Class 0917

Go to h:\shares\physics and open the program entitled Multiple Choice Generator.

Run the program and do as it says. Type in your VCCS login name, if you know it, and if not just type in your first initial and last name (no punctuation). Then type in quizzes for your course.

The sequence of buttons is Next Question, Display Choices, Enter Answer and See Results, or something very much like that.

Experiment: Rubber band force vs. length.

Measure the the number of units of water suspended vs. length of your rubber band and make a graph.
A unit of water is up to the 3 cm height as measured from the lowest point of the cup, with the cup vertical.
Your graph won't be a perfect straight line. Assuming, however, that it is, find its slope.

Force to hold block on ramp:

Measure rubber band length vs. ramp slope, keeping rubber band length in the same range as before.

Graph number of force units vs. ramp slope.

Find the slope of the graph.

Suspend the block from enough rubber bands that their lengths all stay in the same range as the one you measured.

Assuming that the rubber bands all have about the same force characteristics, determine the weight of the block in force units.

Experiments

Is acceleration uniform on a uniform incline?

Take a very good set of data for the 15-, 30-, 45- and 60-cm runs, to be analyzed over the weekend and handed in Monday. Include the slope of the ramp in your report.
Estimate how nearly you think you were able to synchronize the pendulums with release and with the end of the ramp.
Be as clever as you can in reducing possible errors.
Report just how clever you were.
Your final report should present your data, your discussion of cleverness, your analysis and a graph complete with error bars.
The final question is whether it is possible to draw a straight horizontal line that passes through all the error bars.

Another question for analysis, using your data from this experiment:

Plot the average velocity you obtained for each distance vs. the halfway time for each run (i.e., the time it took to get halfway down the ramp).
Find the slope of this graph.
Explain what the slope and the graph tell you about the motion of the ball down the incline, assuming its acceleration is indeed uniform.
See if the result of this analysis is consistent with the results of the first analysis.

Roll a ball up the incline and time how long it takes it to go up and come back down.

Assuming that the time up is equal to the time down, what is the acceleration of the ball on the incline? Is this consistent with your other results for acceleration on this incline?
Should the acceleration going up the incline be equal to the acceleration coming down?
What is the displacement from start to finish? What is the time from start to finish? Using this displacement, time interval and your result for acceleration, find the initial velocity of the ball.

Write up the experiments done in class this week. Your experiments should show data, analysis and a discussion of methodology and errors. University physics students should include error bars, based on reasonable estimates of errors. Your reports should ultimately address the following questions:

For motion down a ramp of uniform length but with varying slope, is the average velocity on the ramp a linear function of ramp slope, and if so what is the slope of your graph of average velocity vs. ramp slope. University physics students should work out the theory of why average velocity should or should not be a linear function of ramp slope, assuming that acceleration is a linear function of ramp slope.
For motion down a ramp of uniform length but with varying slope, is the average acceleration on the ramp a linear function of ramp slope, and if so what is the slope of your graph of average acceleration vs. ramp slope.

Note on reporting experiments:

Most of the preliminary writeups for this experiment were good for this stage of the course, containing a lot of good and correct work, but

most were incomprehensible in the sense that it was impossible for a reader to tell what was observed, where it was being used in the calculations and how the reasoning flowed from data to conclusions and
a few reports also lacked the final graph.

It is always up to the writer to figure out how to present his or her information and analysis in a clear and coherent manner. A table such as the one below can be very helpful for the reader. The table should of course be accompanied by explanations of how the various results were obtained.

ramp length	rise of ramp	run of ramp	slope of ramp	`dt on ramp	vAve on ramp	vf on ramp	accel on ramp

0915 Quiz

2. A ball starts from rest on an incline of length 18 cm on which its acceleration is 20 cm / s^2. When the ball reaches the end of this incline it rolls without any immediate change in velocity onto a second incline, on which its acceleration is 40 cm / s^2, and whose length is 24 cm.

Use the equations of uniformly accelerated motion to answer the following:

For the first incline which of the variables v0, vf, `ds, a and `dt do you know?

We know that `ds = 18 cm, v0 = 0 and a = 20 cm/s^2.

Find for the first incline the average velocity, change in velocity and any of the 5 equation variables you don't already know.

Using the fourth equation vf^2 = v0^2 + 2 a `ds we can solve for vf:

vf = +-sqrt(v0^2 + 2 a `ds) =

+-sqrt(0^2 + 2 * 20 cm/s^2 * 18 cm) =

+-27 cm/s, approx..

Since `ds is positive and a is positive, with v0 = 0, the velocity is increasing from 0 and we conclude that the +27 cm/s is the correct solution.

Now using the first equation `ds = (vf + v0) / 2 * `dt we find that

`dt = 2 `ds / (vf + v0) = 2 * 18 cm / (0 + 27 cm/s) = 1.3 sec approx.

vAve = (0 + 27 cm/s) / 2 = 13.5 cm/s approx.

`dv = vf - v0 = 27 cm/s - 0 = 27 cm/s.

For the second incline which of the variables v0, vf, `ds, a and `dt do you know?

v0 = 27 cm/s, as mentioned.

`ds = 24 cm and

a = 40 cm/s^2.

Find for the second incline the average velocity, change in velocity and any of the 5 equation variables you don't already know.

We have the same vbls we had before so we use the same strategy:

vf = +- sqrt( v0^2 + 2 a `ds) = +- sqrt( (27 cm/s)^2 + 2 * 40 cm/s^2 * 24 cm) = +- sqrt(2640 cm^2 / s^2) = +-51 cm/s.

We choose the +51 cm/s since the ball is still accelerating thru a positive displacement in the positive direction and starts with positive velocity.

`dt = 2 * `ds / (vf + v0) = 2 * 24 cm / (27 cm/s + 51 cm/s) = .65 sec.

`dv = (52 cm/s - 27 cm/s) = 25 cm/s.

3. For the situation of #2:

On which of the inclines was acceleration greatest?

Accel is greater on the second incline (40 cm/s^2 vs. 20 cm/s^2).

On which of the inclines did velocity change the most?

Velocity changed by more on the first incline, though the acceleration was less and the distance was also less.

Are your answers to these two questions consistent?

Seems contradictory. Greater accel. on the second, greater displacement on the second, but practically more velocity change on the first.

The key is that because of the greater initial velocity on the second incline, the ball spent less time on that incline, and acceleration is the rate of change of velocity with respect to clock time. So the lesser change in clock time on the second incline gave us less change in velocity on that incline.

Experiments

Experiment 1:

Make the observations necessary to determine the acceleration of a steel ball rolling down an incline vs. the percent incline.

Sketch a graph of acceleration vs. percent incline and find its slope.

Experiment 2:

Set up two inclines with unequal slopes so that the ball will roll down the first incline and onto the second with no significant change in velocity.

Measure the two inclines so you know the rise, run and length of each.

When the ball runs from the start of the first incline to the end of the second, determine how long the ball spends on each incline and see if your results are consistent with the results of your first experiment.

That is, from your data determine the accelerations on the two ramps, and see if those accelerations are consistent with the accelerations predicted by the a vs. slope graph obtained on from the first experiment.

Directions for the VHCC LAN Practice/Quiz Program, accessible through the lab in Room 307 and from 310.

If the Multiple Choice program is on your desktop and you don't have instructions to download a new version, just double-click on that icon and Enter your VHCC username in the box where it is requested.
Enter 201 for your course number.
A list of topics will appear. Enter the number of your choice.
Wait until a message pops up telling you how many questions you will have and OK that box.
The next box allows you to choose whether the questions will have just 1 correct answer or may have multiple correct answers.
Once you have answered this box the screen will tell you to click on the 'next question' button. When you do a question will pop up.
Next you click on the Display Choices button and your choices will pop up.
Once you have decided which choice or choices are true you can click on the Answer Questions button. Enter the letter(s) corresponding to the valid choice(s).
Click on the See Results button, which will give you (often repetitive) feedback on each of your answers.
Click on the Next Question button and repeat the process.

If you are instructed to first download the latest version of the Multiple Choice Generating Program:

Go to Web address www.bb.vccs.edu and log in. If you don't yet have your login name you can log in as vhstudent with password college.
Go to Supervised Study Current Semester (NOT to your Physics page) and Click on Course Documents.
Scroll down that page until you see Multiple Choice Generating Program. Either run the program or copy it to your desktop or some other location on your computer. However don't answer any questions yet.

If you're working at home, once the 201_c.txt file is in the c:\vhmthphy folder and the program itself is on your desktop, you just need to double-click to run the program.

It will be equally easy at VHCC once the network is set up to accomodate the program.