Chapte 4 Newton s Laws of Motion 1 Newton s Law of Motion Si Isaac Newton (1642 1727) published in 1687 2 1
Kinematics vs. Dynamics So fa, we discussed kinematics (chaptes 2 and 3) The discussion, was essentially mathematical No pinciples of physics wee intoduced. Dynamics the elationship of motion to foces that cause it. Dynamics is built on thee pinciples, called Newton s laws of motion. Newton s laws ae the foundation of classical mechanics 3 Two new concepts: ORCE and MASS oce: In eveyday language: push o pull In physics: quantitative desciption of inteaction between a body and its envionment Types of foces new concepts Contact foce involves diect contact between bodies Long-ange foces act even when bodies ae sepaated by empty space. 4 2
foce What foces do we know fom ou expeience? Gavitational oce ictional oce Electomagnetic foce Sping oce Aeodynamic Dag oce Tension foce Note: all foces oiginate fom long-distance inteactions at micoscopical level How about love, hate, cuiosity? 5 foce Thee ae ONLY fou fundamental foces of natue 6 3
OUR o ONE? foce Many scientists think that all fou of the fundamental foces ae, the manifestations of a single foce which has yet to be discoveed. 7 oce is a vecto quantity foce oce has a diection! Notation: Units: Newton (N) (Bitish unit of foce: pound (lb), 1 lb 4.45 N) 8 4
Supeposition of foces foce Any numbe of foces applied at a point on a body have the same effect as a single foce equal to the vecto sum of the foces Equation: = o using components x y z = = = x1 y1 z1 + + + x2 y2 z2 1 + 2 + K+ + K+ n + K n = i xn + K+ yn zn i 9 see also PhEt Coloado Supeposition of foces foce Impotant: foces act independently of each othe: neithe of them is modified by being applied at the same time as the othe Supeposition woks fo any numbe of foces 10 5
Two dogs example Two dogs pull hoizontally on opes attached to a sledge; the angle between the opes is 60 0. Dog A exets a foce of 270 N and dog B exets a foce of 300 N. ind the esultant foce. A x y = 270N cos(30 = 270N sin(30 tan( α) = / y y 0 ) + 300N cos(30 ) 0 0 ) 300N sin(30 ) 0 B 11 Law 1 ist Law of Motion 12 6
ist Law of Motion: omulation An object at est o taveling in unifom motion will emain at est o taveling in unifom motion unless and until an extenal foce is applied Unifom motion is defined as motion with constant velocity: constant speed in an unchanging diection (a linea path) = n i i = 0 13 Inetial fames Newton s fomulation has two impotant implications: 1. Refeence fames that move with constant velocities elative to each othe ae equivalent. These ae called inetial fames of efeence 2. oces ae the same in all inetial fames 14 7
oces and inetial fames State of est fom point-of-view of one obseve is a state of constant velocity fom point-of-view of anothe It isn t mee motion that we need to explain it is the change in state of motion (acceleation) RE: If non-zeo net foce is applied to a paticle - all inetial obseves see the same effect, viz. foce is paallel to acceleation Acceleation is the same in all inetial fames # foce will be the same in all inetial fames All foces behave in the same way: they all poduce acceleations paallel to thei diections 15 Some Histoy Aistotle (384 BC 322 BC, a Geek philosophe) a thing will eithe be at est o must be moving ad infinitum, unless something moe poweful gets in its way But Galileo Galilei (1564 1642, an Italian physicist, mathematician, and philosophe) ealized that foce acting on a body detemines acceleation, not velocity because I stood on the shouldes of giants... Newton 16 8
Cas, cas,??? When a ca stops suddenly, the passenges tend to move fowad elative to thei seats. Why? When a ca makes a shap tun, the passenges tend to slide to one side of the ca. Why? 17 On a bus??? You may play catch with a softball (o a tennis ball) in a bus moving with constant speed on a staight oad, just as though the bus wee at est. Is it still possible when the bus is making a tun at constant speed on a level oad? Why o why not? 18 9
Law 2 Second Law of Motion 19 Second Law of Motion: omulation The ate of change of the momentum of a body is diectly popotional to the net foce acting on it, and the diection of the change in momentum takes place in the diection of the net foce Momentum: Second Law: net = ma p = mv o in the component fom net, x net, y net, z = ma whee is the net o esultant foce that acts on the paticle and m is the mass of the paticle = ma = ma x y z 1 N = 1 kg m/s 2 20 10
Mass mass Second Law effectively defines mass: acceleation and foce can be measued independently mass is then detemined fom = ma Mass in the second Newton s law is a measue of inetia. It is a scala quantity called inetial mass. Notation: m Units: kg 21 One moe mass? mass Gavitational mass m g chaacteizes popety of a paticle to be attacted by any othe paticle with gavitational mass. It is the souce of the gavitational foce (see Newton s Law of Gavitation) 22 11
Inetial vs. gavitational mass Mass m in the 2nd Law measues inetia of a paticle when a foce, not necessaily a gavitational foce, is applied to it. o this eason, we call that mass m I the inetial mass It is not clea a pioi that m g and m I should be the same Expeimentally, no diffeence has been detected: m g = m I = m Equality between inetial mass and gavitational mass is in the foundations of Einstein s geneal theoy of elativity 23 Mass and Weight Mass and weight ae not the same entity: Gavitational mass m g is a scala popety of a paticle Its unit is kilogam (kg). Weight of a paticle is the foce gavity. W = mg Weight is a vecto. Its unit is Newton (N) on it by the eath s Good to know: On Eath, g depends on you altitude. On othe planets, gavity will likely have an entiely new value. Example: on the moon 1.62 m/s 2, o 0.165g. W 24 12
Gym on the Moon???? What gym equipment can be efficient on the Moon fee weights? fitness machines? teadmills? W = mg 25 What is wong with Hollywood movies? Amageddon (1994): A Texas-sized asteoid is headed towad Eath at 22,000 mph and the only way to save humanity is to to land a agtag oil ig cew on its suface, dill an 800-foot-deep hole, plant a nuclea bomb on a convenient fault line, and split the asteoid in half??? Ou heoes have no poblems walking o standing in an Eathlike way even though the gavity foce would have been about a tenth of the gavity foce on Eath. The low gavity cannot suppot an atmosphee and yet we see flames at the cash site of one of the space shuttles. 26 http://www.intuito.com/moviephysics/amageddon.html 13
Stopping a ca example What aveage net foce is equied to stop a 1500 kg ca moving with a speed of 55 mph (88 km/h) within a distance of 200 ft (61 m)? 2 2 v = v0 + 2a( x x0) 2 2 v v0 a = = 4.95 m / s 2( x x0) = ma = 7430 N since 1 lb 4.45 N, then = 1670 lb 2 27 Law 3 Thid Law of Motion 28 14
Thid Law of Motion: omulation o evey Action, thee is an equal but opposite Reaction Note: Action and Reaction both mean oce This law means that foces always occu in pais oces aise fundamentally fom inteaction between two paticles that exet foces on each othe Such foces ae called action-eaction pais of foces If one of them is called the action, the othe is called the eaction 29 Action-eaction pais 30 15
Example: gavitational foce 31 Example: Can it be tue? a = m net Which foce has a lage amplitude, o ae they the same? tack cat 32 16
Example 33 Example 34 17