We were discussing
theÂ projectile motion - trajectory equation,
definition and formulasÂ and
we have also seen the concept ofÂ Terminal velocityÂ and apparent weight of a man in a liftÂ with
the help of our previous posts.Â Â

Now, we will be interested further to understand a very important topic i.e. Lami's theorem in engineering mechanics.Â

We will find out here the statement, explanations, importance, applications and limitations of lami's theorem with the help of this post. We will also see here the Conditions to apply the Lamiâ€™s theorem.Â

###

Let us first see here what
is the statement of Lami's theorem in engineering mechanics.

DoÂ you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update fromÂ www.hkdivedi.com.Â Â Â Â

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###

Now, we will be interested further to understand a very important topic i.e. Lami's theorem in engineering mechanics.Â

We will find out here the statement, explanations, importance, applications and limitations of lami's theorem with the help of this post. We will also see here the Conditions to apply the Lamiâ€™s theorem.Â

###
**Lami's theorem in engineering mechanicsÂ **

Let us first see here what
is the statement of Lami's theorem in engineering mechanics.
Lamiâ€™s theorem states thatÂ

If three coplanar, concurrent and non-collinear forces are in equilibrium, the magnitude of each force will be proportional to the sine of the angle between the other two forces.Â

###

There are following four
conditions, as mentioned below, in order to apply the Lamiâ€™s theorem.

If three coplanar, concurrent and non-collinear forces are in equilibrium, the magnitude of each force will be proportional to the sine of the angle between the other two forces.Â

###
**Conditions to apply the Lamiâ€™s theoremÂ **

There are following four
conditions, as mentioned below, in order to apply the Lamiâ€™s theorem.
We must have to remember
that all the three forces acting on a body must be in a same plane.Â Â

We must have to remember that these three forces must be concurrent i.e. these three forces must be acting through a same point.Â

We must have to remember that these three forces must be non-collinear i.e. these forces must not be acting in a same line of action.Â

We must have to remember that these three coplanar, concurrent and non-collinear forces acting on a body must be in equilibrium i.e. there must not be any acceleration in the body upon the application of these three forces. We can also say that there must be zero net force over the body when these three forces will be applied.Â

If these three forces are not following the above mentioned conditions, Lamiâ€™s theorem will not be applicable.Â

###

Let us assume that there is
an object or a body of any given shape, as mentioned below, are exerted by
three forces A, B and C. Angles made by these three forces with each other are
displayed here in following figure as Î±, Î² and Î³.Â

According to Lamiâ€™s theorem statement, we will have following equation as mentioned here.Â

####

We must have to remember that these three forces must be concurrent i.e. these three forces must be acting through a same point.Â

We must have to remember that these three forces must be non-collinear i.e. these forces must not be acting in a same line of action.Â

We must have to remember that these three coplanar, concurrent and non-collinear forces acting on a body must be in equilibrium i.e. there must not be any acceleration in the body upon the application of these three forces. We can also say that there must be zero net force over the body when these three forces will be applied.Â

If these three forces are not following the above mentioned conditions, Lamiâ€™s theorem will not be applicable.Â

###
**Explanation of Lamiâ€™s theoremÂ **

Let us assume that there is
an object or a body of any given shape, as mentioned below, are exerted by
three forces A, B and C. Angles made by these three forces with each other are
displayed here in following figure as Î±, Î² and Î³.Â According to Lamiâ€™s theorem statement, we will have following equation as mentioned here.Â

####
A Î± Sin Î±, A = K Sin Î±
B Î± Sin Î², A = K Sin Î²
C Î± Sin Î³, A = K Sin Î³Â

Or we can also redefine it
asÂ

###

There are few limitations
of Lamiâ€™s theorem as mentioned here.Â

There should be only three forces acting on the object. If there are more than three forces or less than three forces, we may not apply the Lamiâ€™s theorem.Â

Lamiâ€™s theorem is applicable to only coplanar, concurrent and non-collinear forces.Â

Therefore, we have seen here the basics of Lamiâ€™s theorem, proof of Lami's theorem and its limitations.Â

Further we will find out another concept in engineering mechanics with the help of our next post.Â Â

#### K = A/ Sin Î± = B/ Sin Î² = C/ Sin Î³Â

Therefore, according to Lamiâ€™s theorem statement, we will have following equation which could be used in order to secure the magnitude of the unknown force in a case where object will be exerted by three coplanar, concurrent and non-collinear forces and object or body is in equilibrium.Â Â###
**Limitations of Lamiâ€™s theoremÂ **

There are few limitations
of Lamiâ€™s theorem as mentioned here.Â There should be only three forces acting on the object. If there are more than three forces or less than three forces, we may not apply the Lamiâ€™s theorem.Â

Lamiâ€™s theorem is applicable to only coplanar, concurrent and non-collinear forces.Â

Therefore, we have seen here the basics of Lamiâ€™s theorem, proof of Lami's theorem and its limitations.Â

Further we will find out another concept in engineering mechanics with the help of our next post.Â Â

DoÂ you have any suggestions? Please write in comment box and also drop your email id in the given mail box which is given at right hand side of page for further and continuous update fromÂ www.hkdivedi.com.Â Â Â Â

###
**Reference:Â Â **

Engineering Mechanics, By
Prof K. RameshÂ Â

Image courtesy:
GoogleÂ Â Â

###
**Also
readÂ ****Â Â **

Reciprocating pumpÂ

Main components of a reciprocating pump

Working principle of reciprocating pumpÂ

Ideal indicator diagram of reciprocating pumpÂ

Effect of acceleration and friction on indicator diagram of reciprocating pumpÂ

Expression for acceleration head in the suction pipe of a reciprocating pumpÂ

Double acting reciprocating pump: working principle, discharge, work done and power requiredÂ

Slip and negative slip in reciprocating pumpÂ Â

Maximum speed of a reciprocating pump

Main components of a reciprocating pump

Working principle of reciprocating pumpÂ

Ideal indicator diagram of reciprocating pumpÂ

Effect of acceleration and friction on indicator diagram of reciprocating pumpÂ

Expression for acceleration head in the suction pipe of a reciprocating pumpÂ

Double acting reciprocating pump: working principle, discharge, work done and power requiredÂ

Slip and negative slip in reciprocating pumpÂ Â

Maximum speed of a reciprocating pump

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