Introductory Motion Experiments

Video Versions Introductory Motion Experiments

Instructions: You are responsible for reading and following these instructions.
The video clips for these experiments are on CD #0; the number(s) of the required clip(s) is(are) referred to in this document under the writeup for each experiment.
There is a q_a_ version of each of these experiments, which are recommended as an alternative if you have difficulty following the instructions on this page. If you can follow the instructions given here it might be more efficient to use them than the q_a_ version. If you wish to use this option download the file q_a_ph1_vid_exp_2_6.exe from the Downloads page under Course Documents on the Supervised Study Current Semester pages.

Video Version Experiment 2: Average velocity vs. slope for a ball on a single ramp; rate of change of velocity.

Video Version Experiment 3: The final velocity of a uniformly accelerating object released from rest is double its average velocity.
Video Version Experiment 4: Acceleration is constant for an object rolling down a uniform incline.
Video Version Experiment 5: Determination of the acceleration of gravity using acceleration vs. slope (ramp slope < .1) and by synchronizing time of fall with pendulum.
Video Version Experiment 6: The horizontal range of a projectile with initial velocity in the horizontal direction is an accurate indicator of its initial velocity.

Instructions:

Writeups of all experiments in this course are to be submitted electronically as Rich Text files, according to the following guidelines:

Except where inappropriate, all raw data are to be presented the form of clearly labeled tables, and are to be indicated as raw data. (Note: 'Raw data' refers to anything you observe directly, without doing any calculations of any kind).
All questions posed in the experiment are to be answered in self-documented form.
Procedures and analysis are to be described in self-documented narrative form.
When analysis involves repeated use of a calculation procedure, only a single example of that procedure is required. For subsequent uses of the procedure, it is sufficient to say something like 'using the same procedure we obtain the results inthe third column ... '
Wherever appropriate, significant intermediate calculations and results are to be presented in the form of clearly labeled tables.
Whenever appropriate, results are to be presented in the form of clearly labeled graphs.
Graphs are to be included in Microsoft Excel format, using a scatter plot (no other type of plot is appropriate to the graphing of most scientific information). If you with to use another format, specify that format and submit a sample for the approval of the instructor. Do not use bitmaps (e.g., graphs created using Paint or Paintbrush). You may if you wish scan neatly made handdrawn graphs into your document.
When you are asked to do something with a graph that is not easily accomplished with Excel or an approved alternative, describe in words what you did and what results were obtained.

Experiment 2: Measuring average velocity for a cart rolling from rest down a uniform incline; Average velocity vs. slope; Inferring acceleration.

Read the following notes:

The video clips for these experiments are on CD #0; the number(s) of the required clip(s) is(are) referred to in this document under the writeup for each experiment.
It is suggested that you use the Pearl Pendulum rather than synchronizing a handheld pendulum as shown in the experiment. The Pearl Pendulum is easier to use and gives more accurate results.
There is a q_a_ version of this experiment, which is recommended as an alternative if you have difficulty following the instructions on this page. If you can follow the instructions given here it might be more efficient to use them than the q_a_ version. If you wish to use this option download the file q_a_ph1_vid_exp_2_6.exe from the Downloads page under Course Documents on the Supervised Study Current Semester pages.

See the corresponding video files on the CD (see note in red at the top of this document) entitled Introductory Video Experiments, video clips # 3. Reference also #'s 1 and 2 for pendulum as a timer. You run the CD by running the disk_0.htm file in the root folder of the CD. Access Video Experiments by clicking on the Video Experiment Clips link in that document.

We measure the time required for a cart to accelerate from rest down various uniform inclines with slopes between 0 and .1. For each incline we determine the average velocity of the cart. We then plot average velocity vs. slope and determine whether the graph appears to follow a straight line. Using the asserted propositions that the cart accelerates uniformly and that the final velocity of an object which accelerates uniformly from rest is double its average velocity, we determine for each incline the average rate at which the velocity of the cart changes. We then construct a graph of the average rate of velocity change vs. incline slope. We finally determine the slope of the straight line which best fit our data points.

As instructed on the video clip, determine the time required for the cart to roll the length of the ramp, starting from rest, for each of the four ramp slopes.

Note the following:

The slope of the ramp is the rise divided by the run between the two measured points.
The run is the distance parallel to the tabletop.

Put your data into a table:

Decide how the data can best be organized to allow a reader to make a quick comparison between the motion resulting from the different slopes.
Include in your table everything that was measured, including your pendulum lengths and the number of swings down the incline.

Describe exactly what you did to obtain the data. Describe your procedure in detail.

Analyze the data:

For each pendulum length determine the time of a complete cycle of oscillation. Then use this information to determine the time required for the cart to accelerate down the incline.

Determine the average velocity for each slope, using the distance the cart traveled and the time required.

Sketch a graph of average velocity vs. ramp slope.

Is the graph linear (that is, does it seem to stay close to some straight line)? If not describe how it varies from linear.

For a straight ramp, if the cart starts from rest (and not otherwise), we expect that the final velocity will be double the average velocity.

Using this fact, make a table of final velocity vs. ramp slope.

Using your table of final velocity vs. ramp slope, keeping in mind that since the cart starts from rest its initial velocity is zero, determine for each ramp the rate at which velocity changes.

Plot the rate of velocity change vs. ramp slope.

Fit the most appropriate straight line to your graph.
Determine the slope of this line.

Submit results, including

an organized data table
each of the tables you constructed in the process of analyzing the experiment
an explanation of how you analyzed your data
a detailed description of each graph and how well the straight line fits
complete and detailed, self-documented answers to all questions

Experiment 3: The final velocity of a uniformly accelerating object released from rest is double its average velocity.

The video clips for these experiments are on CD #0; the number(s) of the required clip(s) is(are) referred to in this document under the writeup for each experiment.

There is a q_a_ version of this experiment, which is recommended as an alternative if you have difficulty following the instructions on this page. If you can follow the instructions given here it might be more efficient to use them than the q_a_ version. If you wish to use this option download the file q_a_ph1_vid_exp_2_6.exe from the Downloads page under Course Documents on the Supervised Study Current Semester pages.

By timing an object as it accelerates from rest down one uniform incline, then as it travels along a second slight incline elevated just enough to keep the object moving at a uniform velocity, we test the previously asserted hypothesis that when an object accelerates uniformly from rest, its final velocity will be double its average velocity. We do this by graphing the velocity on the second ramp vs. the velocity on the first. We interpret the slope of this graph to test our hypothesis.

Observe the two-ramp system on the CD (see note in red at the top of this document). Select Introductory Video Experiments and view video clips #'s 7 and 8.

Using the first of the two clips attempt to synchronize a pendulum so that the time required to accelerate a distance down the first ramp from rest corresponds to precisely one-half of a complete cycle (i.e., from release to the far point on the other side of equilibrium). See if the pendulum then returns to its original position in precisely the time required for the ball to move double the first distance on the second ramp, on which its velocity is reasonably constant. When we have this synchronization we know that the time spent on the first ramp is equal to the time spent on the second.

If the pendulum synchronizes in this way, then we have good evidence that the average velocity on the second ramp is double that on the first (since the ball traveled twice as far on the second as on the first in the same elapsed time).

Using the second clip and the TIMER program (you should have downloaded the program along with the rest of the programs for the course; if not go to the appropriate page and download it now), time the ball as it travels down the first ramp and an appropriate distance across the second, obtaining the time interval on each ramp. If you can't figure out how to use the TIMER program, you may use a pendulum as a timer, but this would be cumbersome. The TIMER program is very convenient and easy to use.

The motion of the ball down the two-ramp system is accompanied by three sounds:

a. The sound of the starting event,

b. The 'clink' that occurs in the transition from the first to the second ramp, and

c. The sound of the object striking the obstacle on the second ramp.

Don't look at the video clip when timing, just listen, so you don't anticipate events. Clicking on each of the three events in turn, time the ball from the instant of release to the instant it reaches the end of the first ramp, then for a measured distance across the second ramp.
When timing, be conscious of your tendency to anticipate some events more than others (e.g., some people might anticipate the bump at the end more than the 'clank' from the first ramp to the second), and try to control the tendency. Relax and let your finger on the keyboard respond to the sounds, don't try to anticipate.
Repeat your timing for the 20-cm distance two more times, so that you have 3 timings for this 20-cm distance.
Repeat for rolls of 10 cm, 15 cm, 25 cm, 30 cm, 35 cm, ..., 50 cm down the first ramp.
Present your data in a clearly labeled table.

Determine average velocities and plot a graph of your results:

For each distance, use the median (the 'middle') value of the time required to roll down the first ramp to determine the average velocity of the ball on that ramp.
For each distance, use the median value of the time required to roll along the timed portion of the second ramp to determine the average velocity of the ball on that ramp.

For each distance on the first ramp, plot the average velocity on the second ramp vs. the average velocity on the first. Be sure you follow the appropriate conventions in interpreting the 'vs.' in those instructions--get the right quantity on the vertical axis, and get the right quantity on the horizontal axis. If you aren't sure you have it right, stop at this point and email the instructor with everything you have so far and a request to check your work.

Sketch a straight line which comes as close as possible, on the average, to your data points.

Don't worry about whether the straight line actually goes through any of the data points, worry about average closeness; a perfect graph of real data will rarely go through the precise position of of any data point.

Extend your straight line in both directions, slightly beyond the first and last data points.

Analyze your graph and answer questions:

By measuring the rise and the run of your straight line, determine its slope.
Does your straight line pass near the origin of your coordinate system? Why should it or should it not do so?
On which ramp does the ball have the greater average velocity? Why should this be so?
Which is the greatest and which is the least of the following: the average velocity of the ball on the first ramp, the initial velocity of the ball on the first ramp, or the final velocity of the ball on the first ramp?
Place in order, from the smallest to the largest, indicating any 'ties':

the average velocity of the ball on the

the average velocity of the ball on the second ramp,

the initial velocity of the ball on the first ramp,

the initial velocity of the ball on the second ramp,

the final velocity of the ball on the first ramp, and

the final velocity of the ball on the second ramp ( i.e., its velocity at the instant the timing ceased, not after you changed everything by stopping it).

Sketch a graph of the velocity of the ball vs. clock time from the instant it is released until the instant timing stops on the second ramp. Indicate the instant at which you think the ball reaches its average velocity on the first ramp.
Why might we suspect that the average velocity on the second ramp should be double that on the first, and how well does this experiment validate that hypothesis?

Analyze the potential effect of timing errors on your results for the 30-cm first-ramp distance (Principles of Physics students do only parts marked *)

* For the 30-cm distance, what do you think is the uncertainty in your measurement of the time interval on the first ramp (e.g., +-.01 sec, +-.05 sec, +-35 hours)? Why do you think that this is an appropriate value for the uncertainty?
* For your estimated uncertainty, we would expect that the actual time required was between the observed time minus the uncertainty and the observed time plus the uncertainty

For example, if the observed time is 2.3 seconds and the uncertainty is +-.02 sec, then we expect that the actual time lies between 2.3 - .02 sec and 2.3 + .02 sec, or between 2.1 sec and 2.5 sec.

We might say that the actual time `dt satisfies 2.1 < `dt < 2.5.\

In symbols, if the actual time is `dt, the observed time is `dt_obs and the uncertainty is t_unc, then we can say that `dt lies between the 'low estimate' `dt_obs - t_unc and `dt_obs + t_unc.

Written in the form of an inequality, we would say `dt_obs - t_unc < `dt < `dt_obs + t_unc.

* Based on your observed time and your expected uncertainty, what are the minimum and maximum values between which the actual time should lie?
* Had the actual time `dt been equal to the minimum expected value, then what would have been the average velocity on the first ramp?
* Had the actual time been equal to the maximum value, what would have been the average velocity on this ramp?
* What therefore do you expect is the minimum value that the actual average velocity might have had on this ramp? What is the maximum?
* On your last graph, near the point corresponding to the 30-cm distance, indicate this range of velocities as explained under Q & A on the homepage, under topic Error Bars, Rectangles and Linearity.

Repeat this process for the second ramp, and indicate the corresponding range of velocities as explained under Q & A on the homepage, under topic Error Bars, Rectangles and Linearity.
Block in the rectangle defined by your velocity ranges and see if your straight line actually passes through this rectangle.

Repeat this analysis for every data point on your graph (Principles of Physics students: repeat the analysis only for the 10-cm point and the 50-cm point).

For each data point, use the uncertainty in `dt that is appropriate to your means of timing for each point.
Does your straight line pass through all the resulting rectangles?
If not, is it possible to draw a straight line that passes through all the resulting rectangles?

We have analyzed the possible effect of timing errors.
We might also have analyzed the effect of errors in distance measurements.
Would you expect these errors to be more or less significant than timing errors, and why?

Submit results, including

an organized data table
a table of average velocity on the second ramp vs. average velocity on the first
a detailed description of your graph of second-ramp ave vel. vs. first-ramp ave. vel. and how well the straight line fits
a report of the slope of your line and whether the line seems, within experimental uncertainties, to pass through the origin.
a description of your graph of the vel. vs. clock time from release to the end of the second ramp
complete and detailed, self-documented answers to all questions.

Experiment 4. Acceleration is constant for an object rolling down a uniform incline.

Read the following notes:

The video clips for these experiments are on CD #0; the number(s) of the required clip(s) is(are) referred to in this document under the writeup for each experiment.
The Pearl Pendulum is an acceptable substitute for any timing process, but you may also use the timing process as described on the CD. The choice is yours.
There is a q_a_ version of this experiment, which is recommended as an alternative if you have difficulty following the instructions on this page. If you can follow the instructions given here it might be more efficient to use them than the q_a_ version. If you wish to use this option download the file q_a_ph1_vid_exp_2_6.exe from the Downloads page under Course Documents on the Supervised Study Current Semester pages.

By timing an object as it accelerates from rest for various distances down an incline, we infer its average acceleration for various distances and average speeds. We then test to validate the hypothesis that the acceleration is in fact uniform lawn the incline.

See the corresponding video files on the CD (see note in red at the top of this document) entitled Introductor Video Experiments, video clip #4.

You may use some of your data from a preceding experiment.

By timing a ball as it rolls from rest through distances of 10, 15, 20, 25, 30, 35, 40, 45 and 50 cm down a uniform incline, we determine whether the acceleration on the incline seems to be related to either the distance the ball rolls down the incline or to its average velocity on the incline.

Use data from your previous experiment.
Present your data in a clearly labeled and organized table.

Determine the average acceleration corresponding to each distance:

For each distance, make any calculations necessary to determine the time required for the object to accelerate through that distance from rest.
Using the results of the preceding experiment (i.e., the relationship between average and final velocities on the first ramp), the average velocity and the fact that the ball started from rest, determine the final velocity of the ball for each distance.
Determine the change in velocity for each distance, then using the time required for each distance determine the average acceleration for each.

Graph acceleration vs. distance and draw conclusions:

Plot average acceleration vs. distance traveled on the first ramp and decide whether the acceleration changes with the distance in some systematic way, or whether the apparent variations in acceleration are simply the result of unavoidable experimental uncertainties.
How did you make use of the results of the preceding experiment to justify your calculation of the acceleration in this experiment?
Are the variations in acceleration observed in this experiment within the range of variations to be expected with the equipment you are using?
Do your results support the hypothesis that the acceleration of the ball rolling down a uniform incline is indeed independent of how fast the ball is rolling and of where the ball is on the ramp? If so, how do the results support hypothesis? If not, how do the results fail to support the hypothesis?

Analyze errors:

Using a procedure similar to that in the preceding experiment, determine the uncertainty in the acceleration for each point (Principles of Physics: analyze only the 10-, 30- and 50-cm points) and indicate these uncertainties on your graph as explained under Q & A on the homepage, under topic Error Bars, Rectangles and Linearity.
Is it possible to draw a straight horizontal line that passes between the error bars for every graph point?

Explain why, if it is so, then we have good support for the hypothesis that the acceleration on the ramp is constant.

View Introductory Video Experiments video clip #5.

Submit your results

Submit results in the usual manner. Since you use data from a previous experiment you don't need to describe the setup, etc.. But do describe the process of determining acceleration from you data.

Experiment 5. Determination of the acceleration of gravity using acceleration vs. slope (ramp slope < .1), and then by using time of fall as indicated by the pendulum timer.

The video clips for these experiments are on CD #0; the number(s) of the required clip(s) is(are) referred to in this document under the writeup for each experiment.

For ramp slopes between 0 and .1, the acceleration of a cart down the slope is very nearly a linear function of ramp slope, with only a 1/2 % deviation from linearity within this range of slopes. In this experiment we determine the accelerations of the friction car corresponding to a selection of ramp slopes within this range, and plot acceleration vs. ramp slope. Since frictional forces and tabletop deviations from linearity will be very nearly the same for all trials, the slope of the graph gives us the acceleration of gravity.

Using the pendulum timer we can measure the time required for a dropped object to fall various distances from rest under the acceleration of gravity. We can calculate the acceleration for each distance and test hypothesis that the acceleration is the same for all heights.

Alternatively using the pendulum timer we can synchronize the dropping of a ball with the time required for the pendulum to complete a quarter-cycle for each of several drop distances. If the acceleration of the dropped object is uniform, then the time required for the object to drop should be proportional to the square root of the distance dropped. Since the period of the pendulum is proportional to the square root of its length, it follows that if gravity accelerates objects uniformly then the distance dropped should be proportional to the length of the synchronize to pendulum. From the associated proportionality constant, and from the proportionality constant for the pendulum period, we can determine from our data the acceleration of gravity.

Part 1

For the first part of the experiment we use the data collected in the Video Version of Experiment 2. Recall that we observed the motion of a low-friction cart on a series of small ramp slopes to obtain data for the acceleration of the cart vs. the ramp slope.

Determine the acceleration and ramp slope for each incline.

For each ramp slope use your measurements of the heights of the ramp ends and ramp length to determine the slope of the ramp.
For each ramp slope use your T = A * L^p function from the pendulum experiment to determine the time interval corresponding to each cycle of the motion of the pendulum, and
use the number of cycles to determine the time required for the car to travel the measured distance.
Use the time required to accelerate down the ramp from rest, and the distance traveled during this time, to reason out the average velocity, final velocity and acceleration on each ramp slope.

Graph and interpret your results.

Construct an accurate graph of y = cart acceleration vs. x = ramp slope.
Your graph points should lie near a straight line. Draw your best fit of the straight line and determine its x and y intercepts and its slope.
From the slope of the line, determine the change in acceleration that would correspond to a change of 1 in the slope.
For reasons you probably do not yet understand, if you have done the experiment correctly and accurately the slope of your graph should be equal to the acceleration that would be experienced by the car if it was simply dropped (or, equivalently, rolled down a vertical ramp).
This acceleration is called, for reasons that should be apparent, the acceleration of gravity.

Assess the quality of your results and analyze the potential effects of various potential errors on your determination of the acceleration of gravity. (Principle of Physics: * only)

* How accurately do you think you determined the time for each ramp slope? Describe how you made sure that your times were accurate and consistent.
* How close was your result to the accepted value of the acceleration of gravity, which is 980 cm/sec/sec?
* Exactly what is the significance of the point where y = car acceleration is equal to zero? What therefore is the significance of the x intercept of your graph?
What is the significance of the y intercept of your graph, which occurs where x = ramp slope is zero?
* Do the x and y intercepts of the graph have effect on your result for of the acceleration of gravity?
* Suppose that the table itself had a slope of .01, in the direction down the ramp.

Then every actual ramp slope on your table of acceleration vs. ramp slope should be .01 greater or less than the ramp slope you used on your table.

Which should it be, greater or less?

What effect would this have on your graph?

What effect would have on your result for of the acceleration of gravity?

Suppose that you had consistently misread the length of the pendulum, so that for every reading it was in fact 5 cm longer than you thought. How would this affect your graph, and what would be the effect on your result for of the acceleration of gravity?

Analysis of Errors (Principles students use only first, middle and last data points)

Using a procedure similar to that in the preceding experiments, determine the uncertainty in the acceleration for each of your final graph points and indicate these uncertainties on your graph in the usual manner.
Estimate the uncertainty in the measurements that you used to determine each ramp slope, and determine the range of possible ramp slopes for each data point. Indicate these uncertainties on your graph in the usual manner.
For each graph point sketch the rectangle defined by your minimum and maximum possible acceleration and your minimum and maximum possible ramp slope.
What is the slope of this steepest line that can pass through all these rectangles?
What is the slope of the least steep line that can pass through all these rectangles?
What therefore is the range of possible values of the gravitational acceleration, according to your experiment?

Part 2

See the corresponding video files on the CD (see note in red at the top of this document) entitled Introductor Video Experiments, video clips #4.

Construct a pendulum out of a washer and a thread or light string.

Synchronizing the time of fall of a second washer with the time required for a pendulum to complete a quarter-cycle, determine pendulum lengths corresponding to a fall of 1 meter (if you don't have a measuring device marked in meters you can convert the lengths to inches: just multiply the number of meters by 39.37).

Be sure to drop the washer and release the pendulum simultaneously.
Be sure to position the pendulum so that it is just barely touching the wall when in its equlibrium position, so that when it is released the pendulum strikes the wall just as it reaches its natural equilibrium position. It is probably best if using a washer pendulum if the washer of released with its edge directed toward the wall so that the edge rather than the flat face of the washer will strike the wall. Again, position the top of the string so that the pendulum is at equilibrium when the edge of the washer is in contact with the wall.

Do a couple of trials to convince yourself that if the pendulum length is half the distance the object falls, the pendulum will strike the wall before the object reaches the floor.
Do a couple of trials to convince yourself that if the pendulum length is double the distance the object falls, the pendulum will strike the wall after the object reaches the floor.

Now determine the range of pendulum lengths for which the sound of the object striking the floor and the sound of the pendulum striking the wall sound simultaneous--i.e., so you don't hear one sound and then the other, but hear them both at the same time.

Adjust the length of the pendulum up, starting from a length equal to half the distance of the fall, until the two sounds are simultaneous. Note the length at which the sounds become simultaneous. Repeat several times to be sure you have the right length. Be sure you are measuring length to the center of the pendulum bob (the washer, or marble, or whatever is being suspended to form the pendulum).

Continue increasing the length of the pendulum until the two sounds are no longer simultaneous. Again repeat several times to be sure you have the right length.

Use your data to determine the acceleration of gravity:

Assume that the length at which the two sounds really were simultaneous is halfway between the two lengths you measured.
Using the period vs. length relationship T = .2 * `sqrt(L), T in sec when L in cm, for a pendulum determine the time required for a quarter-cycle at each length.
Assuming that the time of fall was identical to the time of the quarter-cycle reason out the average velocity, final velocity and acceleration for each trial.

Required for University Physics students, Optional for Principles of Physics and General College Physics students:

Modify your procedure to accomodate a drop of .5 meter.

Analyze errors:

How much error do you think there is in the times you measured?
How much error do you think there is in your distance measurements for pendulum length and for the distance of fall for the ball?
How much possible error would therefore follow for your calculated accelerations?

Submit your results

Describe the experience of listening for the two sounds. How convinced are you that you got the right range of lengths?

Give the lengths at which the two sounds were first simultaneous, and at which the sounds were again possible to distinguish.

Include your entire reasoning procedure, starting with finding the period of the pendulum and ending with your result for the acceleration of gravity.

University Physics students: Do your results support the hypothesis that the acceleration of gravity is constant?

Experiment 6. The horizontal range of a projectile with initial velocity in the horizontal direction is an accurate indicator of its initial velocity.

The video clips for these experiments are on CD #0; the number(s) of the required clip(s) is(are) referred to in this document under the writeup for each experiment.

See the corresponding video files on the CD (see note in red at the top of this document) entitled Introductor Video Experiments, video clips #11. View also #10.

In this experiment we measure the horizontal range of a ball projected horizontally from a ramp. Using the time required to fall to the floor we then determine the average horizontal velocity of the ball during its fall. We test the hypothesis that the horizontal velocity of the falling ball remains the same as at the instant the ball left the ramp.

Because of the horizontal orientation of the ramp at the edge of the table, the ball leaves the end of the ramp with a velocity which is in the horizontal direction, with no vertical component.

The time required for the ball to reach the floor is independent of its horizontal velocity, as we see from dropping a coin from the edge of a table with one hand as with the other hand we flick another coin off in the horizontal direction (the coins hit the floor simultaneously).

We can therefore use the distance of fall and the horizontal distance traveled to obtain the average horizontal velocity of the ball.

By intercepting the ball at various heights we can determine the horizontal range and therefore the horizontal velocity of the ball as it leaves the end of the ramp.

First, using washers or coins as on the video clip convince yourself that the time required for an object to reach the floor when it initially travels in a purely horizontal direction is independent of its initial horizontal velocity.

Take data:

Record each vertical distance of fall and determine the horizontal distance for each vertical distance as instructed on the video clip.

Analyze Data:

Determine the time required to fall each distance, and use this time with the horizontal distance to find the average horizontal velocity for each vertical distance.

Using the distance fallen by the ball use the formula `ds = .5 g `dt² for a freely falling object falling from rest to determine the time required to fall each distance, using at `dt the median time observed for each distance. Note that g stands for the acceleration of gravity, which is close to 980 cm/s^2
Using the horizontal distance traveled by the ball during this time interval and the time required to fall, determine for each vertical distance the average horizontal velocity of the ball as it falls.

Plot y = average horizontal velocity vs. x = time of fall and use your plot to determine whether there is any experimentally significant dependence of average horizontal velocity on time or whether average horizontal velocity seems to be independent of time and therefore constant.

Do the differences in the horizontal velocities seem to be the result of random experimental uncertainties and errors in timing, or does there seemed to be a definite progression in the horizontal velocities as time increases?

Analysis of Errors

Estimate the uncertainties in your data, and indicate the results of these estimates on your graph in the usual manner.
Discuss the implications of these uncertainties.

Submit a report with all data and results in table form, with an explanation of each step of the analysis, and with all questions answered.

Video Versions Introductory Motion Experiments

Instructions: You are responsible for reading and following these instructions.

The video clips for these experiments are on CD #0; the number(s) of the required clip(s) is(are) referred to in this document under the writeup for each experiment.

Video Version Experiment 2: Average velocity vs. slope for a ball on a single ramp; rate of change of velocity.

Video Version Experiment 3: The final velocity of a uniformly accelerating object released from rest is double its average velocity.

Video Version Experiment 4: Acceleration is constant for an object rolling down a uniform incline.

Video Version Experiment 5: Determination of the acceleration of gravity using acceleration vs. slope (ramp slope < .1) and by synchronizing time of fall with pendulum.

Video Version Experiment 6: The horizontal range of a projectile with initial velocity in the horizontal direction is an accurate indicator of its initial velocity.

Instructions:

Experiment 2: Measuring average velocity for a cart rolling from rest down a uniform incline; Average velocity vs. slope; Inferring acceleration.

Experiment 3: The final velocity of a uniformly accelerating object released from rest is double its average velocity.

Experiment 4. Acceleration is constant for an object rolling down a uniform incline.

Experiment 5. Determination of the acceleration of gravity using acceleration vs. slope (ramp slope < .1), and then by using time of fall as indicated by the pendulum timer.

Part 1

Part 2

Experiment 6. The horizontal range of a projectile with initial velocity in the horizontal direction is an accurate indicator of its initial velocity.