3.8 WEDGE FRICTION
A wedge is a piece of metal or wood which is usually of a triangular or trapezoidal in cross-section. It is used for either lifting loads through small vertical distances or used for slight adjustments in the position of a body i.e., for tightening fits or keys for shafts.
When lifting a heavy load the wedge is placed below the load and a horizontal force P is applied as shown in Fig. 3.41. If the force P is just sufficient to lift the load, the wedge will move towards left and load will move up. When the wedge moves towards left, the sliding of the surfaces AC and AB will take place. At the same time load moves up and sliding of the load takes place along GD. Thus for the wedge and load shown in Fig.3.41 sliding takes place along surface AB, AC and DG. Hence there will be three normal reactions at AB, AC and DG.
The problems on wedges are generally the problems of equilibrium on inclined planes. Therefore, these problems are solved by equilibrium method or by applying Lami’s Theorem.
Equilibrium Method. In this method, the equilibrium of the load (or the body placed on the wedge) and the equilibrium of the wedge are considered.
Equilirbium of Wedge
Consider the equilibrium of the wedge. The forces acting on the wedge are shown in Fig. 3.42. They are:
(i) The force P applied horizontally on face BC.
(ii) Reaction R1 on the face AC (The reaction R1 is the resultant of the normal reaction N1 on the rubbing face AB and force of friction on surface AC). The reaction R1 will be inclined at an angle θ1 (when θ1 is angle of friction) with the normal.
(iii) Reaction R2 on the face AB (The reaction R2 is the resultant of normal reaction N2 on the rubbing face AB and force of friction on surface AB). The reaction R2 will be inclied at an angle Φ2 with the normal.
When the force P is applied on the wedge, the surface CA will be moving towards left and hence force of friction on this surface will be acting towards right. Similarly, the force of friction on face AB will be acting from A to B. These forces are shown in Fig. 3.42.
Resolving the forces horizontally, we get
By Lami’s Theorem
The wedge is in equilibrium under the action of three forces namely R1, R2 and P. These forces, when produced, will meet at a point as shown in Fig. 3.43.
Applying Lami’s theorem, we get
Equilibrium of Body placed on the Wedge
The forces acting on the body are shown in Fig.3.44. They are:
(i) The weight W on the body.
(ii) Reaction R3 on the face GD. (The reaction R3 is the resultant of the normal reaction N3 on the rubbing face GD and force of friction on surface GD).
(iii) Reaction R3 on the face GF (The reaction R2 is the resultant of the normal reaction N2 on the rubbing face GF and force of friction on surface GF).
These forces are shown in Fig. 3.44.
Resolving the forces R2, R3 and W horizontally, we get
By Lami’s Theorem
The forces R3, R2 and W are produced to meet at a point as shown in Fig. 3.44.
The body is in equilibrium under the action of these forces.
Hence applying Lami’s theorem, we get