- For a body to be in equilibrium (neither moving nor rotating), under the action of parallel
forces, the following conditions will be satisfied;

- The sum of upward forces must be equal to the sum of downward forces.
- The sum of clockwise moments equals the sum of anticlockwise moments.

- The two are called the first and second condition of equilibrium respectively.

#### Practice Example 1

1. A uniform rod of length 1.0 m is hung from a spring balance as shown and balanced in
horizontal position by a force of 1.6 N. Determine:

a) The weight of the rod.

b) Reading of the spring balance.

##### Solution

a) Let the weight of the rod be 'W'. W acts at 50 cm mark, therefore taking moments
about point of suspension, clockwise moments = W x 0.2 Nm = 0.2W Nm.

Anticlockwise moments = 1.6 x 0.3 = 0.48 Nm.

Using the law of moments, then

Anticlockwise moments = clockwise moments

0.48 = 0.2 W, hence W = 2.4 N

b) Upward forces = downward forces

Downward force = W + 1.6 N

= 2.4 + 1.6 = 4.0 N

Upward force = reading of the spring balance = 4.0 N

#### Practice Example 2

2. A uniform rod is 1.0 m long weighs 5 N. It is supported horizontally at one end by a
spring and the other end rests on a table as shown below. A mass of 2 kg is hung from
the rod as shown; determine:

a) Reading of the spring balance

b) Reaction force, F, from the table.

##### Solution

a) The 2kg mass and the weight of the rod (5 N) gives clockwise moment while the
spring balance provides anticlockwise moments.

Clockwise moments = (2 x 10) x 0.4 + (5 x 0.5) = 10.5 Nm.

Anticlockwise moments = S x 1 (reading of the spring balance)

1S = 10.5, hence S = 10.5 N.

b) Upward forces = downward forces.

Downward forces = (2 x 10) + 5 = 25 N.

Therefore F + 10.5 = 25, hence F = 14.5 N.