Acceleration vs. Ramp Slope

These should be submitted by Monday, Nov. 1.

We are going to modify the acceleration vs. ramp slope experiment to see if we can arrive at even more consistent results.  Results obtained by the first run, using the TIMER, were overall good.  Just about everyone got, or once they use the definition of average rate correctly will have gotten, results within the expected range.  However that range is +- 10% or so from experimental predictions.

We will refine the experiment in three ways:

1. Synchronize the pendulum with motion on the ramp.
2. Use projectile motion.
3. Use a sound editing program (Audacity).

The question we are trying to answer:

• What is the rate of change of the acceleration of an object moving down a ramp, with respect to the slope of the ramp?

You can report each of the three refinements separately, or you can report them all in one submission.  Mix and match as you wish.

For each you need to describe your setup, report your data, document your analysis, analyze errors and report your conclusion.  Your conclusion will be the rate of change of acceleration with respect to ramp slope, reported in the form a +- b, where b is the uncertainty.

Synchronizing the pendulum with motion on the ramp.

Using the bracket pendulum and a domino or stack of dominoes, adjust the slope and/or the length of the pendulum to the point where the arrival of the ball at the end of the ramp coincides, as precisely as possible, with a strike of the pendulum.  The pendulum will have been released simultaneously with the ball, and you will be able to count the 'strikes' of the pendulum with the bracket.  You will need to collect data sufficient to determine the slope of the ramp and the time required for the ball to travel the length of the ramp.

You will repeat this for two slopes.  Both slopes should be small but should differ by at least .04.

Some advice:

• Release the ball without disturbing it.  If you give it the slightest initial velocity either up or down the ramp, your results will be significantly affected.
• Mark or otherwise identify the domino used for each trial so you can accurately measure it in the lab.  Naturally you will want to accurately measure the distance between the end of the ramp resting on the tabletop and the point of contact with the domino.  You could if you wish mark that point and measure it in the lab.
• You can best judge the simultaneity of the ball reaching the end of the ramp and the strike of the pendulum by placing an obstacle at the end and listening.
• Be sure you accurately observe the distances traveled by the ball.
• It's probably best not to start the ball from the same exact point each time.  The track isn't completely smooth and if you start on top of a small bump, or in a small depression, your results will be affected.  A millimeter of difference between two starting points is sufficient to minimize this effect.

Using projectile motion.

Using two different slopes you can observe the slope of the ramp, the distance the ball travels before leaving the end of the ramp, its landing position on the floor (probably better on your book), and the position of the end of the ramp.  The carbon paper can be used to clearly mark landing points.

Advice:

• If you have carpet on your floor the ball is not going to make a good mark on the paper.  If you have a hard floor it will, but most hard floors can sustain damage when struck by a steel ball.  So put something reasonably hard and flat, that won't be subject to damage, on the floor.  Your book might be a good choice.
• Observe the straight-drop landing positions, and the landing positions that result from the two different slopes.
• Make sure the ramp doesn't move between trials; if it does make sure you return it and the supporting domino (or stack of coins, or whatever) to their original positions.  make sure the paper is in the same position on each trial.
• Do enough trials to judge the approximate uncertainty in landing positions.

Use the sound editing program.

You can use any decent sound editing program.

One freeware program:  Audacity.  Search 'audacity sound editor' and check it out.  I have heard of no problems with the download, nor have I experienced any, but of course you should assess the safety of the download yourself.

The program has a Start and a Stop button.  It records the waveform of sounds detected by a microphone connected to your sound card, and has good resolution at 10^-4 seconds.  To use:

• Just record a few seconds of something.
• There are some magnifying glass icons along the top of the screen.  Some of them 'spread out' the time axis, some compress it.  Spread it out to the point where the times have 3-decimal-place accuracy.  Click on a point on the graph and note how the corresponding time is displayed near the bottom left of the screen.
• At this point you know what you need to know to use the program.
• Record your hands clapping as fast as possible.  Take a look at the result.  Estimate how quickly your hands clap, and compare to your results from fast clicks in the TIMER experiment.

The setup is very similar to the preceding.  This time use start the ball with something that makes a sound, and put an obstacle at the end of the displacement interval.  For each trial record the sounds that mark the start and end of the interval, and use the display to accurately determine the time interval.

Think about the following:

• In .001 second sound travels about a foot, so the time it takes sound to get from the starting and stopping points to the microphone can be a factor.
• There could be energy introduced into the system when you strike an object to start the motion.  Some of this energy could affect the initial velocity of the ball.  Do whatever is necessary to avoid that.