1.4 PHYSICS OF FORCE, WORK, POWER, VELOCITY AND ACCELERATION

PHYSICS OF FORCE, WORK, POWER, VELOCITY AND ACCELERATION

1.4.1 General: Physics relating to the force, work, power, velocity and acceleration defines the quantities and establishes their relationship with mathematical treatment. This helps us establishing thrust formula, power and work expression for aircraft gas turbine engines. 

1.4.2 Force: Force is defined as external influence acting on a body to make a change in the state of rest or state of motion of the body. It is a vector quantity having a magnitude and direction of action.

1.4.3 Velocity: This is the change in speed of a moving body per unit time in a specific direction of motion. This is a vector quantity having a magnitude and the direction.

1.4.4 Acceleration: This is the rate of change of velocity of a moving body.

1.4.5 Relationship of Force, Velocity and Acceleration: The relationship is established on the basis of Newton’s Laws of motion. There are 3 Laws stating the nature of state of rest and state of motion of a body. These Laws are as follows:

First Law: "A body will continue its state of rest or of uniform motion in a straight line unless compelled by some external force to change its state."

This is actually the law of INERTIA. It is due to the inertia that body at rest tends to remain at rest, and a body in motion tends to continue its motion with the same velocity (speed and direction), in a straight line. The law expresses the necessity of an external force to overcome the effect of inertia.

An aircraft in level flight (cruise) is under zero resultant force, but it continues to fly at constant speed and direction due to inertia. To accelerate (or decelerate) the aircraft, Pilot must increase throttle to create extra thrust as an unbalanced force.

This law has a close relationship with ‘momentum’. Momentum is the product of mass (m) and velocity (V) and is a vector having magnitude and direction. The direction of momentum of a body is the same as the direction of related motion.

From Newton's first law, under no external force, momentum of a body is constant (either ZERO or a non-zero constant quantity). To change the momentum, an external force must act on to the body.

How much force will be required to make a change in motion or momentum, or, how much change in momentum will be effected by a force, is expressed in the 2^nd Law.

Second Law: "The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts."

This law states the relationship between the force applied to an object and the resultant change of momentum in that direction.

Normally, the mass of an object is constant and the relation becomes:

F = (mv-mu)/t = m(v-u)/t =ma

Where, m is the mass, u is the initial velocity, v is the velocity after t second, F is 

the applied force acting in the direction of motion, a is the acceleration, mu is the initial momentum, mv is the momentum after t seconds.

This formula has direct application in mathematical treatment of jet-propulsion of an aircraft gas turbine engine.

Third Law: "For every action, there is an equal and opposite reaction."

This law gives the mutual relationship between bodies acting on each other with or without contact. The action and reaction always exist in a pair.

The condition of a book resting on a table will produce an action and reaction pair. The weight of the book will exert a force on the top of the table, and the table will exert a lift on the book to prevent it from falling down under gravity.

In the physics of jet-propulsion, the 2^nd Law is used in mathematical formulation of the action force applied by the engine on to the working fluid (air and gas flow) undergoing change in momentum. According to the 3^rd law, there is a reaction pair of this action force applied on to the engine by the gas. This reaction is the propulsive force or the thrust. Thus, the 2^nd law action force formula is taken as the reaction force (thrust) formula. 

1.4.6 Work: Work is a quantity found by multiplying force acting on a body and the distance through which the body has displaced in the direction of the force due to its action. It is a scalar, having only the quantity. If there is no displacement in the direction of force, it is said that the force has not performed any work, or the work performed is zero.

1.4.7 Energy: This is the capacity of doing work.

1.4.7 Power: Rate of doing work by applying force is called power.