lecture_1 (dragged) 1

lecture_1 (dragged) 1 - 2 MA 36600 LECTURE NOTES MONDAY...

This preview shows page 1. Sign up to view the full content.

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.”
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue.

Ask a homework question - tutors are online