Hedge Clippers as a Combination of Two Simple Machines

Measuring the arms of a hedge clipper to calculate the mechanical advantage.
Measuring the arms of a hedge clipper to calculate the mechanical advantage.

Now that we’ve studied simple machines, we’re practicing by calculating the mechanical advantage of some of the complex machines students have around the school. The clippers my outdoor group uses every Friday, for example, are a combination of a lever (the arms) and a wedge (the blade).

For levers the mechanical advantage (M.A.) is:

M.A._{lever} = \frac{\text{length of input arm}}{\text{length of output arm}}

which in this case is measured as the distance from the bolt that the arms pivot about to the handholds (for the input force) and the stick (for the output force):

M.A._{lever} = \frac{60 \text{cm}}{5 \text{length of output arm}}= 12

The wedge is an inclined plane, and its mechanical advantage is:

M.A._{\text{inclined plane}} = \frac{\text{length of ramp}}{\text{height of ramp}}

which we calculated to be about 3.

M.A._{\text{inclined plane}} = \frac{12 \text{mm}}{4\text{mm}} = 3

Combined, the two mechanical advantages multiply each other to give a total mechanical advantage of 36, which means that any force you apply to the handles of the clippers gets multiplied 36 times to the thing you’re trying to cut.

Diagram showing the dimensions of the lever on hedge clippers. The input arm is about 60 cm from the pivot point to the hand holds while the output arm goes from the pivot point to the stick being cut.
Diagram showing the dimensions of the lever on hedge clippers. The input arm is about 60 cm from the pivot point to the hand holds while the output arm goes from the pivot point to the stick being cut.

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