In this problem we will be solving for the ideal mechincal advantage of a compound bevel edge knife going through a block of cheese. The ideal mechanical advantage assumes no losses due to friction and the compound bevel edge refers to a set of 2 wedges with 2 different slopes or inlclines. So we will be finding the mechanical advantage at 2 points the first point has a length of .78 milimeters and a thickness of .7 mm
The second point has a length of 9.2 mm and a thickness of 2 mm
The wedge is another form of an incline plane. Much like other simply machines where if you convert a force with a larger displacement to a force with a smaller displacement the force increases. The amount this force increases by is the mechanical advantage.
Now to find the ideal mechanical advantage we will be taking the length or distance traveled down on the cut divided by the thickness of the blade at the desired point.
So pluggin in the length and thickness we measured for point one we get a mechanical advantage of 1.11. This means that the force outwards is 1.11 times the force that is being pushed down on the knife.
Doing the same thing for point 2 the mechanical advantage is 4.6 this means that the force downwards is multiplied times 4.6 to get the force acting outwards.
So at point one there is less of mechanical advantage but the block of cheese is moving apart faster and at point 2 there is more mechanical advantage but the block of cheese is moving apart slower. More displacement less force less displacement more force. So your probably thinking wouldn’t it make sense to make the breaking edge as gradual of an incline so you have a greater force multiplier acting outwards to tear apart the cheese. Well if we were to make the edge very thing there is less material to hold the edge in place. After fewer impacts the edge of the blade would dull faster. This is why a compound bevel edge is used. Think about how quickly razors dull verse kitchen knifes.
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