How Does a Wedge Work? Two Ramps Back to Back

Look at an axe from the side

Look at an axe head from the side, or at a doorstop from the end. Both are shaped like a skinny triangle that gets thinner toward one edge. Press that edge into something and the object opens up around it. That shape is a wedge, the sixth of the six classic simple machines after the lever, pulley, ramp, wheel and axle, and screw.

Alloprof, an educational website for students, describes a wedge as two inclined planes joined back to back. It says a wedge helps to separate objects, and that its shape reduces the force needed to push it into them. Picture a wedge cut in half down the middle: each half is a ramp, like the ramp in an earlier lesson.^[1]

A ramp that moves

Sciencing, a science explainer website, names the key difference from the ramp lesson. An inclined plane stays still while a load moves along it. A wedge is a moving inclined plane, made of two triangles joined base to base, so it tapers to a thin edge. The ramp stays put and the load climbs; the wedge is driven and the material is pushed aside.

Look at the diagram. You push on the wide back of the wedge, straight down. Wikipedia explains that a wedge converts a force on its blunt end into forces perpendicular to its sloping faces, which means at right angles to them. In a thin wedge the faces are nearly upright, so those pushes point mostly sideways. That is our own reading of the diagram. The result is that a wedge changes the direction of a force: a push down goes in, and pushes sideways come out, and they pull the log apart.^[3]

Thin or thick, long or short?

Alloprof describes a trade-off. A thin wedge with gently sloping sides must be driven in deeper to separate an object, but it takes less force. A steep, blunt wedge needs less depth to split the object, but it takes more force. This is the same bargain the other simple machines make: a smaller push is paid for with a longer path.

Wikipedia gives a rule for an ideal wedge: its mechanical advantage, or force gain, is the ratio of the length of its slope to its width. Here is an invented example with easy numbers. Wedge A is 12 centimetres long and 3 centimetres wide at the back. Wedge B is 6 centimetres long and 3 centimetres wide. Twelve divided by three is four, and six divided by three is two. So in an ideal wedge with no friction, Wedge A multiplies the push about 4 times and Wedge B about 2 times.

The price is distance. To open the same 3-centimetre gap, Wedge A has to travel 12 centimetres into the wood, twice as far as Wedge B. Edinformatics, another educational website, says the force gain varies with the wedge angle: a sharp wedge with a small angle gives a large force. A wedge does not make the job free. It trades extra travel for a smaller push.^[1]

Friction: a thief and a helper

No real wedge is frictionless. As the faces rub against the wood, some of your push is used up, so a real wedge needs a little more push than the ideal number says. This is the same idea as in the screw lesson, and the 4 times in our example is a best case, not a measurement.

Wikipedia also shows a helpful side of friction. A wedge-type door stop works largely because of the friction between the bottom of the door and the wedge. The door presses on the wedge, yet friction grips and the wedge stays where it is. The same article says a wedge can bind, or stay stuck, when its angle is small enough compared with the friction. That is why a very thin wedge hammered deep into a log can be hard to pull out.^[2]

Wedges you already use

Wikipedia lists several wedges: axes, which separate wood fibres, and chisels, which cut wood and even stone. Knives are wedges too, and Wikipedia says they let people cut with much less force than tearing by hand. The tips of forks and nails are also wedges. Sciencing adds a shovel digging into a snowbank, and Alloprof notes that the pointed body of a northern gannet cuts through water with little effort.

Sciencing also counts a zipper as a machine that combines inclined planes and a wedge. Try this with an adult and an old jacket. Pull the slider along the teeth and watch what happens at the front of the slider as the teeth part. Then ask what shape you see. That observation is our own invitation to check, not a claim from the sources.^[3]