Class 090826

look at email from Monday

Testing:

Asking a Question:

The idea of 'clock time'.:  We imagine a clock which, once it starts running, continues running.  The clock can measure the passage of time in any units (e.g., seconds, minutes, milliseconds, hours, days, years, centuries).  Times measured in one unit can of course be converted to different units.

A pendulum could constitute a 'clock', which runs in units of 'cycles' or 'half-cycles'. 

Quick Exercise:

Using the short pendulum, set up an incline so the marble will roll off the incline and fall to the floor.  Release the pendulum and start counting.  Then release the ball at the top of the incline, and count its half-cycles until it reaches the floor.  Note the count at the instant of release, at the instant it reaches the end of the ramp and at the instant it strikes the floor.

Your counts are the 'clock times' for this clock.

You observed three 'clock times' with this clock.  What were they?

Your three 'clock times' define two 'time intervals', one that lasted from release until the ball reached the end of the ramp, and another from the end of the ramp to the floor.

What were the two time intervals?

When you analyze situations involving a clock, you will need to take care to distinguish between clock times and time intervals. 

Definition of Average Rate of Change:

The average rate of change of A with respect to B is defined to be

Examples:

A child's height is 100 cm on Jan 1, 102 cm on May 1 of the same year, 105 cm on October 1 of the same year. 

To answer a question related to an average rate of change on an interval, always answer the following questions:

Answer these questions for the above example.

For a marble rolling down a ramp, off the edge and falling to the floor:

For the same marble on the same ramp:

Do the following, as best you can.  We've had limited discussion of graphs so if you don't do well, it's OK.  We'll have further discussion in our next class.  However do the best you can.

Describe the four graphs you have constructed (again do your best; we will soon develop some language for describing graphs).

A 'graph rectangle' is a rectangle, one of whose sides is part of the horizontal axis.

On a graph of speed in miles / hour vs. clock time in hours, we find a graph rectangle with base 3 and altitude 40.

On a graph of income stream in dollars per month vs. clock time in months, we find a graph rectangle with base 36 and altitude 1000. 

On a graph of force in pounds vs. position in feet, we find a graph rectangle with base 200 and altitude 30. 

On a graph of density in grams / centimeter vs. position in centimeters, we find a graph rectangle with base 16 and altitude 50.

A 'graph trapezoid' is defined by two points on a graph, as follows:

The 'graph slope' between two points is the slope of the 'slope segment' of the graph trapezoid defined by the two points.

On a graph of speed in miles / hour vs. clock time in hours, we find graph points (2, 50) and (7, 60)

On a graph of income stream in dollars per month vs. clock time in months, we find the two points (16, 1000) and (40, 1200). 

On a graph of force in pounds vs. position in feet, we find a graph rectangle with base 200 and altitude 30. 

On a graph of density in grams / centimeter vs. position in centimeters, we find the points (5, 12) and (20, 10).

 

Explain how you construct a 'graph rectangle' from a 'graph trapezoid'.

Explain how to find the area of a 'graph trapezoid'.

Ongoing question:  What is the smallest possible percent difference you think you could detect, using the pendulum, in the times required for the ball to travel down two ramps?

Drop a coin simultaneous with the release of a quarter-cycle long pendulum.  Find the minimum height at which the pendulum clearly strikes the wall first, and the maximum height at which the coin clearly strikes the floor first.

Walk down the sidewalk at constant velocity while someone times you with a pendulum of appropriate length.  Can they verify that you walked at constant velocity?

Walk down the sidewalk, increasing your velocity gradually while someone times you with a pendulum of appropriate length.  According to their results, did you speed up at a constant, an increasing or a decreasing rate?  According to your perceptions, did you speed up at a constant, an increasing or a decreasing rate?

Describe the motion of the dice on the ends of the strap, as you see them from your perspective.

Homework:

Your label for this assignment: 

ic_class_090826

Copy and paste this label into the form.

Take a pendulum home and give it an accurate count.  You should do this for three different pendulum lengths.  The first length should be the distance between your wrist and your middle fingertip.  The second should be double this length.  The third should be double the length of the second.  Submit your results using form at Pendulum Counts Report

Report your results from today's class using the Submit Work Form.  Answer the questions posed above.

Read Chapter 1 of your text again.

View Key Systems:

http://vhcc2.vhcc.edu/ph1fall9/frames_pages/introduction_to_key_systems.htm