Chap 6.1-6.4: Dynamics I
Start by reading the textbook carefully using paraphrasing and do the examples
without looking at the solutions.
There are a total of 11 worked examples in the textbook in chapter 6 and all
of them are important (except the "challenge example" #11 which is a bit
beyond what we will do in this class). The only way to learn dynamics is to
practice it in multiple contexts. Make sure you look carefully at all
exercises. Do them without looking at solutions.
Section 6.1 to 6.3 discusses two models of Nature.
-
Mechanical Equilibrium
. This is for objects where the net
force is zero (or close to). The object could be at rest or moving at
constant velocity and Newton's First law states that the sum of the forces
should be zero \vec{F}_{net} = \vec{0}
-
Constant Force
. This is for objects on which the net force
is constant. In this case there will be a constant acceleration in the same
direction as the net force. One can use
\vec{F}_{net} =m\vec{a}
and the constant kinematic
equation we have learned before.
Kinematics is still a crucial part of all of our problem solving skills. Since
we will mostly work with the constant force model at first, we will get a
constant acceleration. The question may be asking about velocity and position
in which case we need to use constant acceleration kinematics to solve for
these variables.
The problem solving strategy 6.1 is super important. In a nutshell it is.
-
Model
: the object as a dot and decide which force should
be included or neglected. (use Tactics Box 5.2 to remember how to identify
forces).
-
Visual
: You need a sketch, a coordinate systems
(important!) and a free body diagram (look back at Tactics Box 5.3 on how
to draw free-body diagram)
-
Solve
: Write
\vec{F}_{net} =m\vec{a}
for each direction (x and
y). Solve for acceleration or for forces. Use kinematics if needed.
-
Assess
: Check units and whether the number make sense.
Mechanical Equilibrium.
In the following video, I illustrate the problem solving strategy.
and here is a real demo with this cart on ramp example.
Tips to remember from the video and your readings
-
It is always good to tilt your coordinate axes to align as many forces as
possible (or align with the acceleration vectors).
-
When we write Newton's Law in component forms, we write the magnitude of
forces (like n and T) and put the sign directly in front (+ or -). We
account for direction by using \cos\theta
or
\sin\theta