25.5: Wedge and Screws
- Page ID
- 92234
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The wedge is a movable inclined plane, used to split a body. Examples are axes, chisels, knives, nails, and pins. Because friction plays a large role in the operation of the wedge, it is difficult to determine its mechanical advantage.
Screws
The screw is essentially an inclined plane wound around cylinder. A common example is a jackscrew (Figure 22.4.2). Let \(\ell\) be the length of the arm, and let \(p\) be the pitch of the screw (the distance between successive threads). Then one complete turn of the arm will move the end of the arm a distance \(2 \pi \ell\), and this will result in the load being moved a distance \(p\).
Since the input work is equal to the output work,
\[W_{i}=W_{o}\]
or
\[F_{E}(2 \pi \ell)=F_{R} p\]
The mechanical advantage of the jackscrew is then \(F_{R} / F_{E}\), or
\[M . A .=\frac{2 \pi \ell}{p}\]