Isaac Newton first published his three laws of motion in 1687 in his monumental
Mathematical Principles of Natural Philosophy.In these three simple laws, Newton sums up everything there is to knowabout dynamics. This achievement is just one of the many reasons why heis considered one of the
greatest physicists in history.
While a multiple-choice exam can’t ask youto write down each law in turn, there is a good chance you willencounter a problem where you are asked to choose which of Newton’slaws best explains a given physical process. You will also be expectedto make simple calculations based on your knowledge of these laws. Butby far the most important reason for mastering Newton’s laws is that,without them, thinking about dynamics is impossible. For that reason,we will dwell at some length on describing how these laws workqualitatively.
Newton’s First Law
Newton’s First Law describes how forces relate to motion:
An object at rest remains at rest, unlessacted upon by a net force. An object in motion remains in motion,unless acted upon by a net force.
A soccer ball standing still on the grass doesnot move until someone kicks it. An ice hockey puck will continue tomove with the same velocity until it hits the boards, or someone elsehits it. Any change in the velocity of an object is evidence of a netforce acting on that object. A world without forces would be much likethe images we see of the insides of spaceships, where astronauts, pens,and food float eerily about.
Remember, since velocity is a vector quantity,a change in velocity can be a change either in the magnitude or thedirection of the velocity vector. A moving object upon which no netforce is acting doesn’t just maintain a constant speed—it also moves ina straight line.
But what does Newton mean by a
netforce? The net force is the sum of the forces acting on a body. Newtonis careful to use the phrase “net force,” because an object at restwill stay at rest if acted upon by forces with a sum of zero. Likewise,an object in motion will retain a constant velocity if acted upon byforces with a sum of zero.
Consider our previous example of you and yourevil roommate pushing with equal but opposite forces on a box. Clearly,force is being applied to the box, but the two forces on the box canceleach other out exactly:
F + –
F = 0. Thus the net force on the box is zero, and the box does not move.
Yet if your other, good roommate comes along and pushes alongside you with a force
R, then the tie will be broken and the box will move. The net force is equal to:
Note that the acceleration,
a, and the velocity of the box,
v, is in the same direction as the net force.
Inertia
The First Law is sometimes called the law of
inertia.We define inertia as the tendency of an object to remain at a constantvelocity, or its resistance to being accelerated. Inertia is afundamental property of all matter and is important to the definitionof
mass.
Newton’s Second Law
To understand
Newton’s Second Law, youmust understand the concept of mass. Mass is an intrinsic scalarquantity: it has no direction and is a property of an object, not ofthe object’s location. Mass is a measurement of a body’s inertia, orits resistance to being accelerated. The words
mass and
matterare related: a handy way of thinking about mass is as a measure of howmuch matter there is in an object, how much “stuff” it’s made out of.Although in everyday language we use the words
mass and
weightinterchangeably, they refer to two different, but related, quantitiesin physics. We will expand upon the relation between mass and weightlater in this chapter, after we have finished our discussion ofNewton’s laws.
We already have some intuition from everydayexperience as to how mass, force, and acceleration relate. For example,we know that the more force we exert on a bowling ball, the faster itwill roll. We also know that if the same force were exerted on abasketball, the basketball would move faster than the bowling ballbecause the basketball has less mass. This intuition is quantified inNewton’s Second Law:
Stated verbally, Newton’s Second Law says that the net force,
F, acting on an object causes the object to accelerate,
a. Since
F =
ma can be rewritten as
a =
F/
m,you can see that the magnitude of the acceleration is directlyproportional to the net force and inversely proportional to the mass,
m. Both force and acceleration are vector quantities, and the acceleration of an object will always be in the
same direction as the net force.
The unit of force is defined, quite appropriately, as a
newton (N). Because acceleration is given in units of m/s2 and mass is given in units of kg, Newton’s Second Law implies that 1 N = 1 kg · m/s2. In other words, one newton is the force required to accelerate a one-kilogram body, by one meter per second, each second.
Newton’s Second Law in Two Dimensions
With a problem that deals with forces acting in two dimensions, the best thing to do is to break each force vector into its
x- and
y-components. This will give you two equations instead of one:
The component form of Newton’s Second Law tells us that the component of the net force in the
direction is directly proportional to the resulting component of the acceleration in the
direction, and likewise for the
y-component.
Newton’s Third Law
Newton’s Third Law has become a cliché. The Third Law tells us that:
To every action, there is an equal and opposite reaction.
What this tells us in physics is that everypush or pull produces not one, but two forces. In any exertion offorce, there will always be two objects: the object exerting the forceand the object on which the force is exerted. Newton’s Third Law tells us that when object
A exerts a force
F on object
B, object
B will exert a force –
F on object
A.When you push a box forward, you also feel the box pushing back on your hand. If Newton’s Third Law did not exist, your hand would feel nothing as it pushed on the box, because there would be no reaction force acting on it.
Anyone who has ever played around on skates knows that when you push forward on the wall of a skating rink, yourecoil backward.
Newton’s Third Law tells us that the force that the skater exerts on the wall,
, is exactly equal in magnitude and opposite in direction to the force that the wall exerts on the skater,
. The harder the skater pushes on the wall, the harder the wall will push back, sending the skater sliding backward.
Newton’s Third Law at Work
Here are three other examples of Newton’s Third Law at work, variations of which often pop up on
SAT II Physics:
You push down with your hand on a desk, and the desk pushes upward with a force equal in magnitude to your push.
A brick is in free fall. The brick pulls the Earth upward with the same force that the Earth pulls the brick downward.
Whenyouwalk, your feet push the Earth backward. In response, the Earthpushesyour feet forward, which is the force that moves you on your way.
The second example may seem odd: the Earthdoesn’t move upward when you drop a brick. But recall Newton’s SecondLaw: the acceleration of an object is inversely proportional to itsmass (
a =
F/m). The Earth is about 1024 times as massive as a brick, so the brick’s downward acceleration of –9.8 m/s2 is about 1024 timesas great as the Earth’s upward acceleration. The brick exerts a forceon the Earth, but the effect of that force is insignificant.
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本帖最后由 端木·宇 于 2008-6-19 19:52 编辑 ]
