These are the foundations you’ll use constantly in performance and flight… — Page 11, Lesson 12

Let’s pick up right where we left off — we’ve just finished work, and now I want to take you through the next block of ideas, because they all build on each other: power, energy, kinetic energy, and then Newton’s laws of motion. These are the foundations you’ll use constantly in performance and flight mechanics. First, power. Power is simply the rate of doing work — in other words, how much work is done in a given time. The unit is the watt, abbreviated W. The formula is power in watts equals force in newtons times distance in metres, divided by time in seconds. Let me give you the worked example from the text: if a force of 10 newtons moves a mass 2 metres in 5 seconds, then the power is 4 joules per second. And a joule per second — J/s — is exactly what we call a watt. So in that example, the power used is 4 watts. Notice the connection: work was force times distance, and power just adds the time dimension. Now, energy. The unit is the joule, same as work. Here’s the key definition: 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. That’s why the unit of energy is the same as the unit of work — joules. Energy and work are two sides of the same coin. Next, kinetic energy. This is a specific type of energy, and the definition is: the energy possessed by mass because of its motion. A mass that is moving can do work in coming to rest. The formula is KE equals one-half m V squared, in joules. Let me unpack that: m is the mass in kilograms, V is the velocity in metres per second, and you square the velocity. The worked example in the text: a 1 kilogram mass of air moving at 52 metres per second — that’s 100 knots — has kinetic energy of 1352 joules. The calculation is 0.5 times 1 times 52 times 52, which gives 1352 joules. Now here’s the crucial point the text makes: doubling the velocity has a greater impact on kinetic energy than doubling the mass, because velocity is squared. So if you double the speed, you quadruple the kinetic energy; if you double the mass, you only double it. That’s why airspeed matters so much in aviation. Now we move to Newton’s First Law of Motion. The statement is: a body will remain at rest or in uniform motion in a straight line unless acted on by an external force. In plain terms, to move a stationary object, or to make a moving object change its direction, a force must be applied. Without an external force, nothing changes — a body keeps doing exactly what it’s doing. That leads directly to inertia. Inertia is defined as the opposition which a body offers to a change in motion. It’s a property of all bodies. Now here’s an important distinction: 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. And note this carefully — inertia refers to both stationary and moving masses. So a parked aircraft has inertia resisting being pushed, and a moving aircraft has inertia resisting being stopped or turned. Finally, Newton’s Second Law of Motion. The statement is: 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. So more force gives more acceleration, and more mass gives less acceleration for the same force. That’s the direct link between force, mass, and acceleration. And then we close with velocity. The unit is metres per second, m/s, and the definition is: rate of change of displacement. Displacement is the straight-line distance in a given direction, so velocity is how fast that displacement changes with time. So the whole chain is: work is force times distance, power is work per unit time, energy is the ability to do work, kinetic energy is the energy of motion with that squared velocity term, and then Newton’s laws tie force, mass, and acceleration together, with inertia as the resistance to change. That’s the complete picture from this section.