21-Sept-2016: Modeling Friction Forces

Lab 7 Modeling Friction Forces
Date: 21 September 2016
Lab Partner: Richard Mendoza, Mohammed Karim, Lynel Ornedo
Name: Andrew Martinez

Introduction: Conducting five different experiments that involve static and kinetic friction.

Apparatus:
- Wooden blocks
- Various mass plates
- String
- Wooden Panel
- Hanging mass
- Computer
- Ring Stand
- Focus Sensor
- LabPro
- Clamps
- Motion Detector

Procedure
Part 1: Static Friction
- Set up apparatus on uniform surface as shown adding weights for each block until it moves.
- Record the mass of each block until reach 4 and the weight it moved on
- Plot data into computer

Apparatus for part 1 with maximum number of blocks

Hanging Mass and pulley along with the string for tension

Blocks with tension from string

Part 2: Kinetic Friction
- Calibrate the force sensor
- Plug force sensor into LabPro and connect to computer via USB. Set to 10-N range
- Use 500-gram for calibration
- Find the mass of one of the wooden blocks
- Collect data from force sensor by moving the block horizontally at a constant speed along a uniform surface as LabPro
- Repeat till the last block
- Plot data and the slope gives the kinetic friction

Example of calibration of the force sensor

Part 3: Static Friction From a Sloped Surface
- Place the wood panel at an incline angle while leaving a block on it
- Raise until the block begins to move downward on its on
- Take the angle of that moment in order to help determine the coefficient of static friction

Part 4: Kinetic Friction From Sliding a Block Down an Incline
- Attach a motion sensor just above the wooden panel
- Leaving the Panel at the same incline find the coefficient of kinetic friction by using the motion sensor to find the acceleration.

Used for Part 3 & 4 to determine the static and kinetic friction. On top of the board is the motion sensor.

Part 5: Predicting the Acceleration of a Two-Mass System
- Use the kinetic friction you got from part 4 and derive an expression for the acceleration of a block with a hanging mass

Data:
Part 1
Block 1: 179.1 g
Block 2: 177.5 g
Block 3: 181.7 g
Block 4: 190.1 g
Hanging Mass
B1: 85 g
B1B2: 150 g

B1B2B3: 200 g
B1B2B3B4: 310 g

X:Normal Force vs Y:Force of static friction
By listing the normal force with its force of static friction we get our slope

Slope is .4106 making the coefficient of static .4106

Part 2

Using the data given by these charts plug there values into the Y for the graph below

With the Y from the graphs on top we can find the kinetic friction from the slope.
Uk = .2300

Part 3

Using the angel we found the block to move out we can determine the coefficient of static friction by substitution and plugging in.
Us = .4306

Part 4

Using the angel we found the block to move at and continue to move we can determine the coefficient of kinetic friction by substitution and free body diagram.
Uk = .2295

Part 5

Used Block 1 mass: 179.1 g hanging mass at B1: 85 g
Experimental a=2.068 m/s^2

Using the motion sensor then recording the acceleration the block moves out at the given masses.
Actual a(slope) = 1.682

Percent error: 22.94%

Conclusion: Aside from part 5 the experiments went according to plan. Part 5 has a large percent error due to human or systematic error. There could have been mistakes in which block was used or the pulley system was properly put in place or the motion sensor might have been placed to far. Whatever the case the majority of the experiment was a success and if part 5 were to be redone I am sure it would achieve more favorable results.

7-Sept-2016: Propagated uncertainty in measurements

Lab 6 Propagated Uncertainty in Measurements
Date: 7 September 2016
Lab Partner: Richard Mendoza
Name: Andrew Martinez

Introduction: Use propagated uncertainty to find the propagated error in the density of the metal cylinders

Apparatus:
- Iron Cylinder
- Aluminum Cylinder
- Calipers
- Mass scale

Procedure: Using the scale and caliper find the mass, height, and diameter of the cylinders as well as there expected error and use these measurements to determine density with propagated error.

Caliper used to find the length and diameter to an .01 expected error

Aluminum Cylinder

Iron Cylinder

Mass Scale with an .1 expected error

Measure Data
Aluminum Cylinder: M(29.1 g +/- .1 g), H(7.83 cm +/- .01 cm), D(1.29 cm +/- .01 cm)
Iron Cylinder: M(30.2 g +/- .1 g), H(3.07 cm +/- .01 cm), D(1.24 cm +/- .01 cm)

Picture shows the work done to find the density and its propagated error

Density for aluminum is 2.84 g/cm^3 +/- .288 g/cm^3
Density for iron is 8.14 g/cm^3 +/- .826 g/cm^3

Conclusion: The experimental measurements with their expected errors yielded fairly accurate results for density and the propagated error. Random errors that may have occurred is misreading on the measuring scales. Systematic errors might be user resulted in the calculations of the math problems.

14-Sept-2016: Trajectories

Lab 5 Trajectories
Date: 14 September 2016
Lab Partner: Richard Mendoza
Name: Andrew Martinez

Introduction: Using your understanding of projectile motion estimate where the ball will impact on an inclined board.

Apparatus:
- Aluminum "v-channel"
- Steel ball
- Board
- Ring Stand
- Clamp
- Paper
- Carbon paper

The launcher without the board. You can see the ring stand, aluminum "v-channel", clamp, and steel ball.
V-channel is placed at an incline to cause downward acceleration.

Launcher with board. Wood board placed at a 19.2 degree angle, carbon paper on board, and paper underneath carbon paper.

Another view of the inclined view of the apparatus. 

Procedure: Set up apparatus without wooden board. Determine height of the ramp from the floor and incline. Let the steel ball launch from the ramp and determine its range. Does this five times with carbon paper placed under the assumed impact point. Find the distance for each and find the overall average in distance. Place wooden board on table directly underneath the ramp launch point. Using the information learned determine the expected landing point on the wooden table and then place carbon paper on the wooden ramp to measure the actual.

Measured Data
h=94.2 cm
Theta=19.2
D1=108.7 cm, D2=108.1 cm, D3=106.4 cm, D4=106.1 cm, D5=105.8 cm

Finding Velocity
V=242.5 cm/s

Velocity was determined by using the distance, height, and gravity.

Finding Impact Point
Use the angle and velocity found earlier to determine impact point
Estimated distance is 44.25 cm

Distance was determined by using the found angle and velocity as well as subtitution to account for unknowns

Actual distance is 44.6 cm

Conclusion: The percentage error between the approximated and the actual was found to be .78%. This makes the calculations to be extremely accurate. One systematic error would be at what height the steel ball was released on the steel ramp. This could give some increase acceleration at different points.

19-Sept-2016: Modeling the fall of an object falling with air resistance

Lab 4: Modeling the fall of an object falling with air resistance
Date: 14 & 19 September 2016
Lab Partner: Richard Mendoza
Name: Andrew Martinez

Introduction: Air resistance applied to an object depending on its speed, shape, and the material. This model can be seen as a power law.

Apparatus:
- 150 coffee filters (mass= 134.2 g)
- Meter stick
- Computer

Procedure:
- Take the coffee filters and measure their mass
- Find a high balcony inside a building to minimize air resistance
- Bring laptop to record with logger pro
- Use a meter stick for a point of reference for the recording
- Drop the filters 5 times recording each instance
- Using logger pro graph each video and find the liner fit to plug into part 2 of excel
- Use excel to find terminal velocity

Part 1 Data
The five graphs seen here are position vs time graphs of each of the five videos. The data was taken by scaling the one meter mark and using dots to follow the distance the filters had moved per frame during free fall. This was then calculated by the computer and put into graph form.

Video 1

Terminal Velocity (Slope): 3.088 m/s

Video 2

Terminal Velocity (Slope): 2.156 m/s
Video 3

Terminal Velocity (Slope): 2.842 m/s
Video 4

Terminal Velocity (Slope): 3.373 m/s
Video 5

Terminal Velocity (Slope): 3.100 m/s
Using a power law Fresistance = kv^n (k=a, b=n)
Terminal Velocities Graph

K= .0001901 +/- 0.0002173
N = 4.476 +/- 0.9853

Part 2
Measured Data
Excel spreadsheet to model the fall of an object with air resistance using the terminal velocities.

The predicted terminal velocity for various coffee filters appears to be 5.5 m/s
Plug it into power law Fresistance = kv^n. 0.0001901*(5.5^4.476) = .39 N

Conclusion: K and N are determined from the linear fits done to the video graphs and the results that appear of the terminal velocity graph. There is an uncertainty in terms of how accurate the graphs are depending on the user accuracy on plotting the dots. Air resistance was found to be .39 N and based on the model it was effective in determining the air resistance. Other might like to use this method because it requires less analytical work.

12-Sept-2016: Non-Constant acceleration problem/Activity

Lab 3 Non-Constant Acceleration
Date: 12 September 2016
Name: Andrew Martinez
Lab Partner: Richard Mendoza

Introduction: Using analytical and numerical approach determine how far the elephant goes before coming to rest.

Apparatus: While there is no apparatus we are given a problem to solve. "A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a hill and arrives on level ground. At that point a 1500-kg rocket mounted on the elephant's back generates a constant 8000 N thrust opposite the elephant's direction of motion. The mass of the rocket changes with time (due to burning the fuel at a rate of 20 kg/s) so that the m(t) = 1500 kg - 20 kg/s*t." Two ways to do this are through analytical means or numerical means.

Measured Data:
Elephant Mass: 5000-kg
Initial Velocity: 25 m/s
Rocket Mass: 1500-kg
Rocket Force: 8000 N opposite elephant's direction
Rocket Fuel Depletion: 20 kg/s

Analytical Method:

1. Set as a function of time

2. Find delta V and then derive an equation for V(t)

3. Integrate the velocity from 0 to T to find delta x and then derive an equation for x(t)

Plug it all in and you get time 19.6 seconds and distance 248.7 meters

Numerical Method:

By opening up an excel spreadsheet and plug the equations into there appropriate columns  

Once everything is plugged in and the relevant data has been inputted the distances can be determined by dragging down

 At 19.6 seconds the distance is 248.5 meters

Conclusion: 

1. Comparing the results it is clear that both analytically and numerically results are reasonably close to one another. Though numerically requires less work on the user.

2. By obtaining the time given in the analytical approach or by seeing when the velocity reaches zero

3. Time 13 seconds and distance 164 meters

07-Sept-2016: Free Fall Lab determination of g

Lab #2 Free Fall and the determination of g

Andrew Martinez
Lab Partner: Richard Mendoza

Statement: Use the apparatus to demonstrate the motion of free falling bodies and learn how to determine acceleration through a position vs time graph and

Theory/Introduction:To analyze how to determine g based on the apparatus of a free falling object and using statistic to analyze gathered data through excel. Gravity is present in all case whether something is fall or not gravity is constantly pulling with a force of 9.8 m/s^2

Apparatus: An electrical device magnetically suspends the a wooden cylinder by its metal ring. A length of tape is vertically pulled down to match the length of the vertical device. Once the electromagnet turns off the wooden cylinder will fall which an active electric current going off every 1/60 of a second marks the position of the object at that moment. This can be used to make a time vs position graph.

Procedure: For this lab several steps had already been done that resulted with the tape having the spark marks finished. Next you open up excel to begin recording the data and using the program to find the time and distance. Once done create charts to fine the R and the chart equation.

Measured Data:
Part 1

Table 1

A Column: Time in 1/60 of second. B column: Position the rod was at when the time was recorded. C colum: Distance displacement. D column: Time recorded at 1/120 of second. E column: The velocity recorded at the mid-interval time.

Graph 1 (Table 1)

Graph 1 has a linear fit done to it with the equation shown

Graph 2 (Table 1)

Graph 2 has a polynomial fit done and the equation is given

Part 2

Table 2

A column is the listed groups data, B column is the deviation from the A column mean at A10, C column is the standard deviation or range that most fall within and is considered acceptable.

Calculated Results:
Part 1
1.

 As shown the resulting average velocity is nearly the same as the mid-interval time displaying how constant acceleration effects velocity.

2. You can get acceleration by deriving the equation provided after doing a linear fit on the velocity/time graph.

3. To get the acceleration from a position/time graph you take the second derivative of the equation provided from the polynomial fit.

Part 2
1. Most of the values of our g seemed to be constant with an R^2 value of .998.
2. The average value of g given by the group data is 9.48 m/s^2 while the accepted value is 9.8 m/s^2. This puts the difference between expected and experimental at -4% well within acceptable range.
3. The pattern between the class value seem to centered around 9.48 m/s^2 where the majority of values falling within one standard deviation.
4. Random errors that could have occurred are changes in the electric current which could have effected how often a mark was left on the tape. A systematic error could be misreading measurements on the meter stick as the marks were sometimes between measurements and assumptions had to be made.
5. The main point of part 2 of the Lab was to become familiar with Excel and learn useful programming for gathering data and analyzing it. That through analyzing the data we can find the standard deviation and means and see how accurate our results are to the actual.

Conclusion: While the calculated g for our group was 9.57 m/s^2 and the actual value is 9.8 m/s^2  the relative difference is -2.34% which is an acceptable margin. There are some inherit uncertainties such as the accuracy of the meter stick. Since the most accurate we could be was to the millimeter that leaves a .001% uncertainty. Though this should not effect the results to much.

29-Aug-2016: Finding a relationship between mass and period for an inertial balance

Lab #1 Inertial Balance

Andrew Martinez
Lab Partners: Richard Mendoza

Statement: Use an inertial balance and power-law type equation to determine the mass and period and there relationship to each other.

Theory/Introduction: Measuring mass is usually done by spring scales and balances that depend on gravity to help in the measurement and is known as gravitational mass. However, there is another means of measuring mass by measuring inertial mass. This is done with an inertial balance and comparing the object resistance to change in its motions. We will also determine the relationship between mass and period by deriving a power-law type of equation.

Apparatus:

Left: Photogate attached to standing pole
Right: C-clamp holding inertial balance to table, tape placed on the open end to reach photogate
On table: Photogate attached to LabPro with USB connection to computer for data collection

Procedure: Set up apparatus by attaching the photogate to the standing pole at inertial balance level. Use C-clamp to hold inertial balance in place to the table. Next place a length of tape on open end of the balance to block the photogate laser. Using the LabPro connect to both the photogate and computer to begin collecting data. Using a series of 100g, two 200g, and one 500g masses to find the periods of 0g to 800g moving up every 100g. Once the data has been collected the data is organized under user parameters and into new calculated column where the data can be plotted. Once that is done the user can perform a linear fit and using the equations provided derive the estimated masses and periods. Finally use two random objects to measure using the inertial balance to determine their estimated masses and period ending with exactly finding the mass using a gravitational scale mass and period calculated from the computer.

Measured Data:
0-800g slotted masses









Calculated Results: Plot of ln(T) vs ln(m+Mtray)

Upper Mass: 360g Correlation: .9998 Slope: .7585 Y-intercept: -5.701s

Lower Mass: 280g Correlation: .9998 Slope: .6605 Y-intercept: -4.971s

Derived equation from the graphs

Calculated results of unknown mass of phone and water bottle

Conclusion: After finding the derived equation of the power-type problem in order to test out its accuracy two randomly selected objects were used to find the estimated mass and then were actually measure using a scale. The results were not within range of our estimated calculations. There are a number of reasons why this could be true such as the water in the bottle sloshing around and thus displacing the mass during its oscillations. The phone was not stable during the inertial balance oscillations either contributing to the inaccuracy of the results. Despite the inherit uncertainty of measurements these results are more likely user error and does not necessarily mean that the equation is wrong but that more suitable objects should have been used.