#### Force-Centre of Gravity and Equilibrium, Physics tutorial

Concept of Force:

Define: Force might be stated as a push or a pull that modifies or tends to change the shape or state of rest or uniform motion of a body in a straight line.

Nature of Force: The nature of force might be sum up as shown:

• Force is basically a push or a pull.
• It is the thing or entity which causes objects to move.
• This is a vector quantity, that is, it for all time consists of both magnitude and direction.
• Force is not a visible entity and can be explained via its effects that are simple to see.
• If a body A applies a force (or action) on a body B, B as well applies an equivalent force (or reaction) in the opposite direction.

Types of Force:

There are basically two kinds of forces:

1) Contact Forces:

It is a force that is applied if two bodies or surfaces are in contact by one other, directly or indirectly. Illustrations comprise a pull, a push, reaction forces, tension forces, friction, thrust forces.

2) Non-contact Forces or Force Fields:

This is a force which is exerted between objects that are not in contact with one other. A force field makes itself felt devoid of the presence of any material connection among the bodies comprised. Force fields are of the action at a distance kind.

Illustrations of force fields are magnetic, gravitational, electrostatic or electric force fields and nuclear force fields.

a) Gravitational Force Field:

Each and every object in the universe attracts other objects by a gravitational force. This gravitational force is responsible for the orbital motion of moon round the earth or the planets round the sun. It was introduced by Sir Isaac Newton (1642-1727).

b) Electrostatic or Electric Force Field:

Electrostatic force is the force among two electrical charges. A force of attraction is experienced when the two charges are dissimilar (that is, positive and negative) whereas a force of repulsion is experienced when the charges are similar (that is, positive and positive or negative and negative). The law governing the force among electrical charges was discovered through a French scientist, Charles Coulomb (1736-1806).

c) Magnetic Force Field:

A permanent magnet or an electromagnet (that is, a wire or coil carrying current) sets up a force field in the area or neighborhood surrounding it. The other magnet or electromagnet at any point in this area or neighborhood undergoes a force of attraction or repulsion due to the magnet or electromagnet. Such kind of force is termed as a magnetic force field. A moving charge as well sets up a magnetic force field in addition to the electric field which surrounds it. A second charge in such two combined fields will experience a force due to the magnetic field only when it is in motion.

d) Nuclear Force Field:

There exists, in nucleus of an atoms, the strongest force in nature that holds altogether the protons and neutrons which make up the nucleus. When this force weren't there, then the electrostatic forces of repulsion between the protons that carry positive electrical charges would cause the nucleus to disintegrate. A much significant characteristic of nuclear forces is that they are short ranged-two nuclear force among two nucleons is negligible when the separation between the nucleons is greater that around 10-15m.

Concepts of Equilibrium:

A body is stated to be in equilibrium when its acceleration is zero, that is, there is no total force acting on it in any direction. Thus, the body might be at rest or moving by constant velocity.

Types of Equilibrium:

There are mainly two kinds of equilibrium: Static equilibrium and Dynamic equilibrium.

1) Static Equilibrium:

When a body consists of zero acceleration by virtue of being at rest, the body is stated to be in static equilibrium. An illustration is a book resting on a table.

2) Dynamic Equilibrium:

Whenever a body is moving by a constant velocity in a straight line or is rotating by a constant angular velocity regarding a fixed point or axis via its centre of mass, the body is stated to be in the dynamic or kinetic equilibrium.

An illustration is a car whose engine is running at constant speed for a considerable length of time.

Resultant and Equilibrium Forces:

1) A resultant force is that single force that, acting alone, will encompass the similar effects in magnitude and direction as two or more forces acting altogether.

2) The equilibrium of two or more forces is that single force that will balance all the other forces taken altogether. It is equivalent in magnitude however opposite in direction to the resulting force.

Equilibrium of three Forces acting at a Point:

1) Parallelogram of Forces:

The principle of parallelogram of forces defines that when two inclined forces are symbolized in magnitude and direction through the adjacent sides of a parallelogram, their resultant is signified in magnitude and direction through the diagonal of the parallelogram passing via the point of intersection of the two sides.

2) Triangle of Forces:

The principle of triangle of forces defines that when three forces are in equilibrium, they can be represented in magnitude and direction via the three sides of a triangle taken in order.

Moment of a Force:

The moment of a force regarding a point or axis is the turning effect of the force about that point or axis. It is equivalent to the product of the force and the perpendicular distance of its line of action from the point or axis.

Mathematically,

Moment = Force x perpendicular distance of pivot to the line of action of the force.

Unit of moment:

As force is in Newton (N) and distance is in meters (M), the SI unit of moment is Newton-metre (Nm).

Principles of Moments:

The principle of moments defines that when a body is in equilibrium beneath the action of a number of coplanar forces, then the sun of the clockwise moment regarding any point on the body is equivalent to the sum of the anticlockwise moment about similar point.

Couples:

Define: A couple is a pair of equivalent however oppositely directed and parallel forces that are not acting in a straight line.

Characteristics of a couple:

1) The couple consists of a zero resultant force however consists of a turning effect on the body on which it acts.

2) A couple can just cause a body on which it acts to rotate however not to move linearly.

3) The moment of a couple is the product of one of the forces and the perpendicular distance among the lines of action of the two forces.

4) The moment of a couple is as well termed as a torque.

5) The distance among the two equal parallel forces of the couple is termed as the 'arm of the couple'.

6) A couple can be councelled or neutralized through applying an equivalently similar couple of opposite moment to the body experiencing the couple.

Conditions of Equilibrium:

Conditions of Equilibrium beneath the Action of Parallel Coplanar Forces:

The Coplanar forces are the forces which lie in the similar plane. Parallel forces are the forces whose lines of an action are all parallel to one other.

1) Forces: The algebraic sum of the forces in any given direction should be zero. Therefore signifies the sum of forces acting in one diction should be equivalent to the sum of forces working in the opposite direction.

2) Moments: The algebraic sum of the moments of all forces regarding any point on the body should be zero or the net clockwise moments of the forces around any point on the body should be equivalent to the total anti-clockwise moments of the forces around the similar point.

Conditions of Equilibrium beneath the Action of Non-Parallel Coplanar Forces:

A set of non-parallel coplanar forces can act on the body to keep it in the equilibrium. The non-parallel forces can simply be resolved into vertical and horizontal components, giving mount to two parallel forces at right angles to one other.

1) Forces: The vector sum of all forces acting on the body should be zero. This signifies that the arithmetic sum of the forces or components of the forces acting on the body on any direction should be zero, that is, ΣFx = 0 or any algebraic sum of the horizontal should be zero and ΣFy =0 or the algebraic sum of the vertical components should be zero.

2) Moments: The algebraic sum of moments of all the forces regarding any point on the plane or axis perpendicular to the plane of the forces should be zero.

Equilibrium beneath the Action of three Non-Parallel Forces (Special Case):

To be in equilibrium, the given conditions should be satisfied:

1) The three forces should lie in a plane (that is, they should be coplanar forces.

2) The line of action of forces should intersect in a general point.

3) The vectors representing the three forces can be ordered to form a closed triangle with side correspondingly parallel to the direction and proportional in length to the magnitude of the forces.

Centre of Gravity:

Define:

a) The centre of gravity (CG) of a body is stated as the point via which the line of action of the weight of the body for all time passes irrespective of the point at which the whole weight of the body seems to be concentrated.

b) The centre of mass of a body is stated as the point at which the net mass of the body seems to be concentrated.

Types of Stability of Equilibrium:

There are three kinds of stability of equilibrium that a body at rest might experience:

1) Stable Equilibrium: A body is stated to be in stable equilibrium when it tends to return to its original position if slightly displaced.

Illustrations of bodies in stable equilibrium are:

• A rectangular block resting in the horizontal surface.
• Cone resting on its base.

2) Unstable Equilibrium: A body is stated to be in unstable equilibrium when it tends to move further away from the original position or topples over if slightly displaced.

Illustration of bodies in unstable equilibrium:

• Cone resting on its apex.
• An egg resting on its pointed end.

3) Neutral Equilibrium:

A body is stated to be in neutral equilibrium when it tends to come to rest in its new position if slightly displaced.

Illustrations:

• A sphere or ball on a smooth horizontal table (or surface).
• A cone or cylinder or an egg resting on its side.

Equilibrium of Bodies in Liquids:

Concept of Upthrust:

General experience exhibits that if a box is totally or partially immersed in a liquid like water, the body appears to be lighter. Such an object appears heavier if fully out of water. This proposed that there is an upward force applied by a liquid on an object fully or partially immersed in it. As an outcome of this upward force there is therefore an apparent loss in weight of the immersed object. This upward force is termed as the 'upthrust' of the liquid on the object.

Archimedes Principle:

Archimedes principle defines that if a body is completely or partially immersed in a fluid (that is, liquid or gas); it undergoes an upthrust that is equivalent to the weight of fluid displaced.

Formula for upthrust:

An object fully immersed in a liquid shifts a volume of liquid equivalent to its own volume.

Upthrust = volume of object x density of liquid x g

Here, Upthrust = U, Volume of object = V, Density of liquid = ρ and g is acceleration due to gravity.

U = Vρg

When the object is partially immersed in the liquid (example: only 2 of the object is immersed in the liquid), then

U = (2/3) V x ρ x g

U = (2 V ρ g)/3

Principle of Floatation:

The Principle of floatation defines that an object will float in a fluid (that is, liquid or gas) if the upthrust applied by the fluid in which it floats is equivalent to the weight of the object.

From the principles of floatation it can be stated that:

1) A floating body moves its own weight of the fluid in which it floats.

2) Any floating body is in equilibrium beneath two forces, namely its own weight acting downwards and the upthrust of the liquid acting upwards.

3) A body will float in a liquid when the density of the object is less than the density of the liquid.

4) A body denser than a liquid can still float in the liquid, when the body is shaped in such a manner that its volume can move its own weight of the liquid.

Density and Relative Density:

Density: The density of a substance is stated as the mass per unit volume of the substance.

S.I. unit of density is kilogram per metre cubed (kg/m3 or kg m-3) and its symbol is ρ ( rho).

Relative Density: The relative density (R.d) of a substance is stated as:

R.d. = mass (or weight) of a substances/Mass (or weight) of equivalent volume of water

Alternative definition of relative density is:

R.d. = density of substances/Density of water

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