Download Newton`s laws of motion

Newton’s laws of motion
THEORY
Isaac Newton formulated his three laws of motion in the 1600’s. These form
the foundation for understanding motion in the everyday world. Two new
concepts appear: force and mass.
Definitions
 Force  a push or a pull, measured in units called Newtons.
 Mass  the amount of resistance to acceleration (inertia) a body offers
Alternatively, mass is a measure of the amount of matter a body contains.
Mass has units of kilograms.
Here are the three laws of motion,
Law of inertia: Law One
A particle moves in a straight line with constant speed if no net force acts on
it. That is,
F = 0  v = constant.
Most famous equation in physics: Law Two
If a net force acts on a particle of mass m then the particle accelerates,
F = Fnet = m a.
Law of action-reaction: Law Three
If particle two exerts a force on particle one, F12 , then particle one exerts
a force on particle two, F21. These forces are equal in magnitude but
opposite in direction,
F12 = -F21 .
Comments
 We will expend a considerable amount of time getting to understand these
laws since they are the heart of classical mechanics. Much about these laws
is counter-intuitive, only because we live in a region of space where gravity
exists and therefore, friction is important.
 What does F mean?
This is the (vector) sum of all of the forces that on the particle in question.
To do this sum it is very important to be clear about what you are calling the
system under study.
 The laws imply the effect of a force is to cause acceleration.
Some important forces
 Weight
One of the most important forces we will encounter is weight. The weight of
a particle is the force on the particle by the earth. If weight is the only force
then according to Newton’s second law,
FW = m g.
We have made use of the fact that (near earth and neglecting friction) all
bodies have an acceleration of magnitude, g.
 Elastic force
Another important force is the elastic force a spring exerts on a particle
attached to it,
Fel = -kx
(Hooke’s Law)
Here k is a measure of the stiffness of the spring called the spring constant
and x gives the distance from equilibrium, the stretch or compression.
 Friction
Finally, the importance of the frictional force will be addressed. When a
body is at rest it can experience static friction, if the body is moving across
a surface the friction is called kinetic friction. If both cases the friction is
proportional to the “normal” force acting on the body by the surface it is
placed on. The laws of friction will be presented in class.
APPLICATIONS
In class we will take up a number of applications of these laws:
mass on an inclined plane
pulling on a mass with a rope (tension)
masses attached to each other over a pulley (Atwood’s machine)
elevator problem
A general scheme of solving such problems will now be introduced, what I
call THE NEWTON’S LAW RECIPE:
Step One
Define the system and draw the free-body diagram for the system,
possibly using Newton’s third law.
Step Two
Choose a coordinate system and resolve the force vectors along
the coordinate axes.
Step Three
Use Newton’s second law in component form to obtain the
equations of motion and then solve the equations for the unknowns
in terms of the knowns.
As in all physics problems, make sure the units work out and as
the final step, make sure your final answer seems reasonable.
Examples [in class]