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big and small scissors

Which will require more force (kgf)? small or big scissors?

What is the reason behind it?

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    $\begingroup$ We know what scissors look like. Please explain what you think about the problem. $\endgroup$ Commented Dec 1, 2016 at 15:42

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If this is about the force you must apply to cut paper, it depends on the lever arm of the handle-pivot distance, and the lever arm of the pivot-paper distance. The handle of the larger scissors can be gripped at a variety of distances, and each scissors can engage a piece of paper at a variety of throat distances (anywhere along the cutting edge), but if the paper is as close to the pivot as possible, and the grip on each scissors is 'centered' onthe fingerhole, it looks like the smaller pair has the better lever advantage.

So, the smaller scissors can cut paper with less applied force at the handle.

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If we are comparing the scissors in the image, from experience I have found the larger scissors are easier to cut paper with.

The most basic consideration is the Lever Principle : the ratio of load to effort forces is the same as the ratio of effort to load distances from the fulcrum. In this case there isn't much difference.

Other factors are probably more important here. The large scissors allow a much better grip and the blades are not so easily forced apart sideways along the fulcrum. When that happens the paper bends and is squeezed between the blades without being cut. The sharpness and shear angle of the blade also make a big difference : the smaller scissors shown here typically have a much wider shear angle at the cutting edge. (Scissors are a combination of 2 simple machines : the lever and the wedge.)

Anatomy is also a factor. The nearer the design allows the hand to maintain an open 'high five' posture, the more comfortable the hand and the more repetitions can be made before tiring. The smaller scissors here force the hand into an uncomfortable cramped posture which cannot be sustained for long. (The scissors shown in the link have the thumb much closer to the pivot than the other fingers. The most ergonomically advanced - and the most expensive - scissors are those used by hairdressers and pet groomers.)

So I think the design and quality of the scissors can have at least as important effect as the Lever Principle. For example, the smaller scissors as often sold in corner shops for cutting paper are usually poor quality, but a similar design occurs in hospitals and clinics for cutting bandages and clothing, when the quality is far better, with the result that cutting with them is much easier.

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Assuming all other factors such as friction between the blades,distance from the force applied by your fingers to the pivot and degree of blade separation when opened stays the same for both scissors,The big one would require more force. The mass in the big scissors is obviously more than the small one (in the photo). By Newton's 2nd law (F=ma),since m (mass) is larger for the big scissors,the force required to use it would be larger (assuming acceleration of the handles stays the same)

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  • $\begingroup$ I don't think Newton's 2nd law is relevant here. Scissors operate on the lever principle, not by speed or impact. $\endgroup$ Commented Dec 1, 2016 at 15:45
  • $\begingroup$ It's really a leverage and contact area argument. Force approx = ((contact area) * (paper shear strength) + paper friction)* (paper-side lever arm length)/ (hand-side lever arm length). Same answer, different reason, as the paper-side length and (probably) contact area are significantly larger for larger siccors. $\endgroup$ Commented Dec 1, 2016 at 16:33
  • $\begingroup$ What I actually mean is that with all other factors the same for both scissors (lever arm lengths,contact area etc.), it would require slightly more force to use the larger scissors due to the extra mass. However all other factors being the same is usually not the case in real life,in which I recognize that there would be other,more relevant factors to have as a basis for calculating the force needed. In which the question actually needs to be more specific regarding the scissors's specific properties and its strict definition on "using" them. I have just used the picture provided as a basis. $\endgroup$
    – Dt roid
    Commented Dec 2, 2016 at 8:55

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