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Instructions

  1. Watch these three lessons about data in the real world. It’s important that you have a solid grasp of what standard deviation means.
  2. Go through the Excel Coef of Resitution workbook. There are three tabs to do.
    1. The first tab is an intro.
    2. The second tab is simulated data, letting you get some idea of what might happen.
    3. The third tab is where your data goes
  3. Complete the Lab Report, the Word document below.
    1. There are only certain blocks where you can enter info 
    2. Upload your report to the appropriate assignment folder.

Accuracy and Precision

Error Distribution (A)

Error Distribution (B)

Intro

© 2015 Sean M. Cordry and Walsters State Community College

initial h

final h

Simulation

This is simulated data, showing a random initial drop height (h_i) and it’s corresponding bounce height (h_f).
On the next worksheet, you’ll enter your own data.
The letter “e” stands for the coefficient of restitution.
Press “F9,” and then you can see a new set of simulated data.
Descriptive Statistics
h_i h_f e Average 0.8642 center bin freq
1 0.699 0.505 0.850 Median 0.8724 1 0.61 0.6 0 s.d. select % select
2 0.459 0.345 0.867 2 0.63 0.62 0 s.d. off 0 0 0 s.d. display % contains
3 0.999 0.719 0.849 Max 0.9077 3 0.65 0.64 0 1 s.d. 0.0254 0 0 0.0761550934 99.7
4 0.961 0.674 0.837 Min 0.8112 4 0.67 0.66 0 2 s.d. 0.0507700623 0 0
5 0.95 0.746 0.886 5 0.69 0.68 0 3 s.d. 0.0761550934 0.0761550934 99.7
6 0.832 0.585 0.838 Standard Deviation 0.0254 6 0.71 0.7 0
7 0.544 0.448 0.908 Standard Error 0.0051 7 0.73 0.72 0
8 0.48 0.376 0.885 8 0.75 0.74 0
9 0.738 0.568 0.877 How do these values relate to what is happening in the histogram? 9 0.77 0.76 0
10 0.389 0.305 0.885 10 0.79 0.78 0
11 0.845 0.606 0.847 11 0.81 0.8 1
12 0.321 0.224 0.836 12 0.83 0.82 6
13 0.854 0.602 0.840 13 0.85 0.84 3
14 0.461 0.359 0.882 14 0.87 0.86 7
15 0.981 0.645 0.811 15 0.89 0.88 7
16 0.776 0.592 0.873 16 0.91 0.9 1
17 0.57 0.434 0.872 17 0.93 0.92 0
18 0.818 0.650 0.892 18 0.95 0.94 0
19 0.763 0.520 0.825 19 0.97 0.96 0
20 0.837 0.667 0.893 20 0.99 0.98 0
21 0.531 0.426 0.896
22 0.59 0.454 0.877
23 0.655 0.457 0.835
24 0.931 0.706 0.871
25 0.694 0.530 0.874 Select Standard Deviation Display Reported Value for CoF
CoF is 0.8642 ± 0.0051
3 s.d. (avgerage value) (standard error)
Contains
99.7 %
of data points
Simulated Data
© 2015 Sean M. Cordry and Walsters State Community College

Simulated Distribution of CoR Data

CoF Frequency 0.61 0.63 0.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.97 0.99 0 0 0 0 0 0 0 0 0 0 1 6 3 7 7 1 0 0 0 0 Average Value 0.86418827589028369 14 Standard Deviation Display 7.6155093422405173E-2 7.6155093422405173E-2 0.86418827589028369 7

Notice that more often than not, the spread in the simulated data resembles a “normal” distribution — like the one shown here. This is the result of random errors in measurements.

Pick the number of standard deviations that you would like to display on your graph, and compare them to the “normal” distribution. (Look for the black horizontal bar.)

More Stuff

To report an actual result, we give the average value and say “plus-or-minus” the standard error.

The value of the standard error is equal to the value of the standard deviation divided by the square-root of the number of data points.

Your Data

This worksheet page is for your data.
If you are getting coefficients that are less than 0.6, you will need to find a harder surface or a bouncier ball.
Be sure to vary your drop height.
(Just copy this histogram into your report. You don’t need the data table.)
Descriptive Statistics
h_i h_f e Average 0.0000 center bin freq
1 1 0.000 0.000 Median 0.0000 1 0.61 0.6 25 s.d. select % select
2 1 0.000 0.000 2 0.63 0.62 0 s.d. off 0 0 0 s.d. display % contains
3 1 0.000 0.000 Max 0.0000 3 0.65 0.64 0 1 s.d. 0.0000 0 0 0 0
4 1 0.000 0.000 Min 0.0000 4 0.67 0.66 0 2 s.d. 0 0 0
5 1 0.000 0.000 5 0.69 0.68 0 3 s.d. 0 0 0
6 1 0.000 0.000 Standard Deviation 0.0000 6 0.71 0.7 0
7 1 0.000 0.000 Standard Error 0.0000 7 0.73 0.72 0
8 1 0.000 0.000 8 0.75 0.74 0
9 1 0.000 0.000 Select Standard Deviation Display 9 0.77 0.76 0
10 1 0.000 0.000 10 0.79 0.78 0
11 1 0.000 0.000 s.d. off 11 0.81 0.8 0
12 1 0.000 0.000 12 0.83 0.82 0
13 1 0.000 0.000 13 0.85 0.84 0
14 1 0.000 0.000 14 0.87 0.86 0
15 1 0.000 0.000 15 0.89 0.88 0
16 1 0.000 0.000 16 0.91 0.9 0
17 1 0.000 0.000 17 0.93 0.92 0
18 1 0.000 0.000 18 0.95 0.94 0
19 1 0.000 0.000 19 0.97 0.96 0
20 1 0.000 0.000 20 0.99 0.98 0
21 1 0.000 0.000
22 1 0.000 0.000
23 1 0.000 0.000
24 1 0.000 0.000
25 1 0.000 0.000
© 2015 Sean M. Cordry and Walsters State Community College

Distribution of CoR Data — Fall 2021

CoF Frequency 0.61 0.63 0.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95 0.97 0.99 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Average Value 0 14 Standard Deviation Display 0 0 0 7

Lavf54.59.106

Ball drop edit v1.mp4

The Coefficient of Restitution

The coefficient of restitution is a quantity that relates before- and after- speeds regarding a collision. It’s related to the word “restore,” and it works like this.

Suppose that a racquetball hits a wall going 50 m/s, but when it bounces away from the wall, it’s only going 40 m/s. The ball’s speed does not experience full “restitution” after the impact, but only an 80% restitution level. (40/50 = 80%) If your racquet ball partner steps in front of your shot, blocking the ball with his left butt-cheek, then the restitution of the collision might only be 20%, so the ball would glance from the gluteal muscle at 10 m/s.

The amount of restitution in any collision depends on the types of objects involved. Today, we’ll be measuring the coefficient of restitution of bouncy rubber ball, which will be done by letting the ball bounce and measuring how high it goes.

Right now, you don’t need to know the theory behind this – this Excel program will do the math for us. We’re interested in seeing how data “smears” out in the real world. Each time you drop the ball from a certain height (
hi
)and record the bounce height (
hf
), the program will calculate a value of the coefficient of restitution (
e
). When you measure your height values, make sure that you always measure to the bottom of the ball.

Check out the video (above and to the right) so that you have an idea of what’s going on.

Since this is a real experiment, the value of
e
will not be consistent: there will be a variety of numbers around some average value. An important number to tell us how “blurry” or how “spread-out” our data is a number called the standard deviation of the mean – or just “standard deviation” – or just “s.d.” – or just “.”

What to do next:

1. Take a look at the simulation tab. It’s “job” is to help you understand the randomness that can occur in actual experiments. Make sure you understand the relationship between the average and the standard deviation.

2. Construct a similar apparatus with your ball and meterstick. Take two pictures of your apparatus: One with your face in the shot and one with the apparatus in action. (The pics are for security purposes – to make sure that everyone does their own work.)

3. Drop the ball from various heights twenty-five times and record the corresponding bounce heights.

4. Answer the questions on the Lab Report about your results and turn them into the Dropbox in eLearn.

Note: You can click on the cells in the next two tabs, but you can only alter some of the info. On the Simulation tab, you can only select the number of standard deviations for the graph to illustrate. On the Your Data tab, you can also enter you data.

The Coefficient of Restitution

The coefficient of restitution is a quantity that relates before – and after- speeds regarding a collision. It’s related to the

word “restore,” and it works like this.

Suppose that a racquetball hits a wall going 50 m/s, but when it bounces away from the wall, it’s only

going 40 m/s. The ball’s speed does not experience full “restitution” after the impact, but only an 80%

restitution level. (40/50 = 80%) If your racquet ball partner steps in front of your shot, blocking the ball

with his left butt-cheek, then the restitution of the col lision might only be 20%, so the ball would glance

from the gluteal muscle at 10 m/s.

The amount of restitution in any collision depends on the types of objects involved. Today, we’ll be measuring the

coefficient of restitution of bouncy rubber ball, which will be done by letting the ball bounce and measuring how high it

goes.

Right now, you don’t need to know the theory behind this – this Excel program will do the math for us. We’re interested

in seeing how data “smears” out in the real world. Each time yo u drop the ball from a certain height ( h

i

)and record the

bounce height (h

f

), the program will calculate a value of the coefficient of restitution ( e). When you measure your height

values, make sure that you always measure to the bottom of the ball.

Check out the video (above and to the right) so that you have an idea of what’s going on.

Since this is a real experiment, the value of e will not be consistent: there will be a variety of numbers around some

average value. An important number to tell us how “bl urry” or how “spread-out” our data is a number called the

standard deviation of the mean – or just “standard deviation” – or just “s.d.” – or just “.”

What to do next:

1. Take a look at the simulation tab. It’s “job” is to help you understand the randomness that can occur in actual

experiments. Make sure you understand the relationship between the average and the standard deviation.

2. Construct a similar apparatus with your ball and meterstick. Take two pictures of your apparatus: One with your face in

the shot and one with the apparatus in action. (The pics are for security p urposes – to make sure that everyone does

their own work.)

3. Drop the ball from various heights twenty-five times and record the corresponding bounce heights.

4. Answer the questions on the Lab Report about your results and turn them in to the Dropbox in eLearn.

Note: You can click on the cells in the next two tabs, but you can only alter so me of the info. On the Simulation tab, you can

only select the number of standard deviations for the graph to illustrate. On the Your Data tab, you can also enter you data.

Lavf54.59.106

Ball drop edit v1.mp4

Pre-Lab

Answer the following questions based on the lessons on data and the instructions provided in the Excel worksheet. Use proper complete sentences for your responses.

Q#

Review Question

Your Answer

Q1

Suppose one set of data has a larger standard deviation than another set of data. What does that mean about the different sets of data?

Your answer for Q1 here.

Q2

In your own words, what is the coefficient of restitution?

Your answer for Q2 here.

Apparatus

Figure 1: Apparatus Selfie Photo

Figure 2: Apparatus in Action Photo

(Click to import your pic.)

(Click to import your pic.)

Caption: Caption for apparatus picture

Caption: Caption for action photo

Coefficient of Restitution Pg. 3

Coefficient of Restitution

© 2015 Sean M. Cordry and Walters State Community College

© 2015 Sean M. Cordry and Walters State Community College

Results

Insert a picture of your histogram below as a Graph of Results. (Use the “Snipping Tool.”) Specify the value of your ball’s coefficient of restitution, including the standard error amount.

Figure 3: Graph of Results

Caption: Explain your graph

ε = your mean +/- standard error

Analysis and Implications

Answer the following questions based on your experience.

Q#

Analysis Question

Your Answer

Q3

What are some factors that contributed to your standard deviation? (In other words, source of error.)

Your answer for Q3 here

Q4

What could you have done in order to reduce the spread in your data? (In other words, have had a smaller standard deviation.)

Your answer for Q4 here

Q5

The value of the coefficient of restitution depends on the properties of both objects involved in the collision. How could you have produced a collision that gives a lower coefficient of restitution?

Your answer for Q5 here

Q6

Provide a real-life example of where you can see different coefficients of restitution at work.

Your answer for Q6 here

Q7

What is something that you gained (knowledge, experience, awareness, etc.) that you did not have prior to completing the experiment?

Your answer for Q7 here

Additional Instructions

· Convert this document to PDF format and then upload it to the appropriate dropbox.

· If you experience technical issues importing your images or graphics, or if you have trouble converting the document to PDF format, you will need to get guidance from someone at your home institution. Partial or fragmented documentation and images will not be accepted.

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