Lecture 2: Physics of Energy & the Environment- PHYS 161

Questionnaire:

Fundamental Kinematics:

For now, let's confine ourselves to motion in a straight line, or one-dimensional motion.

• Distance & position or, "where's Crow, Oregon?"

  

• Motion-- changing position over time, or "time wounds all heels."

• Making, matching and interpreting graphs of position vs. time.
  • Make a graph using a motion detector and the computer, and ourselves as moving objects (see above).
  • How does one move to match the position-time graph given on the computer display?
  • What can we say about the motion associated with different segments of our position-time graphs?
• Speed and velocity-- what's the difference?

  

• Velocity from position vs. time graphs.

  

• Definition: average velocity is the change in position, p, over the time elapsed, t.

  

• Reading velocity from velocity vs. time graphs.
• Moving to match velocity vs. time graphs.
• Acceleration related to velocity vs. time graphs.
  • 
• Definition: average acceleration is the change in velocity over the time elapsed.

  

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 1.1 - 1.3 of the textbook (Energy and Problems of a Technical Society) before Friday's Lecture.

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