Lab #7- Modeling Friction Forces

Lab #7- Modeling Friction Forces

Alexander Reyes

Lab Partners: Mike flores & mike

Performed on: 9/21/16

Theory/Introduction: For this specific lab the coefficient of static and kinetic friction between a wooden block and a table will be calculated. There will be five different experiments performed. Experiment 1 will calculate coefficient of static friction, experiment 2 will calculate kinetic friction, experiment 3 static friction from a slopped surface, experiment 4 kinetic friction from sliding a block down an incline, and experiment 5 will be predicting the acceleration of a two mass system. 

Apparatus/Experimental Procedure: Below is an image of the apparatus that was put together for all experiments. For Part 1, a wooden block was weighed to find its mass and a 50 gram hanging weight was hung over the table attached by a pulley. Masses were added to both the wooden block and the hanging mass  for each trial run until the wooden block began to slide down. once the wooden block began to slide the weight of the hanging mass was recorded. For part 2, a force sensor was used in order to find the average force of a block while sliding horizontally. For each trial run more mass was added to the block and the process was repeated 4 separate times. For part 3, a block was placed on a horizontal surface. The surface was raised by one end until the block started to slip. The angle at which the block began to slip was calculated at 25 degrees. For part 4, a motion detector was used at the top of an incline to find the acceleration of a block going down. The angle 30 degrees and the mass of a block 178 grams was calculated. For part 5, the same apparatus was built as in part 1, but a motion sensor was used in order to find the acceleration of the block sliding down the table.

Part 1 Data: Static friction was calculated by plotting a graph of FsMax vs N.The slope of the graph calculated the coefficient of static friction which was found to be 0.4088.

Part 2 Data: The mean for each trial run was calculated and plotted. A Fk vs N graph was plotted, and the slope of the line was derived. The coefficient of kinetic friction was found to be. 2877.

Part 3 Data:After determining the angle at which the block begins to slide coefficient of static friction was calculate below(0.466)

Part 4 Data: Motion detector was used to find the acceleration of the wooden block sliding down a 30 degree angle incline. Calculation below determined the coefficient of kinetic friction 0.8837.

Part 5 Data: Using the coefficient of kinetic friction from part 4 the acceleration of a block was determined below. Acceleration found by motion sensor was .88 m/s^2 compared to the 1.13 m/s^2 acceleration calculated. 

Conclusion:A total of 5 separate experiments were performed for modeling friction forces lab. For part 1, the coefficient of static friction between the table and the wooden block was calculated to be .4088. For part 2, .2877 was found to be the coefficient of kinetic friction. For part 3, the coefficient of static friction was calculated to be .466. For part 4, .8837 was calculated as the coefficient of kinetic friction. For part 5, the acceleration of the wooden block was calculated to be 1.13 m/s^2. Sources of error could have come from miscalculations in equations.

Lab#6: Propagated uncertainty in measurements

#6: Propagated uncertainty in measurements
Alexander Reyes
Lab Partners: Mike Flores & Mike
Performed on: 9/7/16
Theory/Introduction: In this lab the propagated uncertainty of two density measurements will be calculated for two metals.


Apparatus: The tool used to measure the height, diameter, and mass for the aluminum and iron metal is shown below.



Data: Below is the calculated propagated uncertainty for the aluminum cylinder. Experimental propagated uncertainty calculated was 2.74 +/- 0.2776g/cm^3. Actual density of aluminum is 2.7 g/cm^3, therefore the measurements are within the experimental uncertainty of the accepted values.


Data: Below is the calculated propagated uncertainty for the iron cylinder. Experimental propagated uncertainty calculated was 6.85 +/- 0.6936 g/cm^3. Actual density of iron is 7.87 g/cm^3, therefore the measurements are slightly off from the accepted values for experimental uncertainty.


Conclusion: The height, diameter and mass were experimentally calculated using an apparatus for an aluminum and iron cylinder. By calculating those specific dimensions for the metals the propagated uncertainty in measurements was derived for each using calculus. Sources of potential error could have occurred when measuring the height, diameter, and mass for the metals. The apparatus could have been slightly misused and calculations could have been misread.

Lab # 5- Trajectories

Lab # 5- Trajectories
Alexander Reyes
Lab Partners: Mike Flores & Mike
Performed: 9/14/16
Statement: Using concepts learned from projectile motion in order to predict the impact point of a ball on an incline.
Theory/Introduction: An apparatus will be constructed in order to roll a ball off an inclined board and off the desk. For part one of the experiment the launch speed will be calculated. For part two of the experiment the distance the ball strikes the board from the edge of the table will be calculated.
Apparatus/Experimental Procedure: For this experiment an apparatus was built like the one seen below. The materials used to build the apparatus was an aluminum "v-channel", board, ring stand, clamp, paper, carbon paper, and steel ball. Part 1 of the experiment, a ball was launched from near the top of the apparatus and was observed to identify the landing location. Once the landing location was identified carbon paper was taped onto the floor,  and the ball was launched five times in order to determine that it would land in the same place every time. Part 2 of the experiment, an incline board was attached to the edge of the table. The ball was then launched toward the top of the apparatus five different times at the same height. The landing point onto the inclined board was observed and then carbon paper was taped in order to determine that the ball would land on the same spot each time.


Part 1 Data: Below is the calculation done for the launch speed. The height from the floor to edge of the table was found to be .942 +/- .001 meters and the distance the ball rolled off the table was found to be .780 +/- .001 meters. a kinematic equation was set up to find the launch speed which was 1.78m/s.



Part 2 Data: Below are the calculations done for part 2 of the experiment. An expression was derived below in order to find distance the ball rolled off the table.By determining the angle of the board which was 41 degrees and having the velocity of the ball 1.78m/s, the distance the ball rolled off the table and hit the incline board was found to be .745m.




Conclusion: Projectile motion concepts were utilized in order to conclude the landing location of a ball on an incline board.For part one of the experiment the launch velocity(1.78m/s) was calculated by finding the height from the edge of the desk and the distance the ball landed from the desk. For part 2 of the experiment the distance the ball traveled from the desk and onto an incline board was determined by using the velocity found in part one, and an angle measured(41 degrees). Distance experimentally calculated for part two was .745 m. Uncertainties for this lab could have consisted of small pieces of debris on the aluminum v channel where the ball was launched from and could have slightly altered the launch speed.

LAB #4: Modeling the fall of an object falling with air resistance

LAB #4: Modeling the fall of an object falling with air resistance
Alexander Reyes
Lab Partners: Mike Flores & Mike
Lab Performed:9/14/16 & 9/19/16
Statement: Air resistance force encountered by an object is dependent on its speed, shape and material.
Theory/Introduction:  F(resistance)= kv^n can model the force an object experiences when in free fall. Coffee filters will be dropped from a balcony in this experiment and will determine relationship between air resistance force and speed. Secondly, an excel spreadsheet will be created to model the fall of an object with air resistance and find its terminal velocity.
Experimental Procedure: For part one of the experiment we headed to the design technology building in order to video capture the free fall of 1, 2, 3, 4, and 5 coffee filters. Professor Wolf taped a meter stick to a black tarp and dropped 1, 2, 3, 4, and 5 coffee filters in front of the tarp from a balcony as i video recorded the free fall for each drop. For part two of this experiment an excel spreadsheet was made with the information found for part one in order to calculate the terminal velocity for the falling objects.

Graphs of Data: Below are graphs from the data that was retrieved using video capture. The data was found by scaling the one meter stick, and plotting points onto the coffee filter as it was in free fall  motion until it hit the ground. For each coffee filter drop, i had to find its velocity by using the linear fit line in order to obtain the slop of all plotted points. Coffee Filter #1 velocity=1.338 m/s, coffee filter #2 velocity=1.671 m/s, coffee filter #3 velocity=2.57 m/s, coffee filter #4 velocity= 3.27 m/s, and coffee filter #5 velocity=3.926 m/s. Soon after finding all velocities, i had to multiply acceleration due to gravity(9.8 m/s^2) with the mass of 1, 2, 3, 4, and 5 coffee filters in order to find the force. Forces found are the following: .008722, .017444, .026166, .034888, and .04361 all in (kg*m)/s^2. Once all velocities and forces were obtained a graph was plotted using the values above in order to find k and n in the power law (F(resistance)=kv^n). According to the last graph below the value for k=0.007955 +/- .001130 and n= 1.248 +/- 0.1187








Measured Data: Below is an excel data table with all information from part 1. From the information gathered the terminal velocity of the free falling coffee filters appears to be at 1.07 m/s. Plugging information into F(resistance)=kv^n equation, i get F(resistance)=(.007955)(1.07)^(1.248)=.008655.




Conclusion:The k and n value for the power law were determined within this experiment by video capturing the free fall of 1, 2, 3, 4, and 5 coffee filters. By imputing the information from part 1 of the lab into an excel data table the terminal velocity was found and the air resistance force was obtained. Uncertainties could have occurred when plotting points on the coffee filters on video capture or not scaling the 1 meter stick appropriately , which could have slightly altered the k and n values in the formula.

Lab #3- Non-Constant acceleration problem/activity:

Lab #3- Non-Constant acceleration problem/activity:
Alexander Reyes
Lab Partners: Mike Flores and Mike
Performed on: 9/12/16

Introduction: For this specific lab we had to find the distance an elephant went before coming to rest.Elephant had a mass of 5000 kg, velocity of 25m/s. a 1500 kg rocket mounted on its back generating a constant 8000N thrust. An integral was set up to find the distance analytically and gave us the answer of 248.7 meters. Soon after, we took a numerical approach and created an excel spreadsheet to compare whether we would obtain the same distance for both methods.


Data: After imputing the information from the analytical approach into an excel spread sheet we obtained the information below.  At the 20 second mark the elephant came to a distance of 248.6 meters before coming to rest.


Conclusions: After completing the numerical approach the answer obtained of 248.6 meters is almost identical to the analytical approach of 248.7 meters. I was able to know what time interval was small enough by simply obtaining the time found in the analytical approach which was 19.69 seconds. If i didnt have the analytical part to compare my numerical result, i would simply look at the velocity values in the excel spreadsheet to see when the elephant velocity is close to zero. When the elephant is coming to rest then it should have a velocity near zero and the distance and time could be determined. Another distance was also calculated for the elephant when tweaking our data for the following question: determine how far the elephant would go if its initial mass were 5500 kg, the rocket mass is still 1500kg, but now the fuel burn rate is 40 kg/s and the thrust force is 13000 N? the elephant traveled 164 meters within 13 seconds for those new values.

Free Fall Lab- Determination of g and some statistics for analyzing data

Alexander Reyes

Lab Partners: Mike Flores & Mike

Date Performed: 9/7/16

Purpose: To observe and approve that a falling body will accelerate at 9.8m/s^2 with only gravity acting as a force.

Theory/Introduction: g value of a free falling body must be determined by graphing a velocity vs time graph and a position vs time graph. In this specific case a spark generator with a free falling body would be studied in order to conclude if the falling body accelerated at 9.8 m/s^2.


Apparatus/Experimental Procedure:A spark generator free fall apparatus was used within the experiment. The generator had a column with a 1.5 meter falling distance, and the free-fall body was held at the top by an electromagnet. When the electromagnet was released, the fall was accurately recorded by a spark generator. Markings were engraved on the piece of tape that was attached to the generator in order to record the fall.The distance between each marking on the tape was measured using a meter stick.  Pictures of apparatus and tape from spark generator are provided below.After obtaining all information, a velocity vs time graph and position vs time graph were plotted.






Table of Measured Data:
Below is the data that was needed in order to plot each graph. Time data started from 0 sec, and 1/60th of a second was added continuously. The distance column shows the distance between each marking in centimeters on the spark generator tape.


Position vs Time Graph: In order to obtain the acceleration from the position vs time graph the second derivative must be taken from the equation. After calculating the second derivative the value for g= 9.2m/s^2. Calculation of derivative can be found below. Experimental value is slightly off from the accepted value of 9.8 m/s^2




Velocity vs Time Graph: In order to obtain the acceleration from the velocity vs time graph the first derivative must be taken from the equation. After calculating the derivative the value for g= 9.2 m/s^2. Experimental value is slightly off from the accepted value of 9.8m/s^2




Errors & Uncertainty: Below is an excel spreadsheet which determined the standard deviation of the mean of the class. Every group within the class got a value for g in the 900 mark. The average value of 942.1 is slightly off from the accepted value of 980, but is still close enough to give a good average.


Conclusion:
A spark generator apparatus was used to calculate the acceleration (g value) of a free falling object. Once data was gathered from the apparatus tape an excel spreadsheet was created along with two graphs, a position vs time and velocity vs time graph. The acceleration of the free body object was determined by taking the second derivative of the position vs time graph equation and first derivative of the velocity vs time graph. Experimental acceleration found for the free falling object was 9.2 m/s^2. Another excel spreadsheet was created in order to find the class mean and standard deviation. Sources of uncertainty or error could have occurred when measuring the markings on the spark generator tape that was obtained. Also, the tape could of been placed incorrectly into spark generator.

Finding a relationship Between Mass and Period For an Inertial Balance

Title:Finding a relationship Between Mass and Period For an Inertial Balance
Name: Alexander Reyes
Lab Partners:Mike, and Mike
Date Lab Performed:8/29/16

Purpose: The main purpose is to find a relationship between period and mass  for inertial pendulum.

Theory/Introduction: T= A(Mass + Mtray)^n
Three values had to be obtained from the formula: A, Mtray and n


Apparatus: Metal tray that was clamped on the table and had a piece of tape at the end of it in order to pass and measure the period on the photogate. Masses of 0 to 800 grams were added to the tray and periods were recorded.




Data Table: 0 to 800 grams were placed on the balance and periods were determined by using LabPro. All the data was recorded below.


Graph & Data For Minimum Mtray Mass: The minimum mass for Mtray was at 280g with a correlation of .9998. Found A=.007804 sec and n=.6425 sec/g




Graph & Data for Maximum Mtray Mass: The Maximum Mtray mass for Mtray was 290g with a correlation of .9998. Found A=.007204 sec and n=.6533 sec/g




Extension Calculations: Measured the mass of a phone (189g),  and its period of (.407 sec.)
Measure the mass of a golf ball (45g), and its period (.324). After inputing the calculated values into the formula the inertial mass and the gravitational masses for the phone were almost similar. Where as for the inertial masses and the gravitational masses for the golf ball were slightly off from each other. Calculations below.





Conclusion: An inertial apparatus balance was set up in order to find the periods of 0 to 800 grams. Soon after, three unknown values from the Power-Law equation needed to be obtained. Those three unknown values were found by plotting a lnT vs ln(m+Mtray) graph. A linear fit line with a correlation coefficient of .9998 or .9999 would help us determine which equation was suitable for use. The Relationship found between mass and period would be, the more mass the larger the period.