### Description

in this module you will investigate the relationship between a mass on an incline and the gravitational field. Students will also examine friction of a mass/inline interface. The student will:

Demonstrate gravitational forces on a mass on an incline.

Develop formulas describing the motion.

Investigate forces of friction on an incline.

2- Instructions on viewing demonstrations

When viewing the demonstrations, note the variables. Identify the random error one would encounter in performing the experiment. Look back at what you have learned so far and see what applies here.

Note: Later in your analysis, you will need to refer to these observations.

3- Incline demonstration

You have to watch the video about the physics lab experiment. The video is only thirty seconds long. (Just 30 seconds)

(Video)

4- Prediction instructions

After observing the video demonstration, make a prediction of the relationship between the angle of the incline and the acceleration of the rolling smart car. Keep your prediction handy. Submit it with your final upload. You can attach it to your final spreadsheet upload on a separate tab as a JPEG. Make your prediction in he form of a graph (just draw it on paper and take a picture).

Note: You will not be counted off by being wrong. We just want to see the predictions of our students before the lab. Full credit will be provided with inclusion.

5- Analysis instructions-3

The Excel file attached here contains velocity vs. time data for five angles. For each data set, you are to run a LINEST and determine the slope and the uncertainty in the slope (see previous instructions on LINEST in Excel analysis module). Note: Each data set is in the tab named for the angle that was used (6.0, 7.5, 9.0, 10.0, 10.4). You don’t have to graph the velocity vs. time graphs for presentation. But, you should take a look at a quick graph to observe if there is a linear relationship. Run a LINEST on each data tab with velocity being dependent and time being independent. You will use these slopes for the “acceleration” tab.

According to a simple analysis of a smart car rolling down the incline, assuming friction is negligible, the equation for the acceleration is written as

ax=gsin?. Recall that the velocity as a function of time equation for constant acceleration (here we are assigning the x-direction as being along the inline plane) is written as vx=v0x+axt. Thus, the slope of each of your LINEST results is the constant acceleration for that particular angle.

1. On the next tab, which is called “acceleration”, label column A as angle (cell A1), column B as sin?, and column C as acceleration (the slope of each of the velocity vs. time graphs for each angle. Do not include the uncertainty in this column input).

2. In column A, the angle is in degrees. But, we need radians. So in cell B2, type “=A2*(3.14/180)”. Don’t include the quotes of course. Copy the formula down. Here we just utilized the small angle approximation sin???.

3. Plot acceleration vs. angle and make a nice, formatted graph. Think back to your prediction and make a note of your recollections. Run a LINEST and determine the slope AND the uncertainty. Is this what you expected? Record the slope and the uncertainty along with its units clearly on the page. You can insert a textbox and type this into the textbox.

4. Take a moment and reflect on everything you have done up to this point. Make notes and ask the TA questions if you are not sure what you have done to this point. Save your file for a later upload. You will use the friction and summary tab later.

(I uploaded the excel file and has some data and you have to fill in the data and make what it says in all instructions).

6- Friction demonstration

You have to watch the video about the physics lab experiment. The video is only thirty five seconds long. (Just 35 seconds)

(video)

7- Friction analysis instructions

After viewing the demonstrations of the incline, you will do a simple examination of friction at home.

1. Obtain a uniform inline plane (a clipboard with paper, a cardboard piece from a box,..). This is any surface with uniform conditions and shaped to where you can adjust the angle and take measurements from observations.

2. Obtain three (different) uniform objects (coins, blocks,…) with slightly different surfaces of “roughness”. Take pictures of these objects and of your incline.

Open up your spreadsheet. Go now to the friction tab. You have three objects for which you are providing measurements to obtain the coefficient of static friction. I would use columns A, B, and C for object 1. E, F, and G for object 2, and so forth. Your measurements of height and base can be placed in the first two columns for each object section, and the value of the ratio (static friction) in the third row. When all of that is done, place the picture of that object on the incline underneath each data set. But, if you have a better way to organize, feel free!!

But, take the time to organize!

3. For each item, place at the top of your incline, start at zero angle, and then slowly raise until you (just) see it slip. Record this height (see below). Do this several times for each object to get an average height for best results. In the apreadsheet, you should, for scientific honesty and integrity, record all trials to obtain the average.

4. To determine the angle, use the right-triangle analysis (unless you have an angle indicator): tan?=heightbase. The “base” is a measure of the length of the incline (lay flat down and measure the length of the incline).

5. The coefficient of static friction is defined as:

?s=tan?. Therefore, find the ratio with the height and base to determine this (average) coefficient for each object on the same incline.

Start each object from the same place for consistency.

6. Clearly indicate what the average coefficient for each interface (object/incline) is on the spreadsheet. Indicate this in each object section of the spreadsheet or in a singular textbox with labels.

Note: For a smart car, it is rolling. But, you are still getting an idea of friction by doing this exercise.

8- Final instructions

1. List all random errors associated with the incline demonstration. If you were doing the experiment, minus anything to do with the software or embedded sensors in the smartcar, which random errors can you identify?

2. Do the same thing for your experiment with your own incline. List all random errors associated with your data collection. Make sure to list again what your average values are for each interface. Note: Mentioning the observed “roughness” for each object would help make sense of the numbers.

3. Based on your final value of the slope AND the uncertainty of the acceleration vs. angle analysis, which should be g, is the result reasonable taking into account all random error?

4. Following up on number 3, was it acceptable to neglect friction based on all of your results and observations? Explain.1 attachmentsSlide 1 of 1

• attachment_1attachment_1

### UNFORMATTED ATTACHMENT PREVIEW

Time (s) Velocity (m/s) 0.4 0.006 0.45 0.029 0.5 0.068 0.55 0.118 0.6 0.169 0.65 0.219 0.7 0.269 0.75 0.319 0.8 0.369 0.85 0.42 0.9 0.47 0.95 0.519 1 0.569 1.05 0.62 1.1 0.67 1.15 0.719 1.2 0.769 1.25 0.819 1.3 0.869 1.35 0.918 1.4 0.967 1.45 1.017 1.5 1.066 1.55 1.115 1.6 1.165 1.65 1.213 1.7 1.261 Time (s) Velocity (m/s) 0.8 0.014 0.85 0.053 0.9 0.113 0.95 0.178 1 0.241 1.05 0.304 1.1 0.366 1.15 0.429 1.2 0.492 1.25 0.553 1.3 0.614 1.35 0.676 1.4 0.739 1.45 0.802 1.5 0.863 1.55 0.925 1.6 0.987 1.65 1.049 1.7 1.11 1.75 1.171 1.8 1.233 1.85 1.294 1.9 1.355 1.95 1.415 Time (s) Velocity (m/s) 0.95 0.045 1 0.103 1.05 0.177 1.1 0.255 1.15 0.332 1.2 0.409 1.25 0.486 1.3 0.562 1.35 0.638 1.4 0.715 1.45 0.791 1.5 0.867 1.55 0.9

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