The Physics of Superheroes: Spectacular Second Edition by James Kakalios Read Free Book Online

our earlier example in the Introduction, we employ the three laws of motion as first elucidated by Isaac Newton in the mid 1600s. These laws are frequently expressed as: (1) an object at rest remains at rest or, if moving, keeps moving in a straight line if no external forces act upon it; (2) if an external force is applied, the object’s motion will change in either magnitude or direction, and the rate of change of the motion (its acceleration) when multiplied by the object’s mass is equal to the applied force; and (3) for every force applied to an object, there is an equal and opposite force exerted back by the object. The first two laws can be expressed succinctly through one simple mathematical equation:
    FORCE = (MASS) × (ACCELERATION)
    That is, the force F applied to an object is equal to the resulting rate of change in the object’s velocity (its acceleration a) when multiplied by the object’s mass m, or F = ma .
    Acceleration is a measure of the rate of change of the velocity of an object. A car starting from rest (velocity = 0) and accelerating to 60 mph would have a change in velocity of 60 mph - 0 mph = 60 mph. The acceleration is found by dividing this change in velocity by the time needed to make the change. The longer the time, the lower the acceleration needed for a given change in speed. An automobile speeding up from 0 to 60 mph in six seconds will have a much larger acceleration than if it does so in six hours or six days. 10 The final speed will be the same for all three cases, namely, 60 mph, but the accelerations will be radically different owing to the different times needed to affect this change in velocity. From Newton’s F = ma , the force needed to create the former, faster acceleration is obviously much larger than for the latter, slower case.
    When the acceleration is zero, there is no change in the motion. In that case, a moving object keeps moving in a straight line, or if sitting still, remains so. From the expression F = ma , when a = 0, then the force F = 0, which is the whole point of Newton’s first law of motion.
    While this may be straightforward from a mathematical point of view, from a common-sense perspective it is nothing short of revolutionary. Newton is saying (correctly) that if an object is moving, and there is no net outside force acting on it, then the object will simply continue moving in a straight line. However, you and I, and Isaac Newton for that matter, have never seen this occur! Our everyday experiences tell us that to keep something moving, we must always keep pulling it or pushing it with an external force. A car in motion does not remain in motion unless we keep pressing the accelerator pedal, which ultimately provides a force. Of course, the reason that moving objects slow down and come to rest when we stop pushing or pulling them is that there are forces of friction and air resistance that oppose the object’s motion. Just because we stop pulling or pushing does not mean, in the real world, that there are no forces acting on the object. There’s nothing wrong with Newton’s laws—we just have to make sure we account for friction and air resistance when applying them. It is these unseen “drag forces” that we must overcome in order to maintain uniform motion. Once our pulling or pushing exactly balances the friction or air drag, then the net force on the object is zero, and the object will then continue in straight-line motion. Increasing the push or pull further will yield a net nonzero force in the direction of our push or pull. In this case, there will be an acceleration proportional to the net force. The constant of proportionality connecting the force to the acceleration is the mass, m , reflecting how much the object resists changing its motion.
    It is worth pointing out here that mass is not the same as weight. “Weight” is another term for “force on an object due to gravity.” Mass, on the other hand, is a measure of how much stuff