A joule is defined as kilograms Times Square meters per square seconds so what in tarnation is a square second?

Answer 1

A joule is NOT defined as "kilograms Times Square meters per square second"! The fact that multiplying Mass (kg) by length (m) and acceleration (m/s2) will produce a resulting measure of Energy (Joules) is simply a derivation of certain other physical quantities. Compare Einstein's famous equation: E = mc2, ie: Energy = Mass x the velocity of light2 (m/s)2. This is dimensionally consistent with the definitions of other quantitites. The Joule (Energy/Work) is defined as Force x Distance. Newtons (Force) x Meters (Distance). Hence one Joule is also 1Nm But Force is defined as Mass (kg) x Acceleration (m/s2) so the unit of Force (N) can also be expressed as the kgm/s2. Thus the Joule can also be expressed as N x m or kgm/s2 x m & thence kg x m2 ÷ s2(ie: kg x m2/s2). To talk about a "square second" is meaningless it's just that to arrive at the calculation for energy/work (Joules) involves dividing by time (seconds) twice and this is most conveniently written as division by s2. It really comes from the involvement of Acceleration in the definitions. Most people have no difficulty in recognising Acceleration as change in velocity (in layman's terms, speed). If Velocity is distance (actually Displacement) divided by time we get m ÷ s or m/s! Change in Velocity (Acceleration) would then be measured as m/s per second, ie: m/s ÷ s which equals m/(s x s) or m/s2. For example, a vehicle travelling at 50m/s which accelerates at 5m/s2 (5m/s per second) for 3 seconds will achieve a new velocity of 65m/s (5m/s faster in each of the three seconds, giving a total increase in velocity of 15m/s). So don't worry about square seconds, they have no physical "reality", they're just a feature of a dimensional analysis of Energy. Physicists like to be able to express any quantity in terms of the basic parameters of Mass (kg), Length (m) and Time (s) and that's just how Energy is expressed that way from first principles (kg x m/s2 x m = Mass x Acceleration x Distance = Force x Distance = the real definition of a Joule!) Hope that helps :)