We were discussing the importance of friction
i.e. positive
and negative effects of friction, classifications
of friction, coulomb'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.

###

###

####
-P + Âµ

####
N

####

###

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 Î±.

###
**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. N

_{1}, N_{2}and N_{3}and similarly three frictional forces i.e. f_{1}, f_{2}and f_{3}.
N

_{1}= Normal Reaction force acting on the body by the wedge
N

_{2}= Normal Reaction force acting by the ground over the wedge
N

_{3}= 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

f

_{1}= Âµ_{s}x N_{1}= Frictional force acting between the contact surfaces of wedge and body
f

_{2}= Âµ_{s}x N_{2}= Frictional force acting between the contact surfaces of wedge and ground
f

_{3}= Âµ_{s}x N_{3}= Frictional force acting between the contact surfaces of vertical support provided and body### Let us write here the static equilibrium equations of the wedge

∑ F

_{x}= 0####
-P + Âµ_{s} x N_{2} + Âµ_{s} x N_{1}
Cos Î± + N_{1} Sin Î± = 0

∑ F

_{Y}= 0####
N_{2} - N_{1} Cos Î± + Âµ_{s} x
N_{1} Sin Î± = 0

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

####
N_{3} - N_{1} Sin Î± - Âµ_{s} x
N_{1} cos Î± = 0

-W + Âµ_{s} x N_{3} - Âµ_{s} x N_{1}
Sin Î± + N_{1} Cos Î± = 0

_{3}- N

_{1}Sin Î± - Âµ

_{s}x N

_{1}cos Î± = 0

_{s}x N

_{3}- Âµ

_{s}x N

_{1}Sin Î± + N

_{1}Cos Î± = 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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