CONTENTS

• Conditions for equilibrium
• Principles of moment
• Conditions for equilibrium of a rigid body

CONDITIONS FOR EQUILIBRIUM

A body is said to be in equilibrium if under the action of several forces, it does accelerate or rotate.

1. The sum of the upward forces must be equal to the sum of the downward forces.

2. The sum of the clockwise moment above a point must be equal to the sum of anticlockwise moment about the same point

MOMENT OF A FORCE

The moment of a force is the product of the force and the perpendicular distance

M = F x distance

Unit =Nm

COUPLE

A couple is a system of two parallel, equal and opposite forces acting along the same line

The moment of a couple is the product of one of the forces and the perpendicular distance between the lines of action of the two forces

M = f x 2r

M = f x d

The distance between the two equal forces is called the arm of the couple

The moment of a couple is also called a torque

Application of the Effect of Couples

1.       It is easier to turn a tap on or off by applying couple

2.       It is easier to turn a steering wheel of a vehicle by applying a couple with our two hands instead of a single force with one arm.

CENTRE OF GRAVITY

The centre of gravity of a body is the point through which the line of action of the weight of the body always passes irrespective of the position of the body. It is also the point at which the entire weight of the body appears to be concentrated.

The centre of mass of a body is the point at which the total mass of the body appears to be concentrated. Sometimes, the center of mass may coincides with the centre of gravity for small objects.

STABILITY OF OBJECTS

There are three types of equilibrium- stable equilibrium, unstable equilibrium, and neutral equilibrium.

1. Stable equilibrium: a body is said to be in stable equilibrium if it tends to return to its original position when slightly displaced. A low centre of gravity and wide base will put objects in stable equilibrium e.g. a cone resting on its base ; a racing car with low C.G and wide base; a ball or a sphere in the middle of a bowl.
2. Unstable equilibrium: a body is said to be in an unstable equilibrium if when slightly displaced it tends to move further away from its original position e.g. a cone or an egg resting on its apex. High C.G.  and a narrow base usually  causes unstable equilibrium.
3. Neutral equilibrium: a body is said to be in neutral equilibrium if when slightly displaced, it tends to come to rest in its new position e.g a cone or cylinder or an egg resting on its side.

CLASSWORK

1. When is a body said to be in equilibrium?
2. What is moment?
3. Write short note on the three types of equilibrium

ASSIGNMENT

SECTION A

1. Two forces A and B act at a point at right angles. If their resultant is 50N and their sum is 70N, their magnitudes are: (a) 50N and 20N (b) 20N and 40N (c) 40N and 30N (d) 60N and 10N
2. A uniform metre rule of mass 100g balances at the 40cm mark when a mass X is placed at the 10cm mark. What is the value of X? (a) 33.33g (b) 43.33g (c) 53.33g (d) 63.33g
3. The equilibrant of a system of forces is (a) equal and opposite to the resultant of the forces (b) the force which has the same effect as the system (c) equal to resultant of the system (d) the force that makes the system unstable
4. Two forces forming a couple are separated by a distance of 25cm, if one of the forces equal 40N, what is the moment of the couple? (a) 1000Nm (b) 500Nm (c) 10Nm (d) 5Nm
5. Two forces each of magnitude 10N acts in opposite directions at the end of a table. If the length of the table is 50cm.Find the moment of the couple on the table (a) 0.5Nm (b) 5Nm (c) 50Nm
6. A pole AB of length 5M and weigh 300N has its centre of gravity 2.0M from the end A, and lies on horizontal ground. Calculate the force required to begin to lift this end. (a) 60N (b) 120N (c) 240N

SECTION B

1. (a) Explain with the aid of diagram what is meant by the moment of a force about a point (b) State the conditions of equilibrium for a number of coplanar parallel forces (c) A metre rule is found to balance at 48cm mark. When a body of mass 60g is suspended at 6cm mark, the balance point is found to be at the 30cm mark. Calculate the: (i) mas of the rule (ii) the distance of the balance point from the zero eend if the body were moved to the 13cm mark
2.  State the conditions necessary for a body to be in equilibrium, mention the three types of equilibrium with at least two examples each.