Mass

Unit - Kilogram (kg) - ‘The quantity of matter in a body.’ The mass of a body is a measure of how difficult it is to start or stop. (a 'body', in this context, means a substance. Any substance: a gas, a liquid or a solid.)

  • The larger the mass, the greater the FORCE required to start or stop it in the same distance.
  • Mass has a big influence on the time and/or distance required to change the direction of a body.

    • Force

    Unit - newton (N) - ‘A push or a pull’. That which causes or tends to cause a change in motion of a body.

    There are four forces acting on an aircraft in flight - pushing or pulling in different directions.

    Weight

    Unit - newton (N) - ‘The force due to gravity’. ( F = m × g ) where (m) is the mass of the object and (g) is the acceleration due to the gravity constant, which has the value of 9.81 m/s2. (A 1 kg mass ‘weighs’ 9.81 newtons)

    If the mass of a A320 is 65000 kg and F = m × g it is necessary to generate: [65000 kg × 9.81 m/s2] 637650 N of lift force.

    Centre of Gravity (CG)

    The point through which the weight of an aircraft acts.

  • An aircraft in flight rotates around its CG.
  • The CG of an aircraft must remain within certain forward and aft limits, for reasons of both stability and control.

    • Work

    Unit - Joule (J) - A force is said to do work on a body when it moves the body in the direction in which the force is acting. The amount of work done on a body is the product of the force applied to the body and the distance moved by that force in the direction in which it is acting.

    If a force is exerted and no movement takes place, no work has been done.

  • Work = Force × Distance (through which the force is applied)
  • If a force of 10 newtons moves a body 2 metres along its line of action, it does 20 newton metres (Nm) of work. [10 N × 2 m = 20 Nm]
  • A newton metre, the unit of work, is called a joule (J).

    • Power

    Unit - Watt (W) - Power is simply the rate of doing work (the time taken to do work).

  • Power (W) = Force (N) × Distance (m) / Time (s)
  • If a force of 10 N moves a mass 2 metres in 5 seconds, then the power is 4 joules per second.

    • A joule per second (J/s) is called a watt (W), the unit of power. So the power used in this example is 4 watts.

    Energy

    Unit - Joule (J) - Mass has energy if it has the ability to do work. The amount of energy a body possesses is measured by the amount of work it can do. The unit of energy will, therefore, be the same as those of work, joules.

    Kinetic Energy

    Unit - Joule (J) - ’The energy possessed by mass because of its motion’. ’A mass that is moving can do work in coming to rest’.

    KE = ½ m V2 joules

    The kinetic energy of a 1 kg mass of air moving at 52 m/s (100 knots) is 1352 joules; it possesses 1352 joules of kinetic energy. [ 0.5 × 1 × 52 × 52 = 1352 J ]

    From the above example it can be seen that doubling the velocity will have a greater impact on the kinetic energy than doubling the mass (velocity is squared).

    Newton’s First Law of Motion

    ’A body will remain at rest or in uniform motion in a straight line unless acted on by an external force’.

    To move a stationary object or to make a moving object change its direction, a force must be applied.

    Inertia

    ‘The opposition which a body offers to a change in motion’. A property of all bodies, inertia is a quality, but it is measured in terms of mass, which is a quantity.

  • The larger the mass, the greater the force required for the same result.
  • A large mass has a lot of inertia.
  • Inertia refers to both stationary and moving masses.

    • Newton’s Second Law of Motion

    ’The acceleration of a body from a state of rest, or uniform motion in a straight line, is proportional to the applied force and inversely proportional to the mass’.

    Velocity

    Unit - Metres per second (m/s). - ‘Rate of change of displacement’

    Acceleration

    Unit - Metres per second per second (m/s2) - ‘Rate of change of velocity’.

    A force of 1 newton acting on a mass of 1 kg will produce an acceleration of 1 m/s2

    Acceleration = Force / Mass

  • For the same mass; the bigger the force, the greater the acceleration.
  • For the same force; the larger the mass, the slower the acceleration.

    • Momentum

    Unit - Mass × Velocity (kg-m/s) - ‘The quantity of motion possessed by a body’. The tendency of a body to continue in motion after being placed in motion.

  • A body of 10 kg mass moving at 2 m/s has 20 kg-m/s of momentum.
  • At the same velocity, a large mass has more momentum than a small mass.

    • Newton’s Third Law

    ‘Every action has an equal and opposite reaction’

  • If a force accelerates a mass in one direction, the body supplying the force will be subject to the same force in the opposite direction.

    • Principles of Flight

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