
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What is the work-energy principle? It basically says that the work done on a system is equal to the change in energy of the system. Work is the product of force and distance. (That's the simple version.) If a force is pushing in the same direction as the motion, it's positive work. If the force acts against the motion, it's negative work. Work and energy are both measured in units of Joules.
Now, for energy. If we consider the system of the bolt plus the Earth plus the melon-head, then there are really two types of energy. There is the kinetic energy (K) of the bolt. This depends on both the mass and the speed of the bolt.
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