Lecture 3: Physics of
Energy & the Environment- PHYS 161
OK, so we didn't get all the way through Lecture 2.... So we
return to-
Fundamental Kinematics:
- Remember our definition for average velocity :
- the change in
position, p, over the time elapsed, t (or the slope of a
position-time graph).
- Remember, also, that velocity has direction and
speed does
not.
Now that we have definitions for speed and velocity in terms of
position (& displacement) and time, what about
acceleration?
An
experiment using a
fan cart.
- Average acceleration related to velocity vs. time graphs.
Let the Force be with You...
The fan attachment exerts an almost constant
force on the
cart. What is the relationship between that strength of that force
and the cart's acceleration?
- What are the important and unimportant
variables?
- Hypothesis I:
acceleration is proportional to total
force (for constant mass).
- Experiment I:
test hypothesis I. How do we do this?
- What about when we vary mass?
- Hypothesis II:
acceleration is inversely proportion to
mass (when force is held
constant).
- Experiment II:
test hypothesis II. How do we do this?
- Result:
Hypotheses I and II are correct. They can be summarized as
Newton's Second Law:
Definitions for speed, velocity,
acceleration, force and mass in words.
- Average speed of an object during a
given time interval is the change in its position divided by the
length of that time interval.
- Velocity
is a measurement including both the speed of and the
change in direction of an object. To completely specify an average velocity, one must
describe both its average speed and its average direction over a
given time interval. Average
velocity is the change in position--
including any changes in direction-- divided by the change in
time. --In the simple case of motion along a straight line,
average velocity would be the change in position divided by the
time interval--.
- Acceleration is a measurement of both the change in speed and the
change in direction of an object. Average acceleration is the
change in these two divided by the time interval. --For the case
of motion along a straight line, average acceleration would be the
change in velocity (which can be negative or positive) divided by
the time interval--.
- Experiments show that the acceleration of an object
is directly proportional to the net
force acting on it. This has several
ramifications:
- As the net force applied on an object is
increased, so is the object's acceleration. If the acceleration
of an object is observed to decrease, then the net force acting
on it must also have decreased in magnitude.
- The direction of the acceleration is the
same as the direction of the net force.
- If no net force is exerted on an object,
then its acceleration is zero.
- Experiments also show that, for a given net
force acting on an object, the
acceleration of the object is inversely proportional to its
mass.
- Thus, if the mass of an object is
decreased, its acceleration will increase.
- Mass in this context is sometimes called
inertia--
its resistant to change in motion. An object with greater
inertia will resist change in motion (specifically, it will
accelerate less) than a less massive object, all other things
being equal.
- These two observations taken together can be
summed up as Newton's Second
Law: The
acceleration of an object is proportional to the net force acting
on it, and the constant of proportionality is the object's
mass.
Please read sections 12.1, 12.2 and 12.5 of the
textbook (Energy and Problems of a
Technical Society) before Wednesday's
Lecture.
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