Statistics: Equilibrium, Application and Lami’s Theory

• Definition of equilibrium
• Condition of equilibrium of rigid body
• Application of the condition to solve problems
• Lami’s theorem and application

Definitions

Equilibrium is when a body remains at rest under the action of given forces.

Translational Equilibrium: The state of equilibrium of bodies which remain at rest under the action of forces have tendency to cause translation.

Condition of Equilibrium

When a block is placed on a table as shown below and force F1 and F2 are applied to the block.

The block remains in translational equilibrium if the magnitude of F1 and F2 are equal.

Since F₁ and F₂ are acting in opposite direction, but have equal magnitudes.

Then, F₁ = -F₂

          F₁ + F₂ = 0

Also, the upward force N balances the downward force mg on the block.

:.      N = -mg, N + mg  = 0

Hence, the sum of the vertical components and horizontal components of forces acting on a body in translational equilibrium is equal to zero.

LAMI’S THEOREM

This theorem states that if three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the liens of action of the other two forces.

EVALUATION

A particle of mass 10kg is connected by two strings of length 3m and 4m to two points on the same horizontal level and 5m apart, find the tension in the strings.

GENERAL EVALUATION

1. A particle of mass 98kg is suspended by two light inelastic strings of length 9m and 12m from two fixed point P and which are 15m apart.  Calculate (i) the angles made by the strings with the upward vertical (ii) the tension in the strings.
2. The ends P and Q of an inextensible string 17m long are attached to two fixed points 13m apart on the same horizontal level. A body of mass 20kg is suspended from a point C on the string 5m from P. Calculate  (a) the angle which each part of the string makes with the horizontal  (b) the tension in each part of the string.

READING ASIGNMENT

Read Equilibrium “pages” 170-177 of Further Mathematics Project III.

WEEKEND ASSIGNMENT

Two forces (8N, 030⁰) and (10N, 120⁰) act on a body; find the magnitude of the force that would be applied to keep the system in equilibrium.