Newton’s 2 nd law of motion

1. Newton’s 2nd law of motion Brittany Vincent Newton 1642 -1727

3. Newton's 2nd Law enables us to compare the results of the same force exerted on objects of different mass. Acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object). What does this mean? Everyone unconsciously knows the Second Law. Everyone knows that heavier objects require more force to move the same distance as lighter objects.

4. The second law explains how the velocity of an object changes when it is subjected to an external force. The law defines a force to be equal to change in momentum (mass times velocity) per change in time. Newton also developed the calculus of mathematics, and the "changes" expressed in the second law are most accurately defined in differential forms. (Calculus can also be used to determine the velocity and location variations experienced by an object subjected to an external force.) For an object with a constant mass m, the second law states that the force F is the product of an object's mass and its acceleration a: • F = m * a

5. Equations • The reasoning, given in An Introduction to Mechanics by Kleppner and Kolenkow and other modern texts, is that Newton's second law applies fundamentally to particles. In classical mechanics, particles by definition have constant mass. In case of a well-defined system of particles, Newton's law can be extended by summing over all the particles in the system: • where Fnet is the total external force on the system, M is the total mass of the system, and acm is the acceleration of the center of mass of the system. • Variable-mass systems like a rocket or a leaking bucket cannot usually be treated as a system of particles, and thus Newton's second law cannot be applied directly. Instead, the general equation of motion for a body whose mass m varies with time by either ejecting or accreting mass is obtained by rearranging the second law and adding a term to account for the momentum carried by mass entering or leaving the system:

6. History of the second law • This was translated quite closely in Motte's 1729 translation as: • LAW II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd. • According to modern ideas of how Newton was using his terminology, this is understood, in modern terms, as an equivalent of: • The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed. • Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading: • If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both. • The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton's formulation and modern formulations

7. links • http://www.grc.nasa.gov/WWW/K-12/airplane/newton.html • http://hyperphysics.phy-astr.gsu.edu/hbase/Newt.html • http://en.wikipedia.org/wiki/Newton's_laws_of_motion • http://images.google.com/imgres?imgurl=http://www.lersus.de/res/modules/enu/physics/1/res/files/newtons2law_0__0_.gif&imgrefurl=http://www.lersus.de/res/modules/enu/physics/1/content/example1.html&usg=__QORj6-1nr1Qkni2SvgGpjK4IQxc=&h=256&w=510&sz=13&hl=en&start=5&um=1&itbs=1&tbnid=lMLBINlSa2Hm0M:&tbnh=66&tbnw=131&prev=/images%3Fq%3Dnewton%2527s%2Bsecond%2Blaw%2Bof%2Bmotion%26hl%3Den%26safe%3Dactive%26rls%3Dcom.microsoft:en-us:IE-Address%26rlz%3D1I7ADBS_en%26sa%3DN%26um%3D1