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WEDGE FRICTION AND SELF LOCKING IN ENGINEERING MECHANICS

We were discussing the importance of friction i.e. positive and negative effects of frictionclassifications of frictioncoulomb's law of dry friction, some guidelines for solving frictional problems and concept of rolling resistance or rolling friction with the help of our previous post.   

Now, we will be interested further to understand here the wedge friction and concept of self- locking in engineering mechanics with the help of this post.  

Wedge friction

Let us start here this post with the basics of wedge friction, we will also find out here the way to solve the friction problems based on wedge friction and finally we will see the concept of self-locking in engineering mechanics at the end of this post. 

A wedge is basically defined as a simple tool or device which is used to lift the heavy load or to adjust the position of the body etc. 

Wedge is basically a piece of metal or wood in the triangular or trapezoidal shape as displayed here in following figure. 

A force P is applied over the wedge to lift the body whose weight is W. Let us assume that angle of the wedge is α. 

Let us find out here the free body diagram  

Free body diagram, as shown below, indicates the various forces such as reaction forces, frictional forces and force applied externally i.e. P here. 


There will be three normal reaction forces, as shown in free body diagram, i.e. N1, N2 and N3 and similarly three frictional forces i.e. f1, f2 and f3

N1 = Normal Reaction force acting on the body by the wedge 
N2 = Normal Reaction force acting by the ground over the wedge  
N3 = Normal Reaction force acting on the body due to the vertical support provided 
W = Weight of the body need to be lifted or which position need to be adjusted 
P = External force applied over the wedge in order to push the wedge and to lift the body 
f1= µs x N1 = Frictional force acting between the contact surfaces of wedge and body 
f2= µs x N2 = Frictional force acting between the contact surfaces of wedge and ground  
f3= µs x N3 = Frictional force acting between the contact surfaces of vertical support provided and body 

Let us write here the static equilibrium equations of the wedge

∑ Fx = 0

-P + µs x N2 + µs x N1 Cos α + N1 Sin α = 0


∑ FY = 0

N2 - N1 Cos α + µs x N1 Sin α = 0 


Similarly, we will write here the static equilibrium equations of the body or block 

N3 - N1 Sin α - µs x N1 cos α = 0 

-W + µs x N3 - µs x N1 Sin α + N1 Cos α = 0 

Therefore, we can determine the unknown forces by using these four equations. 

Self-locking 

Now we will see here the basics of self-locking. 

Self-locking means that, when the force P will be removed, the wedge should remain in place. 

It is the desirable effect that we want to system to behave. We do not want to keep the force continuously applying, we want to just hit the wedge and leave it. 

Just try to think that when we will remove the force P, what will be happened? 

When the force P will be removed, the block or body will try to push the wedge in outward direction. 

If the wedge will not be self-locking then there will be impending motion and hence the wedge would be pushed out and we do not want it. 

The condition of self-locking is basically a function of the co-efficient of friction between the surfaces and the angle of the wedge. 

Therefore, we have seen here the way to solve the friction problems based on wedge friction and finally we have also discussed here the concept of self-locking in engineering mechanics with the help of this post. 

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We will find out now the concept of “Archimedes pulley system” in our next post.    

Reference:  

Engineering Mechanics, By Prof K. Ramesh  
Image courtesy: Google     

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