Lab 3

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Pennsylvania State University *

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Mechanical Engineering

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Oct 30, 2023

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A MODEL FOR KINETIC FRICTION - PART 1 INTRODUCTORY INSTRUCTIONS This lab will be partially graded using scientific ability rubrics. To help you know what we expect, the rubrics have been included along with the instructions for each question. If no rubric is indicated, the question is graded on completeness. Lab goals: In this lab, you will 1) Learn to use the force sensor on the IOLab. 2) Determine different methods to measure kinetic friction. Observing experiments: Read carefully the accompanying “Observing experiment” file which explains what we expect you to do in observing experiments such as the ones below and what we expect you to write in response to the questions. Equipment available: You will need the IOLab with computer/software and a horizontal surface. You may need the “hook” attachment and a small piece of string to pull the IOLab. Phenomenon to Observe: When two objects in contact move relative to one another, the atoms at the interface interact electrically to create a force that resists the motion. This force is called kinetic friction and we know that it is always in the direction opposite to motion and parallel to the interface. We would like to investigate different ways to measure and quantify kinetic friction. Variables:  Independent variable: mass of the IOLab  Dependent variable 1: measured kinetic friction  Dependent variable 2: measured kinetic friction by an alternative method.  Controlled variables. Surface on which IOLab slide, temperature of the room or surfaces, etc.. Both dependent and independent variables are quantitative variable (they could be any numbers). Primary Guiding Questions to think about: 1. How can we measure kinetic friction (in Newton?) 2. Does kinetic friction remain mostly the same during the sliding phase. Does the friction change between a big/small push or for a continuous pull?

A Model for Kinetic Friction - Part 1 Page 2 of 7 3. What overall properties of the object does kinetic friction depend on? Does it depend on shape, surface area of contact, mass? Some of these questions can be answered (at least partially) from our analysis in lab 2 “slowing down”. The dependence on shape or surface area are hard to do quantitatively with the material we have so we will focus on dependence on mass. ACTIVITY 1: DISCOVERING THE FORCE SENSOR AND MEASURING THE MASS OF THE IOLAB 1. A first thing to do is to check the direction of pull versus push. Push on the hook. Is the force positive or negative? Does pulling give you the opposite? Does this make sense with the coordinate system given on the IOLab?  Pushing on the hook yields a force in the positive Y-axis. Pulling in the hook yields a force on the negative Y-axis this is indeed opposite. This does make sense with the coordinate system given in the IOLab. 2. Now hold the IOLab by the hook, so that it is hanging in the air. Draw (by hand, take a picture or using software) the FBD for this situation, being careful to draw the coordinate system that corresponds to the one used by the IOLab remote. Write Newton’s Second Law ⃗ F = m ⃗ a for this situation for the component(s) you think is/are relevant. For this situation Newton’s Second law applies as F=W where W = mg Thus F T = mg 3. What is the force of gravity (F G ) on the IOLab? Specify the magnitude and the direction.  The force of gravity on the IOLab is the force pulling on the IOLab cart while the cart is suspended in the air. The magnitude is F G = mg, where the quantity g—a property of the planet in this case 9.8 m / s . Set-up 1. Turn on the IOLab and select the force sensor. 2. Recalibrate the force sensor and the accelerometer to make sure the calibration is up to date. 3. Attach the hook. 4. Hit record and immediately “rezero” the force sensor. You will need to do this frequently.

A Model for Kinetic Friction - Part 1 Page 3 of 7 4. Take a screenshot of your F(t) graph, highlighting the region used to determine the average force with the statistical tool. The average force is -1.93 N. 5. Calculate the mass of the IOLab and explain how you can get this from the measurement of the force of gravity.  If |F|=W and W=mg than 1.93 = m*9.81  M = 0.200 kg 6. Now move the IOLab up or down at constant velocity. Does the tension change? Write Newton’s Second Law when the IOLab moves up or down at constant velocity.  The tension does not change, an object at constant velocity has an acceleration of zero.  Per Newton’s second law F T = mg

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A Model for Kinetic Friction - Part 1 Page 4 of 7 ACTIVITY 2: OBSERVING EXPERIMENT: HOW TO MEASURE KINETIC FRICTION 7. There are two ways to measure the kinetic friction force. **We will always measure the kinetic friction with the wheels up and the IOLab on its felt pads. a. Method A. First, you can push the IOLab and measure the average acceleration during the slide using the accelerometer . b. Method B . Second, you can pull the IOLab with a string or directly with the hook at nearly constant velocity and use the force sensor to measure the tension. Draw a FBD for each situation and explain with equations how the kinetic friction is determined in each case (determined using the IOLab sensor, so accelerometer or force sensor). Take a picture of your work and include it here. Graded correctness. Method A An object pushed with force will acquire velocity, but frictional force will have negative acceleration. - a = F K / mass F K = µ K mg  -a = µ K mg / m -a = µ K g  µ K = -a / g Method B When an object is pulled with tension it will acquire velocity and acceleration, and frictional force will work against it. a = F T – F K  if a = 0 then F T = -F K or µ K

A Model for Kinetic Friction - Part 1 Page 5 of 7 Method A is very similar to the big/small push we did in lab 2 and you should remind yourself your preferred way to measure the average acceleration (from where to where, etc.) Method B is new so let us go into more details before we actually use it to measure the kinetic friction. 8. Pull your IOLab at constant velocity and record its motion. Describe, without trying to explain , what you observe in your data when the IOLab is moving at constant velocity * * In this type of question, you should write everything that could be important for any future investigations, you are making a report on everything you see and notice. Write down even small seemingly unimportant details. Do not seek to explain yet! You may want to look at both the accelerometer and the force sensor. Inadequate Adequate Good Is able to describe what is observed without trying to explain. A description is incomplete. Or, observations are adjusted to fit expectations. A description is complete but mixed up with explanations or pattern. Clearly describes what happens in the experiments.  The force graph starts at zero, slopes down and remains steady for a bit and slopes upward returning to zero 9. Let us summarize. We are interested in measuring the average kinetic friction on the IOLab. Describe precisely how to measure the average kinetic friction using both methods, A and B. Which sensors will you use? What quantities are you measuring? How do you intend to calculate their average values (from where to where)? What computation do you need to do to get the final answer? Inadequate Adequate Good Is able to describe how to use available equipment to make measurements All chosen measurements can be made, but no details are given about how it is done. All chosen measurements can be made, but the details of how it is done are vague or incomplete. All chosen measurements can be made and all details of how it is done are clearly provided.  For method A we know that µ K = -a /g, we also know that g = 9.8 m / s 2 . Using the accelerometer sensor, the average for a is measurable, giving us the average for µ K .  For method B we know that µ K = -F T , Using the force sensor, the average for F T can be measured.

A Model for Kinetic Friction - Part 1 Page 6 of 7 ACTIVITY 3 - METHODS FOR MEASURING KINETIC FRICTION 10.Now that you have explored the phenomena and seen what the data looks like, you can start thinking about the main experiment. The question that we want to answer is: Is there a statistically significant difference between the kinetic friction measured using Method A versus Method B? To answer this question, you will perform multiple (up to you how many you do) method A and method B measurements of the kinetic friction, and for each you should record data in Excel, then use Excel tools to convert your data into the final quantity that you are looking for. Do not forget to regularly zero the force sensor. In the end, you will want to have two columns like this (besides your measured data): Method A or B Average Kinetic friction A/B # Do not record/evaluate experimental uncertainties in measurements. The IOLab is a very sensitive instrument and most of the uncertainties are coming from human errors or from natural variability on the table, etc. We will evaluate “statistically significant” by visualizing the data using StatKey. Perform your designed experiment and record all your data in Excel. Save as a .cvs file. Go to StatKey, go to “One quantitative and One Categorical Variable” and upload your data using the “upload file” button. Create a boxplot. Take a screenshot and upload the boxplot with the statistic on the left. Graded on correctness. See videos on how to use StatKey and csv https://oer.hax.psu.edu/lul29/sites/phys211/the-boxplot-and-statkey

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A Model for Kinetic Friction - Part 1 Page 7 of 7 11.Analyze your data, make sense of it and draw conclusions to answer the question above. Write down any notes here. Make sure you explain how you are accounting for outliers if they are any. Inadequate Adequate Good Is able to identify a pattern in the data The pattern described is irrelevant or inconsistent with the data The pattern has minor errors or omissions. The patterns represent the relevant trend in the data. When possible, the trend is described in words. There were 20 runs of the experiment, 10 for method A and 10 for method B. There are two outliers which are both method A and B maximums this is most likely due to human error. Method B seems to have more friction than method A. This may be due to mats I have on my desk requiring more force to pull across the desk than method A’s push and forget method. Based on the standard deviation of both methods they are within one hundredth of a percentile meaning their bell curves are nearly identical. I do not believe that either method is statistically significant.