Turning Effect of Forces

Turning Effect of Forces

Moments

Hinge Door

Pivot

Force B

A smaller force is needed if applied further away from the hinge

Force A

A larger force is needed if applied nearer to the hinge

Amount by which the door turns depends on two factors:

1. Magnitude of the force used, and

2. Perpendicular distance of the force applied from the force.

Moment of a force = Turning effect of a force

SI unit of the moment of a force is the newton metre (N m).

The moment of force is a vector, it has both a magnitude and direction. The direction of the moment can be either clockwise or anticlockwise about the pivot.

We must describe the magnitude in N m and the direction as clockwise or anticlockwise for a complete description of the moment of a force.

Conditions for equilibrium\

For a stationary object, the forces acting on it are balanced, i.e. Resultant force is zero.

For an object in equilibrium must satisfy both conditions:

1. All forces acting on it are balanced, i.e. Resultant force is zero.

2. The resultant moment about the pivot is zero, i.e. The Principle of Moments must apply.

Levers

Simple machines like the lever make use of the Principle of Moments. When we apple a force or effort at one end of the lever, a load is lifted at the other end. All levers have a pivot or fulcrum about which the lever rotates.

Centre of Gravity

The centre of gravity of an object is defined as the point through which its whole weight appears to act for any orientation of the object.

For a lamina (thin sheet of material), the centre of gravity is at its geometrical centre, it may also lie outside the object, e.g. The ring.

Plumb line: string with a small weight attached.

The plumb line acts as the visible ‘weight’ force acting on the lamina and the lamina is suspended in different ways, the point where the lines intersect is the centre of gravity. Note that only two lines are sufficient to find the centre of gravity.

For solid, draw lines from the vertices to find the centre of gravity.

Stability

The ability of an object to return to its original position after it has been tilted slightly.

Stable equilibrium because it is tilted slightly, it returns to its original position without toppling.

1. Centre of gravity rises, then falls back.

2. Line of action of its weight W lies inside the base area of the cone.

3. The anticlockwise moment of its weight W about the point of contact C causes the cone to return to its original position.

Unstable equilibrium because it is tilted slightly, it topples over.

1. Its centre of gravity falls and continue to fall further.

2. The line of action of its weight W lies outside the base are of the cone.

3. The clockwise moment of its weight W about the point of contact C causes toppling.

Neutral equilibrium because if it is slightly displaced or rolled, it will stay in its new position.

1. Its centre of gravity neither rises nor falls, it remains at the same level above the surface supporting it,

2. The lines of action of the two forces W and R always coincide,

3. There is no moment provided by its weight W about the point of contact C to turn the paper cone.

Thus, to increase the stability of an object:

1. Its centre of gravity is as low as possible.

2. The area of its base is as wide as possible.

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