We all know that the farther from the fulcrum a force is applied to a lever, the greater the force. You can hold a lever steady with a tiny weight against a huge weight, provided the tiny weight is far from the fulcrum and the huge weight is close to the fulcrum, and you can lift anything given a long enough lever. It’s the point of having a lever at all.
Why does this not apply to scissors? Judging by how easily they cut things, the force is greatest closest to the fulcrum. If you want to cut something tough, you don’t use the very points, you open the scissors up as much as possible and put the tough thing all the way in. What is it about scissors that makes them work like that?
Your hands are the input force, a long way from the fulcrum, the cutting edge is the output force, strongest close to the fulcrum. Exactly like a lever.
Good answer, makes sense. But then, and forgive me if this is a stupid question, if I’m swinging a long stick at someone, why do I want to hit them in the head with the end of the stick and not some point closer to my hands?
I believe that the issue is the flexibility of the material. Just to make scissors work, they have to be slightly bent against each other so that the point of contact stays together through the entire stroke. Were they simply made straight, the paper would simply fold over one of the blades and wedge the other blade out around itself, making it ineffective. The bend is why there’s the slight snap as you fully close the scissors - the blades are popping around the edge of each other in order to be able to site alongside each other rather that pushing edge to edge.
The closer to the hinge the metal is, the less the material is able to flex outward, and so the contact between the blades is even more secure and able to bite through the material.
The amount of force necessary to cut through the paper is sufficiently minimal that factors of leverage are inconsequential to the question of how well the blades are able to maintain contact while having something wedged between them.
I get that, but why isn’t it the same deal with scissors then? If I’m closing the scissors, the ends are moving faster than the edged bit closest to the fulcrum.
Scissors are a lever, but the reason they work so well isn’t so much that, as it is that you have a large area to grab with your hands and a very small wedge at the other side to drive through whatever you’re cutting. Ignore the lever part of it for now. A scissors works the same way a knife does. You can cut through a tough steak or an apple without any help from a lever. It’s razor sharp on the business end but half an inch wide at the part where you grab it.
Getting back to a scissors as a lever, if the handle where as sharp as the blade, you’d need it to be considerably further away from the pivot so you wouldn’t have to use as much effort and cut yourself. Similarly, if the blade where as dull as the handle, the handle would still have to be much further away so you could create much more force.
As stated, the end of the stick is moving faster. Having said that I think you’re shoehorning ‘lever’ into places it doesn’t really belong.
A scissors is a lever, but only because that’s what happens when you attach opposing knives to each other.
A swinging stick is a lever, but this is more about tangential velocity.
If you’re smacking someone in the head with a baseball bat, this is a dynamic event: the force being applied to the stick by your hands at the moment of impact is mostly irrelevant, as it’s all about the momentum you’ve delivered to the bat during the swing just prior to impact. Your goal is to create a high impact force; this requires transferring a lot of momentum from your bat to their head, so you want the part of the bat that hits their head to have a lot of speed. For this application, a bat is better than a block of comparable mass because it lets you build up more speed at the point where your bat will impact its target. If you really want to optimize the situation you concentrate as much of the mass as practically possible on the moving end of your weapon, and you end up with a mace or a war hammer. The extreme opposite situation is a spherical ball of wood of the same mass as your baseball bat or mace, and you throw it at your target’s head. You won’t be able to get this ball of wood moving nearly as fast as your bat; yeah, it’ll probably hurt your target if it hits them in the head, but one good hit with a bat will probably kill them.
If you’re cutting material with a pair of scissors, this is a static event: unlike swinging a bat at someone’s head, you don’t build up speed with the scissor blades and then have the cutting edges slam into the material. The force being applied to the material during the cut is due to the force generated by your fingers at that specific moment, modified by the lever ratio. The distance from your fingers to the fulcrum is pretty much fixed, so for max cutting force, you move your material as close as possible to the fulcrum. This exactly obeys the lever rule.
The one exception I can think of is manual hedge clippers, the operation of which is often dynamic: you apply sharp force to get the blades and handles moving, and the momentum stored up in the heavy handles and blades helps keep the blades moving through small twigs and branches. However, the lever rule is still applicable here: maximum cutting force is achieved when the twigs and branches are as close to the fulcrum as possible. Sure, tiny twigs can be cut easily enough out near the blade tips, but when you encounter that one stubborn 5/8" branch, you move it close to the fulcrum so you can hack through it.
My understanding is that the cutting action of scissors has nothing to do with lever action (although it does act like a lever).
The cutting action (or shearing action) has to do with the gap between the sharp edges. Near the pivot (or the fulcrum) the gap is smallest and the gap increases as you go towards the edge. So near the pivot, the shearing or cutting forces are the highest.
The tiny weight (your hands pushing on the handles) is farther from the fulcrum, and the heavy weight is near the fulcrum. The tips of the blades are far from the fulcrum.
When you hold the handles of scissors and close them, you are applying torque. Torque is the twisting force of each blade of the scissors rotating about the pivot pin. The torque shows up on the other side of the pin in the form of the two blades pushing together. Torque is force perpendicular to the blade times the distance away from the pin. So for a fixed torque, near the pin the force perpendicular to the blade is higher; closer to the tip of the blade, the force perpendicular to the blade is lower. This makes sense if you think about the fact that if your hands close the handles a fixed amount of space, the blades near the pin just move a little bit but the blades near the tip have to move a lot more, so they are pushing more weakly. It’s easier to cut cardboard near the pin vs. near the tips.
The same is true of swinging a stick, but if you are trying to hit something with a stick, you want the end of the stick to move as fast as it can, giving it more kinetic energy. You are trying to generate force with scissors, not kinetic energy; moving them faster doesn’t make them work any better. So when swinging a stick (like a baseball bat; let’s not resort to violence) you want to keep adding energy throughout the swing until the point of contact. Once the bat makes contact, most of the force is delivered by the momentum of the bat, not by you continuing to push on the bat past the point of contact.
It should be noted that you could deliver the same amount of energy with a bat moving very slowly, but you would need to push [equally] harder. To do that, you’d likely hold the bat in the same area that it’s going to contact the person and push it through their skull. Or better, imagine trying to brain someone with a brick. You wouldn’t swing it at them, you’d “punch” them with it.
I think the OP even bringing up the swinging stick idea, while an interesting conversation, suggests a confusion between levers (or wedges) and momentum.
One multiples force, the other is about delivering a given mass more effectively. Actually, I think it’s more like a lever multiples force, momentum is about adding a velocity component to it. There’s some crossover, sure, but they’re two separate things.
This won’t work unless the victim’s head is braced against a fixed object; without that, you’ll just push their head out of the way without inflicting any localized damage. Basically, you’d need to put the victim’s head in a hydraulic press. Swinging a bat at an unbraced head works because the victim’s head has its own substantial mass that resists movement during a dynamic impact event, resulting in high impact forces.
Yes, what you describe would certainly work, i.e. holding the bat against their unbraced head and then just pushing it through their skull. You’d need to push with the same amount of force that the bat delivers during its brief impact (as you said), but the trick is that you’d need to develop that huge force within a very short rise time; if you ramp up your pushing force even a little slowly, their head will move out of the way before you get a chance to achieve your maximum pushing force.
Well, for one thing, scissors aren’t a standard lever. Scissors are actually two levers working in concert that apply opposing forces. Also, there is the cutting aspect of scissors, which a standard lever doesn’t have.
