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2. About Vector And Scalar Quantities
What is a vector quantity?
Vector quantities refer to the physical values of a body characterised by a magnitude (or an amount, or a figure), as well as having a direction of application. For example: displacement of an object is accomplished by a vector quantity, or the force exerted by a moving body on another body, the torque generated by the combustion forces on an engine’s pistons that turns the engine, the momentum of a rolling bowling pin, the acceleration of a bullet in a rifle barrel after ignition of the propellant, the velocity of the bullet along its direction of travel, the decellaration of a bullet when it penetrates an animal, etc.
What is a scalar quantity?
A scalar quantity is the single total measurement of the one and only physical value or disposition of an entity. Its whole existence is completely described by only this magnitude. It has only a value number that can be read on a marked scale but nothing else. There is no directional application. A scalar quantity only indicates a singular “amount” – like the temperature reading on a thermometer, for example. The volume of a watertank is a scalar quantity, or the volume of a rifle’s cartridge case, or the density of lead, or the speed of light, or the value of the kinetic energy adopted by a bullet at any one instant in a rifle’s bore and expressed in whatever amount of joules. The mass of the earth, or the time of day are scalar quantities.
Because there is no direction involved in that value there can not be any force involved and therefore scalar quantities can not directly do any work. It certainly can not eject its numerical value into or onto something else. This latter law of physics is the crux of a scalar quantity; it merits to be repeated: There is NO direction where the scalar value of say energy goes to or can go to. It is a value which stays within the carrier of the energy.
Some examples of vector and scalar entities
Temperature. When a nurse takes your temperature she reads the value on the scale of the clinical thermometer (see where the term scalar has its origin?). Since we know that temperature is the measured value on that scale of say 25 – 40 degrees centigrade on the clinical thermometer we know that your temperature value also is the value of your average heat or thermal energy level – the average amount of heat in your body. Your temperature (your thermal energy level) can be measured or calculated or expressed in either degrees or in joules. The temperature / heat energy only exists in, and acts on the carrier of the energy. To express it in a different way: the energy due to existing heat (thermal energy) only acts on the carrier of the energy and that heat can not be ejected to break something.
Movement and Speed. A body or entity that moves has a certain rate of change of position (speed). Sound and light move at a certain speed and is measured on a (speed) meter calibrated in various units of distance divided by time. Speed therefore is a scalar quantity because it is read on a scale on a speed-meter - same as temperature is read on the scale of a heat-meter.
Velocity. While speed is a scalar quantity, velocity is different. Velocity is speed applied in a dedicated direction which makes it a vector quantity. Velocity and acceleration both use speed as a starting point in their measurements. Speed, which is the measurement of distance traveled over a period of time, is a scalar quantity. Both velocity and acceleration are vector quantities, meaning that they use both magnitude and a specified direction of application. Velocity or speed are used to calculate the amount of kinetic energy a body in movement has adopted by virtue of its movement (Greek for movement is called kineses).
The scalar and vector values inside a rifle barrel from the moment the propellant starts to burn after having been ignited by the primer until the bullet exits the muzzle 1.21 thousands of a second later. At the moment of exit the bullet has a velocity of 2,700 ft/sec, which has added 3,950 joule kinetic energy to the total thermal energy value of the bullet. The kinetic energy now resides in the bullet as potential heat. This kinetic energy will be released into the bullet as raw heat should an object cause the bullet to lose its kineses (which is measured / indicated by its velocity).
Kinetic energy. The stationary bullet in the case mouth has some heat energy (its average thermal value above absolute zero heat) given to it by its surroundings. This thermal value as we know is a scalar value. As the heated gas presses on the bullet it absorbs some of that heat and its average thermal value is increased. As the bullet moves out of the case mouth and into the bore the friction between the bullet and the rifling creates added heat into the barrel metal as well as onto the bullet, and so the bullet's thermal value is further increased. Due to its movement (kineses) the bullet is given an added amount of potential heat energy in the form of energy by kineses, which reaches its peak as the bullet reaches the muzzle of the barrel and can be calculated and is expressed in joule. This energy by kineses adds a potential value to the bullet's raw thermal value.
Should something be able to stop a 180 gr bullet leaving the muzzle at 2,700 ft per second its internal thermal value (raw heat value) will immediately receive an additional 3,950 joules of raw heat when the translational kinetic energy is immediately transformed into thermal energy when the kineses stops because energy can not be destroyed. It is important to note that the added kinetic energy was a scalar value that the bullet - as the carrier of the energy - had progresively adopted / absorbed during its acceleration to its exit velocity. When this kinetic energy is translated into thermal energy when the kineses stops, the new total value of energy is the new thermal heat energy value that the carrier of the energy (the bullet) contains. That energy is absorbed and contained within the bullet as it is rapidly slowed and can not be "ejected" to do work. Kinetic energy is a scalar value of potential heat when the kineses condition is removed. It is a calculated figure on an imaginary heat meter and nothing else.
Other conditions showing vector or scalar properties
Acceleration and deceleration. Acceleration measures the rate at which the velocity (speed in a dedicated direction) of an object changes. It factors in a period of time as well as direction - making it a vector quantity. Acceleration / deceleration is one variable that is used to calculate a rifle's recoil force or a bullet's potential penetrating force.
Momentum. Momentum is a vector quantity because it indicates that an object with a certain value is in motion. It is the product of mass and velocity, and can only be calculated if it is known how fast an object is moving and in what direction this change takes place. Momentum is another variable that is used to calculate a bullet's potential ability to overcome any resistance to its movement.
Force. Force has magnitude, direction and time as contributing variables. Force causes an object to change its velocity, or its momentum, or both - so force is a vector quantity. Force is the resulting condition between what happens when a bullet that moves due to its momentum is met by the resistance that is suddenly presented by a object in its way. There always is acceleration or deceleration present when a force is present. Impulse force is another variable that is used to calculate a rifle's recoil force or a bullet's penetration force.
In the next post these boring principles will be matched with the hunting rifle, the bullet's passage in the bore, its exit from the muzzle, it movement through the air - and its impact with the shoulder bones of the 48" kudu bull in the photo.