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Applying Newton's 2nd Law
Learning Goal:
To learn a systematic approach to solving Newton's 2nd law problems using a
simple example.
Once you have decided to solve a problem using Newton's 2nd law, there are steps that will lead
you to a solution. One such prescription is the following:
●
Visualize the problem and identify special cases.
●
Isolate each body and draw the forces acting on it.
●
Choose a coordinate system for each body.
●
Apply Newton's 2nd law to each body.
●
Write equations for the constraints and other given information.
●
Solve the resulting equations symbolically.
●
Check that your answer has the correct dimensions and satisfies special cases.
●
If numbers are given in the problem, plug them in and check that the answer makes sense.
●
Think about generalizations or simplfications of the problem.
As an example, we will apply this procedure to find the acceleration of a block of mass
that is
pulled up a frictionless plane inclined at angle
with respect to the horizontal by a perfect string
that passes over a perfect pulley to a block of mass
that is hanging vertically.
First examine the problem by drawing a
picture and visualizing the motion. Apply
Newton's 2nd law,
, to each
body in your mind. Don't worry about
which quantities are given. Think about
the forces on each body: How are these
consistent with the direction of the
acceleration for that body? Can you think
of any special cases that you can solve
quickly now and use to test your
understanding later?
One special case in this problem is if
, in which case block 1 would simply fall freely under the acceleration of gravity:
.
Part A

MasteringPhysics: Assignment Print View
Consider another special case in which the inclined plane is vertical (
). In this case, for
what value of
would the acceleration of the two blocks be equal to zero?
Express your answer in terms of some or all of the variables
and
.
ANSWER:
=
A force diagram should include only
real
forces that act on the body and satisfy Newton's 3rd law.
One way to check if the forces are real is to detrmine whether they are part of a Newton's 3rd law
pair, that is, whether they result from a physical interaction that also causes an opposite force on
some other body, which may not be part of the problem. Do not decompose the forces into
components, and do not include resultant forces that are combinations of other real forces like
centripetal force or fictitious forces like the "centrifugal" force.
Assign each force a symbol, but don't start to solve the problem at this point.
Part B
Which of the four drawings is a correct force diagram for this problem?
ANSWER:
a
b
c
d
Newton's 2nd law,
, is a vector equation. To add or subtract vectors it is often easiest to
decompose the vector into components. Whereas a particular set of vector components is only valid
in a particular coordinate system, the vector equality holds in
any
coordinate system, giving you
freedom to pick a coordinate system that most simplifies the equations that result from the
component equations.

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