Σ F = Ma. The vector
sum of all forces acting on an object of mass M equals
that mass times the acceleration vector a of the object.
Operationally, the “weight”
of an object, in Newtons, is the force required to support it
completely in any given frame of reference. The mass of an
object is a measure of its inertia, and the operational way to
measure mass is to compare a given mass to a standard mass. Note
that there is no real excuse in physics to ever use the term
“weight.” It does not appear under that name in any physical
law.
The fundamental forces we encounter in
everyday life include gravity, and the electromagnetic forces
between systems of atoms. These are the only two forces
that can act across significant distances. All the forces of
nature involve particles called bosons, or force carriers,
which are emitted by one object and absorbed by the other.
The laws of motion can only be applied
in non-accelerating frames of reference, called inertial.
Viewed in an accelerating frame, a car rounding a curve, a
ball resting on a table appears to accelerate, but there is
no horizontal force acting on it (sketch 1). When we view
the system from outside, where we can see the car is
accelerating, we see the ball is moving at constant velocity
relative to the ground while the car accelerates
perpendicular to that velocity (sketch 2). Do not try
to set up the laws of motion in noninertial
(accelerating) frames of reference!
How do we understand the reading of a
spring scale on which we are standing, in an elevator? The
spring scale measures the normal force n which is
exerted upward on us to support us in that frame of
reference. The only other force acting is gravity, mg.
Thus our acceleration, taking components along y,
satisfies ma = n - mg. Given the acceleration of the
elevator, we can solve for n, the reading of the
spring scale.
The Third Law is used when we have two
or more interacting objects. In such a case the forces
form pairs; a force exerted by object 1 on object 2 results
in a corresponding force exerted by object 2 on object 1.
You can't touch without being touched. All interactions
between objects involve force pairs with the same magnitude
but different directions. By the way, in general the
forces do not have to be in opposite directions, but they do
have to have the same magnitude.
Take components of vector
equations, so that you can do algebra.
Draw ALL forces acting on EACH object,
and use the 3rd Law where appropriate to relate the
magnitudes of different forces acting on different
interacting objects. Then apply the 2nd Law to EACH object,
taking vector components, and using the simplifications that
the 3rd Law indicates; then, do the algebra needed to solve
for whatever quantity is unknown in the problem, in terms of
the others. Here is some good
advice.
To stretch a spring a distance x, a force
Fx = kx must be applied. That
means the spring resists with a force Fs
= − kx. Here k is a constant for the
given spring.
When two or more bodies
interact, the 3rd law of motion must be applied to every
interacting pair. For example, when a force F is
applied to two boxes on a horizontal table with friction
negligible, each box exerts a contact force on the other. If
the force box 1 exerts on box 2 is F12
and the force box 2 exerts on box 1 is F21,
then the two contact forces have the same magnitude.
It is also vital to note that the contact forces are less
than the magnitude of F, since if the boxes are
accelerating, a net force must act on each box, and it
must be a net force on each box that would satisfy the 2nd
Law for each of the boxes, since both boxes have to
move, in contact, with the same acceleration!
