Friction

1.      Lab 7: Modeling Friction Forces

a.      Lab conducted by Mohammed Karim (author), Andrew Martinez, Lynel, and Richard Mendoza.

2.      Objective – There are many objectives for this lab. We conducted five experiments. All of these were done to find data, such as maximum static friction, kinetic friction, static friction of a sloped surface, kinetic friction from sliding a block down an incline, and the acceleration of a two mass system.

3.      Theory/Introduction – Friction is a force that acts perpendicular to normal force. It opposes the Normal force. In this lab, we are tasked with finding different parts of friction. Both when an object is at rest (static friction), and when an object is in motion (kinetic friction). We are going to find friction in five different situations.

4.      Apparatus/Procedure –

a.      Due to there being five parts to this experiment, I will break up this lab with each experiment.

b.      1. Static Friction

                                                                i.     

                                                              ii.     In this part of the lab, the goal is to measure the static friction of the board. We placed a pulley with some weights and measured the weight that would cause the block to move. We then increased the normal force, thus increasing the normal force. After measuring the weight of 5 stacked blocks we plotted that data on a graph (See Figure 7.1). This graph is Force of friction over Normal Force. You can see the data on the left and the graph on the right. We put the graph in terms of a power fit. The slope was 0.416.

c.      2. Kinetic Friction

                                                                i.     

                                                              ii.     This part of the lab is pretty straightforward. We placed a block on the board and pulled on it with a calibrated force sensor. We measured the force emitted. A picture of the force graph can be found. (See Figure 7.2)

d.      3. Static Friction from a Sloped Surface

                                                                i.   Better picture in the next section

                                                              ii.     We placed a block on a board and raised it and measured the highest possible angle that the block wouldn’t move at. It was 23.3 degrees.

e.      4. Kinetic Friction from Sliding a Block Down an Incline

                                                                i.     

                                                              ii.     This part of the lab involved measuring the acceleration of an object down an incline. The angle was 21.5 degrees and the object accelerated at 1.449 m/s^2. The coefficient for kinetic friction was 0.23

f.       5. Predicting the Acceleration of a Two-Mass System

                                                                i.   

  

                                                              ii.     From the previous example, we calculated the expected acceleration with a heavy mass. (See figure 7.3 for worked out calculations)

5.      Data Tables

                                                    Figure 7.1

                                                Figure 7.2

                                               Figure 7.3

6.      Conclusion

a.      We learned how to take into account friction in our lab experiments. We were able to accurately calculate the force of friction. This will lower the margin of error on future experiements.

Trajectories

1.      Lab 5 – Trajectories

Lab conducted by Mohammed Karim (author), Curtis, and Lynel on September 21, 2016.

2.      Objective – The goal of this lab is to use projectile motion to find various unknowns throughout the lab.

3.      Theory/Introduction – After watching a couple of videos on projectile motion, we’re tasked with scenarios. In this lab, we are to find various unknowns, such as the distance an object would land at when going at an unknown velocity.

4.      Apparatus/Procedure

                                   

       As you can see in figure 1, we positioned the ramp at an angle of 53 degrees. The ball rolls off the ramp onto the surface for a small distance, where it falls 89.5 cm. After manipulating the equation:

Y=1/2gt^2

We put the equation in terms of velocity:

V=(g/2y)^1/2 * x

Plugging this in, we get 1.64 m/s. We then mess with more projectile motion equations to get the distance the object will fall at. (See figure 5.2 for the work). After calculating it, we found that the block would land about 60.1 cm. A test run showed that our calculations were correct. The ball went a distance of 59 cm. 5 test runs averaged out to be 56.5 cm with a fluctuation of +/- 2.5 cm. The test runs results were 56.5 +/- 2.5cm.

5.      

Figure 5.2

6.      Conclusion

Our test runs seemed to be very close to the calculated result. We believe that no mistakes were made in terms of balancing equations and conducting the experiment, as we had the professor check our equations and results. The margin of error may be from the following:

“Friction, Potential initial velocity, measurement uncertainty, placement uncertainty, air resistance, and angle uncertainty.”

Lab 4

1.      Lab 4: Modeling the fall of an object falling with air resistance.

a.      Lab conducted by Mohammed Karim, Lynel, and Curtis on September 14^th and 19^th, 2016

2.     Objective – Find an equation that relates air resistance force, weight, and speed.

3.      Theory/Introduction – We know that air resistance is dependent on weight, shape, and speed. However, in this lab, we derived an equation that relates the air resistance force with terminal velocity and weight using a power law:

F=kv^n

4.      Apparatus/Procedure –

For this lab, we ventured to building 13 with coffee filters and dropped them from the ledge and recorded the terminal velocity of multiple coffee filters. First we dropped 1 alone and continued until we dropped five together to see the relation of weight on air resistance.

After returning to lab, we plotted the velocity from each fall using LoggerPro and found values for k and n. Next, we incorporated the values into a mathematical model on Excel by inputting values for time, velocity, etc. Upon plugging in these values, excel predicts the terminal velocity for the different weights and gives us the respective values. The excel was extra. We recieved all the needed data from LoggerPro, but it was done to show us the power of excel.

5. Data Tables/Analysis

Uncomfortable Physics students attempting to record falling coffee filters.

One of five plotted graphs of the falling coffee filters. The other 4 can be provided if needed. It seemed redundant to add all 5 when the plotted points can be seen on the graph.

Final graph modeling the force of air resistance in relation to velocity. Weight of coffee filter was also another variable that was used to help find the relation.

Excel sheet displaying the terminal velocity. The time interval was 1/60 of a second to be precise.

6.      Conclusion

     This lab was still near the beginning of the course, meaning that while it may contain a bit of new physics, it mainly is for students to get to know how to use different programs, like LoggerPro and Excel. We learned its comprehensive abilities. The model we used worked very well. The only problems is that there are many factors we didn’t take into account. 

     Though we were looking for air resistance, we did not take into account the added air resistance that was in the room, due to the air conditioning or opened doors. They may be minute, but they may affect our data. Uncertainties in height, positioning of the filter when plotted on the graph, timing, and the averaged data due to linear fit may also play a role in the slight margin of error.

Lab 3

1.      Lab 3: Non-Constant acceleration problem/Activity

a.      Lab conducted by Mohammed Karim, Curtis, and Lynel on September 12, 2016

2.   

   Objective – Learn how to better use Excel.

3.    

  Theory/Introduction –

        In this lab, we are presented with the scenario that a 5000-kg elephant on frictionless roller skates is moving at a rate of 25 meters per second. The elephant has a 1500-kg rocket that generates a constant 8000 N thrust to slow it down. We are tasked with finding out how far the elephant goes before coming to rest.

        First, we are walked through an analytical approach that uses multiple integrals to move from acceleration to velocity and finally distance. This approach then calculates when the velocity is zero to find out time and plugs it back into the distance equation, which is a function of time. The solution tells us that the elephant will stop at 248.7m. We are able to solve this, but after a lot of work.

        Rather than going through this, we simply used Excel to find out the answer. We plugged in values for the weight, velocity, thrust, force, and time and were given the answer back effortlessly.

4.   

   Apparatus/Experimental Procedure

The only “apparatus” used was Microsoft Excel. This program was used to input our values and distance was given.

5.  

    Data Tables

a.

6.     

Explanation/Analysis

Our data included the excel document. For values that we did not know directly, we entered in equations that would give us the answers and filled it down. As for time, to get a much closer value, we put smaller and smaller periods. For a more precise answer, we set the period to every 0.1 seconds.

7.      

Conclusion

As fun as it is to solve integrals and spend almost an hour painstakingly dealing with algebraically complex equations, it was much easier to use Excel, a program that will deal with all the hard work for us. If we input the values, Excel outputs the values. We knew that the time interval was small enough in that the value matched with the analytical value. Had we not had the analytical value, we could have just made it small enough to find multiple unchanging intervals. This indicates that our value is very precise.

1. Free Fall Lab - determination of g (and learning a bit about Excel) and some statistics for analyzing data

      Lab conducted by Mohammed Karim (author), Lynel, and Curtis on September 5 and 7, 2016.

2. Objective - Find acceleration due to gravity without any other external force.

3. Theory/Introdcution - This lab focuses on deriving gravity and finding the propagated uncertainty and then using statistics to find if the actual acceleration due to gravity (9.81 m/s^2) is within 95% confidence of our answer.

4.  

Pic of Apparatus

This apparatus features a magnet that, upon flipping a switch, drops and experiences free fall for 1.86m. A spark hits the magnet with a frequency of 60 Hz, marking the long strip of paper on the back. After plugging in time and distance to excel,we can use a marked scatter and find the linear fit. (See Figure 1.1) We then use the equation: y=vo*t+1/2*at^2 and multiply acceleration by 2 to find gravity. 

However, not everyone came to the same conclusion. The answers from other classmates varied from 893 cm/s^2 to 985 cm/s^2. This is due to uncertainty and random factors. However, we can say that after multiple trials, the average will gravitate closer to the answer. After finding the standard deviation of the mean, we can say that the answer is within 95 percent confidence within two standard deviations of the mean. The data can be seen in Figure 1.3 . 

6. Data tables-

Figure 1.1

Figure 1.2

Figure 1.3

7. Explanation/Analysis - 

The first figure is the linear fit of the acceleration graph. The second figure is a distance/time graph which is in the form of the kinematics equation y=vo*t+1/2*at^2.  The third figure is a worked out explanation of standard deviation for gravity.

8. Conclusion - 

Not only were we able to derive acceleration due to gravity, but we were able to find propagated uncertainty and find the standard deviation to make an estimated guess on our confidence of the answer. Of course, the results may be inaccurate at the moment, but with more tests it should be much more accurate.

Finding a relationship between mass and period for an inertial balance

1.     Lab conducted by Mohammed Karim (author), Curtis, and Lynel on August 31, 2016.

2.     Objective: Find an equation that can relate mass and period for inertial balance.

3.     Theory/Introduction: Normally, we would use a scale that utilizes spring force to find the mass of an object. However, since mass is independent of weight and independent of gravity, we can use many other methods to find the mass of an object. In this lab, we use inertia as a method of finding an object's mass. In order to find the mass of an object, we first had to find an equation that could relate mass and period. What we did was measure the period of the oscillation at different masses. Once we collected our data, we would derive an equation. With this equation, we could find the mass of an object with an unknown mass.

4.     Apparatus/Experimental Procedure: 

 Lab 1 Apparatus

As shown above, our apparatus consists of an inertial balance clamped to the tabletop with a thin piece of masking tape on the end. A photogate is set up and placed in front of the masking tape. This is so that it can record the number of oscillations. Using LoggerPro, we used an application that measures the period.

After ensuring that the timing of the test run is somewhat accurate, we began to collect data using variable weights, ranging from 0 grams to 800 grams not including the weight of the inertial balance. The data for this portion can be found under the "Data" section (See Figure 1.1). With this data, we decided to find a relationship with a power-law type equation:

T=A*(m+M(tray)) ^n (m+M(tray) as the mass of the tray is always present.)

By taking the logarithm of both sides, we can make the equation resemble the equation of a linear line (y=mx+b). This is done so we could incorporate it into a graph and find the value that would make the line straight. If the line is straight, we could find the value of the tray.

After adjusting many parameters, we found a linear fit with a correlation coefficient of 0.9999. We then found the upper and lower limit of the correlation as there was some uncertainty in conducting the experiment. (This will be further discussed in the "Limitations" portion of the blog.) The graphs of the upper and lower limits can be found under the "Data" section of the blog. (See Figure 1.2/1.3). 

Looking back at the equation: ln(T) = n*ln(m+M(tray)) + lnA, we are finally able to determine the value of the constants A and n. They can be found by looking at the equation of the graph in Figures 1.2/1.3. These equations utilize these values and if we remove the natural log, we can find the value. This gives us a final, working equation:

(T/A) ^(1/n) -M(tray) = m

With this equation, we have to keep in mind that we do not know the exact value of M(tray), and therefore the exact value of A and n. To find an accurate measurement, we take the upper and lower limit and plug them both into the equation to find the range of what the expected mass should be.

Now that we have a working equation, we can put it to the test by finding the mass of two random objects. The objects we picked consisted of a stapler and tape dispenser. First, we put each object on the inertial balance and recorded the period of oscillation. Next, we plugged these values into the equation, twice, bearing in mind the upper and lower limits. The worked out results for both the stapler and tape dispenser can be seen in the “Data” section of the blog. (See Figures 1.4/1.5).

5.     Data

Figure 1.1 (Data Table of Masses)

Figure 1.2 (Graph of Upper Limit)

Figure 1.3 (Graph of Lower Limit)

Figure 1.4 (Worked out Calculations of Stapler)

Figure 1.5 (Worked out Calculations of Tape Dispenser

Figure 1.6 (Period of Stapler)

Figure 1.7 (Period of Tape Dispenser)

• Table of Calculated Results

View figures 1.4/1.5 for calculated results. Figures contain calculations for unknown masses using the derived equation. Each mass required the equation to be used twice, once for the upper limit and once for the lower limit. This was done in order to calculate the range of the object.

• Analysis of Graphs

View figures 1.2/1.3 for graphs. These graphs are the power-law equations, after being manipulated to look similar to y=mx+b form and with a linear fit. As mentioned above, a linear fit means that the parameters are correct and the mass of the tray has been found. Since we cannot find the mass of the tray directly (due to reasons that will be explained in the conclusion), we get a range, hence the need for two different graphs. One graph is for the upper limit, which is the highest amount the tray can be before the line loses its linear fit, while the other is the lower limit, which is the lowest amount the tray can be before the line loses its linear fit.

• Conclusion

Using the equations to find the estimated mass of the stapler and tape dispenser answered some basic level questions and answered our objective in that we've found an equation to relate the two. However, much more work is needed to find a much more accurate answer. While I was able to find a suitable range for the tape dispenser, the stapler's actual mass was outside of my range. However, this could be for many reasons.

First, we do not know how the center of mass of both the object and the inertial balance affects the period. Perhaps if placed differently, the period could change drastically. Another potential foresight would be the propogated uncertainty of the mass of the object and the correlation of the line. We do not exactly know the limits, therefore finding a much closer limit would result in a closer answer. Another reason could be the damping constant of the inertial balance or the amplitude in which the balance is released at. Basically, there were a countless number of factors that could have swayed the results.