EQUILIBRIUM AND CENTER OF GRAVITY.

Specific objectives.

1. Define center of gravity.
2. Determine experimentally the center of gravity of an irregular object.
3. Identify and explain the states of equilibrium.
4. State and explain factors affecting the stability of an object.
5. Explain the application of stability.
6. Solve numerical problems involving center of gravity and moment of force.

            Center of gravity (C. O G)

• Is the point of application of the resultant force due to the earth’s gravitational force acting on the body.
• Is the point on a body where the point of the body appear to act.
• Is a point where the mass of the body is concentrated.

EXP: TO DETERMINE THE CENTER OF GRAVITY OF AN IRREGULAR LAMIN OBJECT.

Requirements.

1. Irregular object.
2. Plumb line.
3. Thread.
4. Stand

Procedure.

1. Make 3 or 4 holes on the edges of the cardboard.
2. Suspend it by a roll through one hole A.
3. Tie a plumb line on the rod beside the cardboard.
4. When they are settled, stop swinging, draw a vertical line on the cardboard as set by the plumb line.
5. Repeat the experiment using the other holes.
6. Balance the cardboard with the top of a pencil at the point of intersection by the three lines. Note the observation.
7. Repeat the experiment with different irregular shapes.

Observations.

The object balances where the lines meet. This is the center of gravity of the object.

State of equilibrium.

• A body is said to be in equilibrium when all the forces acting upon it balances one another.
• Equilibrium is a state of balance or stability of a body.
• There are 3 states of equilibrium;

1. Stable equilibrium.
2. Unstable equilibrium.
3.  Neutral equilibrium.

1. Stable equilibrium.

• An object is said to be at stable equilibrium if it returns to its original position after being displaced slightly.

A vertical line through C. O. G still forces inside the base. When the force is withdrawn, the cone turns to its original position.

        2. Unstable equilibrium.

• An object is said to be in unstable equilibrium if it moves further away from its original position after being displaced slightly.
• The line is outside the base, hence the cone top over and fall.

       3. Neutral equilibrium.

• A body is said to be at neutral equilibrium when it remains where it is after being displaced slightly.
• The line passing through the center of gravity still lies with the base

Conditions for equilibrium.

• The sum of upward forces are equal to the sum of downward forces. The body is said to have transitional equilibrium.
• The sum of clockwise moment are equal to the sum of anticlockwise moment. The body is said to have rotational equilibrium.

Factors affecting stability.

1. Position of the center of gravity.When the center of gravity is near the base, the body is stable but when it is raised or high, the body is unstable.
2. Base area. When the base area is wide, the body is stable. The line passing through the center of gravity is always within the base.
3. The vertical line passing through the center of gravity must fall within the base. When this line falls outside the base, the body topples over and falls.

Application of stability.

1. A motor industry. Low COG. Buses are made more stable by having light materials on the upper part of the body and lower part and heavy engines. The luggage compartments are situated on the lower part so that the center of gravity is lower.
2. A racing car has low COG and wide wheels. The wheel which provides large angle of tilt. This enable the car to negotiate a sharp corner at high speed without toppling.
3. A person carrying a bucket full of water in one hand has to lean/bend his body to the other side to adjust his center of gravity. This is because the additional weight has shifted the position of COG on the other side. As a result, the vertical line passing through the center of gravity falls through the base. The man then bends his body so as to adjust the position of COG of his body and the load.
4. In a double- decker bus, passengers are not allowed to stand at the top end. This is because COG will be raised and the chances of the bus overturning will be increased.
5. A tight- rope- walker uses a pole, umbrella or sways his arms by bending his body to one side to lower the COG and thereby keeps the COG above the rope.

Area of support.

• Most of the objects are made with a wide base area which is heavy e.g. a Bunsen burner which has a wide heavy base which provides a large angle of tilt to avoid toppling, a stool, clump and stand, tables, measuring cylinder.
• When one alights from a moving car or bus, he speeds out his legs to increase area of support.

MECHANICAL PROPERTIES OF MATTER.

Specific objectives.

1. State and explain experimentally hook’s law.
2. Determine the spring constant.
3. Solve numerical problems involving hook’s law.

                                    Mechanical property.

• Is the behavior of matter when subjected to external force.

                        Characteristics used to determine material.

1. Strength.

• Is the ability of a material to oppose or resist breakage when under stretching, compressingor shearing force.
• A material is said to be strong if it can withstand large force without breaking.

2. Stiffness.

• Is the resistance a material offers to the force which tends to change its shape, size or both.

3. Ductility.

• Is the quality of a material which leads to permanent change of size and shape.
• Ductile material e.g. copper, lead and plasticine elongate considerably under stretching force and undergo plastic deformation until they break.
• Is a property of a material to be rolled into sheets, drawn into wires or to be worked into other shapes without breaking.

4. Brittleness.

• Is the quality of material to break just after the elastic limit is reached.
• They do not undergo any noticeable extensions on stretching but snaps suddenly without notice e.g. chalk, bricks and glass.
• They are said to be fragile.

5. Elasticity

• Is the ability of a material to retain its original size after the force causing its formation is removed e.g. rubber, metal and wire.
• These are called elastic materials.

6. Plastic

• These are materials which do not retain or regain their original size or shape when the strength force is removed.