2 MA 36600 LECTURE NOTES: MONDAY, JANUARY 12 Say that we have an object of mass m , perhaps measured in kilograms. Also, say that x = x ( t )isthe position of an object, perhaps measured in meters, at time t , perhaps measured in seconds. Then v = dx dt =˙ x is the velocity measured in meters/second, and a = dv dt = d 2 x dt 2 =¨ x is the acceleration measured in meters/second 2 . Moreover, F denotes the total force on an object, so the expression “ F = ma ” really means “ m d 2 x dt 2 = the sum of the forces on the object.” This is called Newton’s Second Law of Motion . Hence F = ma is really a diFerential equation in disguise. Gravity and Air Resistance. We give more speci±c examples. Say that we have a binary system i.e. a system consisting of two objects which are attracted to each other by gravity. Newton discovered that “any body with mass M attracts any other body with mass m directly toward the mass M , with a magnitude proportional to the (product of the two) masses and inversely proportional to the square of the distance separating them.”
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue.