Back to: Further Mathematics SS3

**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 F_{1} and F_{2} are acting in opposite direction, but have equal magnitudes.

Then, F_{1} = -F_{2}

F_{1} + F_{2} = 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.

**Example**

1. A particle of mass 5kg is supported by two light inelastic strings inclined at angles 30^{0} and 45^{0} respectively to the horizontal. If the system is in equilibrium, calculate the tension in each string.

**EVALUATION**

1.A street lamp of mass 10kg is suspended at a position ) by two wires OP and OQ across a rood such that each wire is inclined at an angle of 80^{0} to the upward vertical, If the system is in equilibrium, calculate the tension in one of the two wires. (Take g = 10ms^{-2})

**TRIANGLE OF FORCES**

If three coplanar forces act on a body in such a way that the system is in equilibrium, then the forces can be represented in magnitude and direction by the sides of a triangle taken in order

**Example**:

1.A body of mass 6.5kg is supported by two strings, One of the stings is inclined at an angle of 30^{0} and the other 40^{0} to the horizontal . Find the tension in each strings, if the system is in equilibrium (take g = 10ms^{-2})

**EVALUATION**

A body of mass s10kg is suspended by means of two light inextensible strings. AP and BP which are inclined at angles 60^{0} and 30^{0} respectively to the downward vertical. If T_{1} and T_{2} are the magnitude of the tension AP and BP respectively, calculate the values of T_{1} and T_{2}.

**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.

Consider the forces F_{1}, F_{2} and F_{3} below

**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, 030^{0}) and (10N, 120^{0}) act on a body; find the magnitude of the force that would be applied to keep the system in equilibrium.

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