Question #14365

how to apply lami's thoerm in problems of vectors,in problems of string tighten with a particle and in problems of components of force and vectors?

Expert's answer

In statics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear forces, which keeps an object

in static equilibrium, with the angles directly opposite to the corresponding

forces. According to the

theorem,

A/sin(a)=B/sin(b)=C/sin(c)

where A, B and C are the magnitudes of three coplanar, concurrent and non-collinear forces, which keep

the object in static equilibrium, and a, b and c are the angles directly

opposite to the forces A, B and C respectively.

Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named

after Bernard Lamy.

Proof of Lami's Theorem:

Suppose there are three coplanar, concurrent and non-collinear forces, which keeps the object in

static equilibrium. By the triangle law, we can re-construct the diagram as

follow:

By the law of sines,

A/sin(PI-a)=B/sin(Pi-b)=C/sin(Pi-c)=>A/sin(a)=B/sin(b)=C/sin(c)

in static equilibrium, with the angles directly opposite to the corresponding

forces. According to the

theorem,

A/sin(a)=B/sin(b)=C/sin(c)

where A, B and C are the magnitudes of three coplanar, concurrent and non-collinear forces, which keep

the object in static equilibrium, and a, b and c are the angles directly

opposite to the forces A, B and C respectively.

Lami's theorem is applied in static analysis of mechanical and structural systems. The theorem is named

after Bernard Lamy.

Proof of Lami's Theorem:

Suppose there are three coplanar, concurrent and non-collinear forces, which keeps the object in

static equilibrium. By the triangle law, we can re-construct the diagram as

follow:

By the law of sines,

A/sin(PI-a)=B/sin(Pi-b)=C/sin(Pi-c)=>A/sin(a)=B/sin(b)=C/sin(c)

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