Mechanical Engineering
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# What does ~200N feel like?

## Question

I have a problem where I'm trying to work out the axial force it takes to sharpen a pencil with a standard pencil sharpener.

I found a textbook that gives a formula to find this axial feeding force but the number seems much too high.

The answer I have currently is a thrust force of 187N. This is 19.12 kg force which if I were to stand the pencil up straight and place a 20kg weight on top, that would seem excessive to what I'm doing on the horizontal. If this the correct way of looking at it?

The formula given is below with variables as:

R = 3220 J/m^2 or 3.22kJ/m^2 (Toughness of cedar wood pencil)

r = 0.0041m (radius of pencil)

p = 23 degrees (angle of pencil)

I've been using SI units in all these variables.

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Where did you get this force expression? Did you check the derivation?

DrD

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It really seems excessive.

If the formula is ok, I would re check the constant R (toughness) and the angle (sometimes the formula refers to half angle)

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The whole purpose of units is to provide a physical feel for quantities. SI units undermine this essential purpose but that means we must work harder to get it right. People often make expensive mistakes by not understanding units, like NASA missing Mars and wasting billion\$. I was recently working on a plant in the Middle East where they installed pumps that were 10x the appropriate size because some engineer didn't know what pump head meant and forgot the implied 9.8 m/sec² of gravity and didn't convert properly between mass and force. Pump head in meters (or feet) of water is actually a pressure, but it physically means how far up water would squirt out of a hose. I often ask someone to push down on my hand with the force of one Newton. Few people, even those who grow up in Europe using the metric system, can do this. It's about one-fifth of a pound (2.2 lb/kg 9.8 m/sec²) or one-tenth of a kgf. We should all know what a pound (or kg force) is from the grocery store. The practicing engineer should be comfortable with any and all systems of units.

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