060920

Note that unless otherwise specified experiments should be done by groups of 2 or 3 people, not more.

Text Assignment:  Read Chapters 1 and 2.  Come in next time with questions about anything you don't understand.

Quiz:

Give your data for the two-ramp system as measured by the pendulum, with the ball traveling down the first ramp from point A to point B, then up the second ramp from point B until it comes to rest for an instant at point C, then back down the second ramp to point B.  

Give your data for the same system as measured using the computer timer:

According to your analysis of the data obtained using the pendulum, fill in the table:

According to your analysis of the data obtained using the pendulum, fill in the table:

Explain how you obtained your results for B to C:

get data for rotating chair, analyze

using the TIMER get angular position vs. clock time data for a person in a rotating chair

Observe the length of a series of rubber bands when it supports 1 domino, 3 dominoes, 5 dominoes, 7 dominoes, etc., until the length of the series exceeds the 1-domino length by 15%.  Take care that the length of the series never exceeds the 1-domino length by more than 15%.

... rb calibration, error analysis labs, paper rules \calipers\ micrometers, data program -> network, accel vs. ramp slope, deterioration of difference quotients, hypothesis testing with pearl pendulum and ball down ramp, ball and ramp projectile behavior, uniformity of accel for ball on ramp (curved ramps ...) by mid October

Summary of uniformly accelerated motion in terms of definitions and graphs:

All of the theory of uniformly accelerated motion comes from two basic definitions  and one fact about the v vs. t graph:

• Average velocity is average rate of change of position with respect to clock time, so vAve = `ds / `dt.
   
• Average acceleration is average rate of change of velocity with respect to clock time, so aAve = `dv / `dt.
   
• If the v vs. t graph is a straight line, then the average of v over a given interval occurs at the midpoint of that interval (from which it follows, among other things, that vAve = (vf + v0) / 2).

In terms of graphs, we first observe the following:

• The change in position over a given time interval is the 'rise' of the s vs. t graph over that interval, from which it follows that slope = rise / run for a given time interval is `ds / `dt, or average velocity for that interval.
• The change in velocity over a given time interval is the 'rise' of the v vs. t graph over that interval, from which it follows that slope = rise / run for a given time interval is `dv / `dt, or average acceleration for that interval.

It follows from what has gone before that:

• The change in position over a given time interval is equal to the corresponding area beneath the v vs. t graph.

Very similar reasoning tells us that

• The change in velocity over a given time interval is equal to the corresponding area beneath the acceleration vs. t graph.

To solve a uniform acceleration problem:

• List the symbols v0, vf, `ds, `dt, a as well as `dv and vAve
• Determine which of these quantities you are given or can immediately determine from the given information.
• List these 'known' quantities at the top of a 'flow diagram'.
• Use the definitions of ave vel and ave accel, along with a v vs. t graph, to figure out everything you can. 

(The v vs. t graph is linear and the average velocity occurs at the middle of the time interval, with v0 and vf at the beginning and the end of the time interval.)

(Use units for every quantity).

• List the equations of motion.
• Circle all the 'known' quantities.
• Find the equations that can be solved for 'unknown' quantities it terms of 'known' quantities. 
• Solve those equations and check that the units work out.
• Substitute the 'known' values (including units) and carefully calculate the 'unknown' values and their units. 
• Make sure the units work.
• Make sure your solutions are consistent.

To analyze today's experiment:

• Analyze the motion from A to B.
• Analyze the motion from B to C.
• Analyze the motion from C back to B.

To 'analyze' means to find the values of all the variables v0, vf, `dt, `ds, a as well as vAve and `dv, using the above procedures.

(unit calculations)

(experiment)

(set up temporary page with paths to sup study etc)