It's easier to follow the rules if you know why they're there at all. In this case, the rule is "Wear your hard hat, fool." On a construction site you should wear a safety helmet if something falls on you. In the video above, you can see what happens when a 1 pound nut and a screw fall 20 feet and then 30 feet onto a watermelon with a face that resembles a head. The head is then protected with a helmet. Maybe you can learn a lesson here.
Let's go over 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 a fall of 20 feet. I'll be honest, I'm skeptical. It is very difficult to calculate the impact force for several reasons. First, the impact force is usually not only a constant value, but changes during the crash during the short time interval. Second, the impact force depends on the braking distance. If the bolt hits a hard surface in a very short time and comes to a standstill, the impact force would be much greater than with a soft surface (as soft as a watermelon head). Sometimes it's just easier to consider the force over a certain impact distance. A shorter impact distance, however, means a shorter impact time.
Let's do it. How do you rate the impact force? The problem of dropping the bolts does not really depend on the time of the fall. (Well, we just do not really care about it.) Focusing on the drop and brake paths, this problem is a perfect situation for applying the principle of working energy.
What is the work? Energy principle? In essence, it says that the work done on a system corresponds to changing the energy of the system. Work is the product of strength and distance. (This is the simple version.) When a force pushes in the same direction as the movement, it is a positive work. When the force acts against the movement, it is negative work. Work and energy are measured in units of joules.
Now for energy. Considering the system of the bolt plus the earth plus the melon head, then there are really two types of energy. It gives the kinetic energy (K) of the bolt. This depends on both the mass and the speed of the bolt.
When the bolt falls and accelerates, its kinetic energy increases. But where does this energy come from? This is where the potential energy of gravity (U) comes into play. This energy depends on the gravity field of the earth, the mass of the bolt and the distance between the two objects. Since these are really only energy changes, I can temporarily call the height of the ground a zero point. Yes, that's wrong – but in the end, everything will work out.
In this expression, m is still mass, y is any height, and g is the local gravitational field (about 9.8 Newtons per ton) kilograms). OK, let's put it all together. Here is a diagram that shows the bolt both during the fall and during the collision with the melon head (not to scale):
There is much to discuss in this diagram. Here are some notes:
- The bolt drops 20 feet. But because I hate Imperial units, I converted them to 6.1 meters (and I call it a distance of h).
- After the bolt touches the watermelon, it still moves a bit. I estimate this braking distance to 2.54 centimeters. (This parameter is very important.) I name the braking distance with the variable s.
- Finally, there is some impact force (called F). This is a back-pressing force on the bolt that has a negative impact on the system.
Let's summarize this in the Work Energy Equation. It looks like this:
During the impact, the bolt performs a negative work that corresponds to the change in kinetic energy plus the change in potential gravitational energy. But wait! Since the bolt ends both and at rest, the kinetic energy does not change (beautifully). For the change of the potential energy of gravity it depends only on the vertical distance (h + s). As the bolt moves down, this change in potential is negative.
Now all I have to do is look for the impact force.
That was & # 39; s. I just have to enter my values from the video. The mass of the screw is 0.454 kg, and I estimated the impact distance (rough estimate). Thus, the power (average force) is 1,073 Newton or 241 pounds. This is a little less than the video's claim of £ 2,000. In order to achieve an average impact force, the bolt would have to stop at a shorter distance.
OK, but what if you drop him from 9.14 meters? Yes, the bolt moves faster when it hits the melon. However, it is still stopped and has a total change in the kinetic energy of zero Joule. The real question will be: How far does she get into the melon? If it stopped at the same distance as before, then yes – it would have a higher impact force. Here's my calculation (in Python, so you can change the values), where I get an average impact force of 1,605 N (361 pounds).
In fact, if you drop the bolt from 30 feet instead of 20 feet The bolt goes all the way through the watermelon, it would probably have a lower impact force than if it hits the melon only from 20 feet up. Honestly, I have no idea where they get their values for this video. (You probably need a good science consultant.) Also, the video shows how the effect increases when the bolt falls – that does not make sense either.
Why does the higher falling bolt break the watermelon? If I had to guess (and me too), I would assume that the melon has a fairly constant punch. As the bolt falls from a higher position, the melon must apply the holding force over a longer distance to stop it. That's why it breaks. If the bolt penetrates far enough into the melon, it passes from the rigid bark (the crust) into the soft, sticky parts. This disturbs the structural integrity of the melon and falls apart.
What about the helmet? Does the helmet reduce the impact force? No! In fact, the helmet will (probably) increase the impact force. If the bolt hits the hard hat and stops for a shorter distance, this would produce a higher average force. But the helmet has a very nice thing. Because the hat has a rigid surface, it distributes the impact force over a larger area, which reduces the impact pressure. Less pressure means less chance of the bolt entering your head.
One last thing from the point of view of a scientific adviser (since I occasionally do this stuff): What is the purpose of this video? Is it to show that bad things can happen if you do not wear a hard hat? In this case, the broken watermelon does a good job to convey the point. But if that's the goal of the video, you do not really need the "Impact Force" numbers – just leave them out. If the goal is to teach people the physics of impact, you should better set those numbers.
You could say the physics here is complicated. It's really hard to get everything right. Yes, I agree. But my most important science communication rule is that you can not be 100 percent correct, but you can be 100 percent wrong. I think in this case these numbers are just wrong.
More great WIRED stories