Download Limitations on Newton`s 2nd Law

Newton's Second Law
Newton's Second Law as stated below applies to a wide range of physical phenomena,
but it is not a fundamental principle like the Conservation Laws. It is applicable only if
the force is the net external force. It does not apply directly to situations where the mass
is changing, either from loss or gain of material, or because the object is traveling close to
the speed of light where relativistic effects must be included. It does not apply directly on
the very small scale of the atom where quantum mechanics must be used.
Data can be entered into any of the boxes below. Specifying any two of the quantities
determines the third. After you have entered values for two, click on the text representing
to third to calculate its value.
Newtons =
pounds =
kg *
m/s2
slugs *
ft/s2
Limitations of Newton's Second Law
Limitations on Newton's 2nd Law
One of the best known relationships in physics is Newton's 2nd Law
but, though extremely useful, it is not a fundamental principle like the conservation laws.
F must be the net external force, and even then a more fundamental relationship is
The net force should be defined as the rate of change of momentum; this becomes
only if the mass is constant. Since the mass changes as the speed approaches the speed of
light, F=ma is seen to be strictly a non-relativistic relationship which applies to the
acceleration of constant mass objects. Despite these limitations, it is extremely useful for
the prediction of motion under these constraints.
Standard Newton's Laws Problems
Index
Some examples of standard "building block" problems which help build
understanding of the principles of mechanics. Click on any of them for further Newton's
details.
Horizontal Pulley
Inclined Pulley
Inclined Pulley with Friction
Application of Newton's second law to mass on
incline with pulley.
Given an incline with angle
degrees which
has a mass of
kg placed upon it. It is
attached by a rope over a pulley to a mass of
kg which hangs vertically. The friction
between the mass and the incline is represented by
a friction coefficient mu=
. Taking
downward as the positive direction for the
hanging mass, the acceleration will be
Acceleration =
Note that the tension in the rope is
NOT equal to the weight of the
hanging mass except in the special
case of zero acceleration.
m/s²
With this acceleration, the tension in the rope will
be
T=
Newtons compared to the weight W =
Newtons for the hanging mass. Exploring
different values for the masses will allow you to
Friction must be treated with care in a show that the tension is less than the weight for
situation like this. If the hanging mass downward accelerations and greater than the
is large enough to overcome friction
and accelerate the mass upward on the
incline, then the friction force will
oppose it and act downward. If the
mass on the incline is large enough, it
will overcome friction and move
downward, pulling the hanging mass
upward. In this case the friction force
will act up the incline. There is an
intermediate range of masses where
the block will move neither up nor
down the incline.
weight for upward accelerations when the net
force on the hanging mass must be upward.
By changing masses, you can explore whether the
mass will move up the incline, downward, or
remain at rest. This calculation tests whether the
masses are sufficiently different to overcome
friction in either direction. If the resulting
acceleration is zero, that indicates that the
imbalance of forces is not sufficient to overcome
friction in either direction.
Elevator Problem
This is an application of Newton's second law to the forces felt in an elevator. If you are
accelerating upward you feel heavier, and if you are accelerating downward you feel
lighter. If the elevator cable broke, you would feel weightless since both you and the
elevator would be accelerating downward at the same rate.
support force F = mass x acceleration + weight
For a mass m=
kg, the elevator must
support its weight = mg =
Newtons to hold
it up at rest. If the acceleration is a=
m/s²
then a net force=
Newtons is required to
accelerate the mass. This requires a support force
of F=
Newtons. Note that the support force
is equal to the weight only if the acceleration is
zero, and that if the acceleration is negative
(downward), the support force is less than the
weight. If you enter a downward acceleration
greater than 9.8 m/s² you will get a negative
support force, showing that you must force it
downward to get an acceleration greater than that
of free fall.
See lifting mass problem
"Weightless" condition if the cable breaks.
You Feel "Weightless" If the Elevator
Cable Breaks
The phenomenon of "weightlessness" occurs when there is no force of support on your
body. When your body is effectively in "free fall", accelerating downward at the
acceleration of gravity, then you are not being supported. The sensation of apparent
weight comes from the support that you feel from the floor, from a chair, etc. Different
sensations of apparent weight can occur on an elevator since it is capable of zero or
constant speed (zero acceleration) and can accelerate either upward or downward. If the
elevator cable breaks then both you and the elevator are in free fall. The resultant
experience of weightlessness might be exhilirating if it weren't for the anticipation of the
quick stop at the bottom.
Newton's Second Law Illustration
Newton's 2nd Law enables us to compare the results of the same force exerted on objects
of different mass.