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Last time my engineering expertise was put to the test when it was discovered that Santa’s sleigh was being hampered by a strong gust of wind. At that time we introduced the Work-Energy Theorem to determine how strong the wind’s opposing force was, and today we’ll work with the Theorem to compute just what Rudolph was up against. Here again is the expanded, workable version of the Work-Energy Theorem as introduced last time, F × d = ½ × m × [v22 – v12] where F is a force acting upon a moving object of mass m over a distance d to slow it from an initial velocity of v1 to a final velocity of v2. Applying the Theorem to the dynamics at play in Santa’s situation, F is the opposing wind force, which acts over a distance, d, to slow his sleigh from an initial velocity of v1 to a final velocity, v2, thus presenting Rudolph and his buddies with a real delivery challenge.
If we know that Santa, his sleigh and reindeer have a combined mass of 900 kilograms — which is pretty standard for a fully loaded sleigh and reindeer team — and their initial velocity was 90 meters per second, final velocity 40 meters per second, and the distance over which the slowing took place was 760 meters, then the formula to calculate the opposing wind force becomes, F × d = ½ × m × [v22 – v12] F = ½ × m × [v22 – v12] ÷ d F = ½ × (900kg) × [(40 meters/sec)2 – (90 meters/sec)2] ÷ 760 meters F = -3848.7 Newtons = -865.2 Pounds The minus sign signifies that the wind must exert an opposing force of 865.2 pounds in order to slow Santa’s sleigh down. In order for Santa to get back on his delivery schedule, Rudolph is going to have to make up for lost time by expending extra energy. We’ll see how he does that next time. Copyright 2015 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |
