8.7 : Wedges

A wedge is a simple machine that serves various purposes, such as adjusting the elevation of structural or mechanical parts, providing stability for heavy objects, and splitting a body into two parts. This versatile tool can amplify an applied force, making it easier to manipulate large or heavy objects.

Consider using a wedge to lift a heavy slab. Here, the wedge functions by converting the applied force into a much larger force directed almost perpendicular to the initial force. This amplification enables the lifting of heavy objects with minimal effort.

There are seven unknown factors involved in the motion of the wedge: the applied force and six normal and frictional forces. In the free-body diagrams, the weight of the wedge is often neglected, as it is small compared to the load.

These unknowns can be determined using four force equilibrium equations applied to the wedge and the slab,

and the remaining three frictional equations (F₁, F₂, F₃) applied at each contact surface are given by the product coefficient of friction and their respective normal forces.

By solving these equations, one can gain insight into the relationship between the applied force and the resulting motion of the wedge.

When lowering the slab, the frictional forces act in the opposite sense. Provided that the coefficient of friction is very small or the wedge angle is large, the applied force must act to the right to hold the slab in place. This balance of forces ensures that the wedge remains stable and maintains its position while supporting the weight of the slab.

Under certain conditions, the wedge may be considered self-locking. This occurs when the applied force is removed, and friction forces alone can hold the block in place. The self-locking condition is valid only when the wedge angle is less than twice the angle made by the reaction forces.

In this case, the wedge's geometry and the friction between the contact surfaces work together to prevent unwanted movement or slippage.

The self-locking property of a wedge can be advantageous in various applications, as it provides added stability and security when manipulating heavy objects. For instance, in construction or engineering projects, a self-locking wedge can help ensure that structural components remain firmly in place during assembly or adjustments.