21-Sep-2016: Lab 7 Modeling Friction Forces

1. Title: Lab 7 Modeling Friction Forces
    Name: Qiwen Ye (Sherry)
    Lab partners names: Jae Yoo, Chandler
    Date: 21-Sep-2016

2. Purpose
In this lab, we did five different experiments involving friction: static friction, kinetic friction, static friction friction from a sloped surface, kinetic friction from sliding block down an incline and predicting the acceleration of a two-mass system. We used the derivation and measurement and capture the appropriate graphs to explain how we can get the friction from each section of the lab in order to find each friction of experimental values compared to the theoretical values.

(1) Static Friction
-- Introduction:
Static friction describes the friction force acting between two bodies when are not moving relative to one another. The coefficient of static friction is defined as:

-- Apparatus/ Experiment procedure:
In this static friction experiment, we added the mass m to the bottom shown a bit of time until the block just starts to slip. First, weigh a wooden block that has felt on one face of it. Placed the felt-side of the block on the lab table. Tie a string to the block and over a pulley at the end of the lab table. Second, opened up a paper clip and bend the ends so that they form a handle on a Styrofoam cup (just line the handle on a pail.) Connected the string to the middle of the handle. Third, Patently the mass to the bottom of the string at a time, until the block finally starts to slide. Record the mass to get the block to start to move. Then, added the mass on the block in order to change the mass of the block, repeated process again to get what mass can start to move the new mass of the block.

-- A table of the Data:
We run the experiment and record the appropriate data by repeating the experiment in four times, so that we got four different values of mass of hanging and mass of block that the block start to move:

-- A table of calculated results/Graphs of data:

Draw the free body diagram we got:

Then, we calculated the values of friction force and normal force by those equation:

Finally, we got the table about the mass of hanging, the mass of the block, the static friction and the normal force of the mass of the block:

By using the LabPro, we got the graph about the friction force vs. normal force.

We calculated our theoretical values of the coefficient of static friction by get the average of four values of friction force and normal force:

That, we got our theoretical values of the coefficient of static friction is 0.26713395638

-- Explanation of graph/analysis

There is the graph about the friction force vs. normal force, and the slope of the graph is the values of the coefficient of static friction between the felt and the track. The slope of the graph is 0.2662, there is our experimental value the coefficient of static friction.

-- Conclusion:

In this experiment, we determined the coefficient of static friction between the felt and the track . The experimental value is 0.2662, and the theoretical values is 0.26713395638. The error percent is 0.34%. This result shows that the experimental value is very close to the theoretical value. Therefore, this experiment is successful. 

(2) Kinetic Friction
-- Introduction:

In our model, the kinetic friction force has a fixed value for a given N, regardless of the speed of the motion. This coefficient, like the coefficient of static friction, depends only on the surface materials, not on the weight of the object or its area of contact. Kinetic friction is independent of the the area or speed of the moving object, it is being proportional to the normal force. That is, we wrote

-- Apparatus/ Experiment procedure:
In this Kinetic friction experiment, we used a Force sensor. First, we had to calibrate the force sensor. Opened in a LabPro and connected it to the computer with the USB cable. Plug the force probe into the LabPro, CH1. Switch the force probe so that it reads in the 10-N range. Second, connected up a force sensor to CH1 of a LabPro and plug the LabPro into the computer, etc. Set the force sensor on the 10-N range. Calibrate the force sensor using a 500-gram hanging mass. Then, determined the mass of  a wooden block that has felt on its lower surface. Hold the force horizontally and Zero the force sensor. Finally, tie a string between the force and sensor and the block to hit "collect" and slowly pull horizontally, moving the block at constant speed along the surface of the table. Store the run, and repeated the above step again to four different mass of the block.

-- A table of the Data:

We run the experiment and record the appropriate data by repeating the experiment in five times, so that we got five different values of the mass of the block and the value of the force senor.

-- A table of calculated results/Graphs of data:

By the free body diagram we got

Then, we calculated the normal force by

We got the new table about the values of the mass of the block, the value of the force senor, and the normal force.

By using the LabPro, we got the graph about the kinetic friction force vs. normal force.

We calculated our theoretical values of the coefficient of kinetic friction by get the average of four values of friction force and normal force:

That, we got our theoretical values of the coefficient of kinetic friction is 0.21309370988

-- Explanation of graph/analysis:

The slope of the graph the kinetic friction force vs. normal force is experimental value of the coefficient of kinetic friction between the block an the table, there is 0.2118.

-- Conclusion:

In this experiment, we determined the coefficient of kinetic friction between the block and the table. The experimental value is 0.2118, and the theoretical values is 0.21309370988. The error percent is 0.61%. This result shows that the experimental value is very close to the theoretical value. Therefore, this experiment is successful.

(3) Static Friction from A Sloped Surface
-- Apparatus/ Experiment procedure:
Placed a block on a horizontal surface. Slowly raised one end of the surface, and tilting it until the block starts to slip. Used the angle at which slipping just begins to determine the coefficient of static friction between the block and the surface.

-- A table of the Data:

Used the iPhone - compact to measure an angle the the block just begins to slip down, the angel is 28 degree.

-- A table of calculated results/Graphs of data:

We calculated the coefficient of the kinetic friction of the sloped surface.

-- Explanation of graph/analysis:

By the equation, we determined the coefficient of static friction between the block and the surface is 0.5095.

-- Conclusion:

In this experiment, we found the relationship between the angle of the surface and the static friction is that the static friction is depended on the angle.

(4) Kinetic Friction From Sliding A Block Down An Incline

-- Apparatus/ Experiment procedure:

Used a motion detector to record the acceleration which at the top of an incline steep enough that a block will accelerate down the incline. Measured the angle of the incline and the acceleration of the block. 

-- A table of the Data:

Used the iPhone - compact to measure an angle, the angle is 27 degree. Through the LabPro, we got the acceleration is this motion. In the graph of velocity vs. time, the acceleration is its slope, a=2.585 m/s^2.

-- A table of calculated results/Graphs of data:

We calculated the coefficient of the kinetic friction of the sloped surface.

-- Explanation of graph/analysis:

The slope of the graph is the acceleration of the block, so that while we plug the number of the acceleration into the equation of the kinetic friction, we can get the value of the coefficient of the kinetic friction in the sloped surface. The coefficient of the kinetic friction is 0.21.

-- Conclusion:

In a incline, the kinetic friction depends on the acceleration of the object and the angle of the incline. 

(5) Predicting the Acceleration of A Two-Mass System 

-- Apparatus/ Experiment procedure:

Set up the motion sensor at end of the table, and placed the block in front of the motion sensor. Used the string to connect the block and the hanging mass. Added the mass of hanging in order to create the kinetic friction that the block was moving forward.

-- A table of the Data:
The mass of block is 0.18 kg, the mass of hanging is 0.08 kg, and we used the kinetic friction results from experiment (4) above.

We got the graph velocity vs. time by the LabPro.

-- A table of calculated results/Graphs of data:
We calculated the Theoretical acceleration in this way.

-- Explanation of graph/analysis:
The experimental acceleration is the slope of the graph velocity vs. time. The experimental value of acceleration is 1.556 m/s^2. The theoretical acceleration is 1.591 m/s^2.

-- Conclusion:

In this experiment, we predicted the acceleration of a two-mass system. The experimental value of the acceleration is 1.556 m/s^2, and the theoretical values is 1.591 m/s^2. The error percent is 2.2%. This result shows that the experimental value is close to the theoretical value. Therefore, this experiment is successful.

19-Sep-2016: Lab 4 Modeling the fall of an object falling with air resistance -Part 2: Modeling the fall of an object including air resistance.

1. Title: Lab 4 Modeling the fall of an object falling with air resistance-Part 2: Modeling the fall of an     object including air resistance.
    Name: Qiwen Ye (Sherry)
    Lab partners names: Jae Yoo, Chandler
    Date: 19-Sep-2016

2. Purpose
The gold here is to apply the mathematical model we developed in part 1 to predict the terminal velocity of our various coffee filters

3. Introduction
This lab is the second part we did in last Monday, this time we used the data from last lab in order to get the terminal velocity. According to Part 1, we have already got the data about five times coffee filler. We used LogPro to analyze the data in order to get the graph about velocity and weight, and used Excel to model the fall of an object with air resistance.

4.Apparatus/Experiment procedure
In order to obtain the terminal velocity, we created four columns in: time, acceleration, the change of velocity, and velocity. First, we used the dates from part one in order to get five different velocity from one to five coffee filter. Assume 150 coffee is 134.2 gram, we can calculus the weight of coffee filter in order to get the graph about velocity and weight. After that, we got the formula similar to Fresistance=k*v^n, and got k and n. Finally, we used Excel to model the fall of an object with air resistance.

5. Data
Here is the data that we got from part 1, the velocity and weight for one to five coffee filters. (150 coffee = 0.1342kg).

6. Result

1)Here is the graph Velocity vs. Weight

This equation is similar to Fresistance=k*v^n. k: 0.000688  n: 1.366, then we got five different data about different coffee filter.

2)one coffee filter

\

3) two coffee filter

 4) three coffee filter

 5) four coffee filter

7. Analysis

Through those Excel data tables, we can see that the velocity of the coffee filter is increasing when the time is increasing. It means that the fall of an object falling with gravity and the velocity always increasing. Also, the mass of object will effect its velocity. 

8. Conclusion

In this lab, we learned how to model the fall of an object falling with air resistance. We acquired the terminal velocity for each trial using Excel.

14-Sep-2016: Lab 5 Trajectories

1. Title: Lab 5 Trajectories
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler
    Date: 14-Sep-2016

2. Purpose
In this lab, to use our understanding of projectile motion to predict the impact point of a ball on an inclined board.

3. Theory/Introduction
When an object be a projectile, it will have a trajectory. Trajectory is the path that a moving object follows through space as a function of time. When the ball has a motion in projectile, we can observe when and where the ball land and we can find the horizontal and vertical distance from start point to the end point.

4. Apparatus/Experimental Produce
We set up the apparatus as below shown. Then, we launched the ball from a readily identifiable and repeatable point near the middle of the inclined ramp because we did not want the ball hit the ground to far away. After that, we released the ball in the middle of the inclined ramp in order to know where the ball landed.

Part 1
We taped a piece of carbon paper on the ground around where the ball landed. Launched the ball five times from the same place as before and verify that the ball lands in virtually the same place. Measured the height of the bottom of the ball when it launched, and measured how far out from the lab table's edge it landed.

Part 2
We set up this part in the same way, except we placed a board such that it touched the end of the lab table and the floor. We put a heavy mass on the ground at the foot of the board and use duct tape to fix the mass in place.The board and the ground provided an angle of theta. We got the angle of theta by iPhone compact function. In this time, we released the ball five times on the board on the same place instead of the ground. So, we taped the carbon paper on the board where the ball landed.

5. Data
In Part 1, We measured that distances by hang a plumb bob in order to get the distance accurately.

In part 2, we got five distances that how far the ball landed on the board from the table's edge.The angle theta is 50 degree, measured by iPhone.

6. Calculated Result
we need to determine the value of d by given v0 and a, here is the expression of d and the distances x.

7. Explanation of graph/Analysis

Through the equation of distance d, we got the theoretical value of d is 66.3+/0.01. 

Compare the experimental values for d, we got the experimental value of d by the average of five distances. Then, used the theoretical and experimental values to get the error percent in this lab experience. The error percent is 6.06%.

8.Conclusion
Through this lab experience, we studied how to use projectile motion to find the impact point of in inclined place. When ball was released from the top to the inclined place, we can get the distance by given the initial velocity and the angle between horizontal to the incline place. We had uncertainty and error in the experiment, the error percent is 6.06. The reason of causing error are the air assistance and the friction between the ball and the Aluminum "V-channel".

12-Sep-2016: Lab 4 Modeling the fall of an object falling with air resistance

1.Title: Lab 4 Modeling the fall of an object falling with air resistance
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler, Jae Yoo
    Date: 12-Sep-2016

2. Purpose

This lab is divvied into two parts: part 1, we need to determine the relationship between air resistance force and speed. To observe the effect of air resistance on falling coffee filters and in determining how the terminal velocity of a falling object is affected by air resistance and mass, choose which of the two force models best represents the air resistance effect on the falling coffee filter. Part 2, the gold here is to apply the mathematical model we developed in part 1 to predict the terminal velocity of our various coffee filters. 

3. Introduction
We have an expectation the air resistance force on a particular objects depends on the objects's speed , its shape, and the material is is moving through. We modeled this expectation as a power law:

4. Part 1

-- Apparatus/Experimental Procedure
We used the Computer,Vernier Motion Detector, Vernier computer interface, 5 basket-style coffee filters in the lab. We went to building 13 - design technology to do our experiment and use video capture to record the coffee filter movement. At first, Professor Wolf dropped the coffee filter from the balcony inside the building. Then, we used laptop to take a video while the coffee filter is falling in order to record this movement. After that, we went back to the class and analyzed the data that we got. 

-- A list of Data
Here is the coffee filters movement the we got from the video is shown

-- A list of Graphs of Data
Here is the data about 1, 2, 3, 4, 5 and 6 coffee filters falling from the balcony:

-- Explanation/Analysis

In order to obtain the terminal velocity, we created four columns in: time, acceleration, the change of velocity, and velocity. First, we used the dates from part one in order to get five different velocity from one to five coffee filter. Assume 150 coffee is 134.2 gram, we can calculus the weight of coffee filter in order to get the graph about velocity and weight. After that, we got the formula similar to Fresistance=k*v^n, and got k and n. Finally, we used Excel to model the fall of an object with air resistance.

Here is the data that we got from part 1, the velocity and weight for one to five coffee filters. (150 coffee = 0.1342kg).

Here is the graph Velocity vs. Weight

This equation is similar to Fresistance=k*v^n. k: 0.000688  n: 1.366, then we got five different data about different coffee filter.

5. Part 2

-- Apparatus/Experimental Procedure

we used the data from part 1 in order to use Excel to model the fall of an object with air resistance. We stared with the following conditions:

-- A list of Data

One coffee filter:

Two coffee filter:

Three coffee filter:

Four coffee filter:

                         

Five coffee filter:

-- A list of calculated results
The percentage difference of the terminal velocities for one coffee filter is 12.55%. The percentage difference of the terminal velocities for two coffee filters was 6.04%. The percentage difference of the terminal velocities for three coffee filters was 9.09%. The percentage difference for four coffee filters was 17.34%. Lastly, the percentage difference for five coffee filters was 19.68%.

-- Explanation/Analysis
When falling, there are two forces acting on an object, the weigh mg and the air resistance. In the real world, because of the air resistance, an object do not fall in definitely with a constant acceleration. At the terminal velocity, the down force is equal to the upward force.

6. Conclusion
In this lab, we learned how to model the fall of an object falling with air resistance. All of the percentage differences are in the range of the uncertainly displayed in the k and n values, roughly 10% - 20%. In order to lower the human error, we need to do the experiment more time to get more data to analyze the results.