09/21/2016 : Modeling Friction Forces

Lab #7: Modeling Friction Forces
Name:   Charles Xu,
Partner: Anthony, Michell
Date:     09/21/2016

Statement:
We did five experiments involving static friction or kinetic friction. We derive equations and collect data and capture the graphs to find coefficient friction

Theory:
This experiment we have five different sets of experiment. First, we want to find the coefficient of static friction between block and table using logger pro. Second, we want to find the coefficient of kinetic friction between the block and table using logger pro. Third, we want to find the minimum angle that will cause the block slices off the inclined. Fourth, we use logger pro motion sensor to measure the acceleration of the block when slices of an inclined at some specific angle. Fifth, we use logger pro motion sensor to measure the acceleration when hanging mass pull the block on the flat surface. 

Summary:
First:
We set up a pulley at the edge of the table. On the left side, we have a block on a flat surface; on the other side, we have a hanging mass on the pulley. We added 5g each time on the hanging mass until the block starts to move. This experiment allows us to find the static friction, which leads us to the coefficient of the static friction. We measure the weight of each block, and we added on block each time during four experiments. Then we plot the datas into logger pro, it provides us a linear fit graph. From the logger pro analysis, we have our coefficient of static friction as conclusion.

The graph after we plot points 

The setup for the first experiment

Second:
We connected the force sensor into logger pro. In this experiment, we pulled different numbers of blocks and recorded different forces. In order to make the experiment data more accurate, we calibrate with a 500-gram hanging mass. We use logger pro to analysis data and found the slope of each graph is coefficient of kinetic friction.

Set up for the second experiment

Time vs. Force graph

adjusted graph for second trail.

Third:
For the third experiment, we simply place the block on the horizontal surface. Then, slowly lift up the surface until the block starts to slice down. Next, measure the angle of the surface. Following, we use the angle we just measured and calculated the coefficient of static friction.

Setup for the third experiment

Calculation for coefficient of static friction

Four:

The fourth experiment is to set up a block on an inclined surface, then use the motion sensor to detect the acceleration of the block.

Acceleration graph and velocity graph 

calculation for coefficient of kinetic friction

Fifth:

The last experiment is use the coefficient of kinetic friction that found in part 4 to derive equation and calculate the acceleration.

calculation for acceleration

Conclusion:

The first two experiments, we measure variables according the basic friction formula to find the coefficient of friction. There might be human error when we adding weight for the first experiment. We might add more force to the system when we adding mass. For the second experiment, we had error when we were doing the second trial. We pulled more mass but recorded with less force, which didn't make sense. Later we redo the trail, and fortunately, we were able to fix the error. For the third and fourth experiment, we taped the phone on the surface, therefore, we could have more accurate measurement when we tilted the board. 

09/14/2016 : Trajectories

Lab #5: Trajectories
Name:   Charles Xu,
Partner: Anthony, Michell
Date:     09/14/2016

Statement:
It is an experiment to predict the impact point of a ball on an inclined board(second set of the experiment) by collecting data and data analysis from first set of the experiment .

Theory:
We want to find the impact point that a ball roll off from an inclined board. We used the understanding of projectile motion to collect datas we needed. We use ∆x=VoxT and ∆y=Voy+1/2aT^2 to find the initial velocity and time interval. Then we calculated the impact point on another inclined board.

Summary:
First part of the experiment, we set up the equipment with an inclined board, ring stand on the table. Then we predicted the area that the steel ball will land when it rolls off from the inclined. We taped a piece of paper on the ground with a piece of carbon paper on it. We let the steel ball rolled off the inclined fives times and measure the distance of X-direction (Distance from impact point to the bottom of the table), and distance of Y-direction (Distance from edge of the table to the ground). We measured with uncertainty and do the calculation to find the initial velocity. 

Second part of the experiment, we set up the equipment with another inclined board at the edge of the table. Therefore, when the ball rolls off the inclined board on the table, it will land on the board at the bottom. We first used data we collected from part one to calculate the landing spot on the board. Then we do the experiment five times. The experiment result support our calculation very well.

Setup for the first part of the experiment

Setup for the second part of the experiment

Setup for the second inclined board

Five impact points we recorded for part two

Calculation of both experiment

Conclusion:

As we measured, five impact points landed on 0.44m +- 0.005m from the edge of the board. which is equivalent to our calculation result. This is a successful experiment. We decreased the error by testing the experiment serval times and we tape our paper on the ground nicely to decrease human error. For measurement, we usually measure more times with different person. This will decrease the reading error, which might affect the experiment result. 

09/09/2016 : Propagated Uncertainty in Measurements

Lab #6: Propagated Uncertainty in Measurements
Name:   Charles Xu,
Partner: Anthony, Michell
Date:     09/09/2016

Statement:

This is a experiment to measure dimensions of different cylinder metal using vernier calipers and calculating the destiny of the metal.

Theory:

Using the vernier calipers to measure the diameter and height of the metal and weight the metal. Then calculate the density using m/v.

Statement:

Vernier calipers have two sets of scale. The one on the top can measure the length precise to 0.1 cm. The one on the bottom has 9 lines. To be perfect measured, only one line can fit perfect with the line on the top, then the reading will be you value on the hundredth. Using this vernier caliper we can have more precise data.

Measuring with Vernier Caliper

Measuring with Vernier Caliper

 Measuring with Vernier Caliper

Measuring with Vernier Caliper

Measuring with Vernier Caliper

Then we use the datas we collected to calculate the density of the metals.

Calculation for density

Conclusion:

This experiment shows how to use vernier caliper and explain how it works. It is a very helpful tool to measure the dimensions of small objects. It provides more accurate datas for later calculation and decreases the error.

09/12/2016 : Modeling the fall of an object falling with air resistance

Lab #4: Modeling the fall of an object falling with air resistance,
Name:   Charles Xu,
Partner: Anthony, Michell
Date:     09/12/2016

Statement:
It is a experiment to determine the relationship between air resistance force and speed. 

Theory:
We use camera from the laptop to capture coffee filters falling from the balcony. Then using logger pro to record terminal velocities for each one by fitting the linear portion for he position vs. time graph. Then use excel to analysis datas and calculate.

Summary:
We capture videos for 1, 2, 3, 4, 5, and 6 coffee filters falling from the balcony. We use logger pro to set the meter stick on the black sheet on the back as 1m. Then get the position of each frame. We use logger pro to find the k and n value of the formula F=kv^n. Then we input the data we collect into excel, such as change in time, mass, k, and n. Each frame is 0.02 s, We calculate change in time (by multiplying acceleration by time. --acceleration will change), velocity(by adding change in velocity and initial velocity), acceleration[F=ma, F=kv^n --> a= g- (kv^n/m)], change in distance(velocity multiply by time), distance(initial distance + change in distance). Then we use fill down to complete the sheet. 

Excel for calculation

Conclusion:

This is another experiment involves with calculating using excel. As before, it is a very useful tool for repeatedly calculation. This method will provide less error once you have the correct setup. We using logger pro to measure the displacement of free falling on the video which make the data more precise. 

09/12/2016 : Non-Constant Acceleration Problem/Activity

Lab #3: Non-Constant Acceleration Problem/Activity
Name:   Charles Xu,
Partner: Anthony, Michell
Date:     09/12/2016

Statement:
On the lab book, it provides a problem to solve. This experiment is to find the method to solve non-acceleration problem.

Theory:
The question will provide a function related to non-acceleration. we derive it into an acceleration function. Then we can take the derivative of the function to get velocity function. Then use excel to do the calculation.

Summary:
We input the given values into excel, and calculate the time, acceleration(F=ma), average acceleration(average from sum of all acceleration) , change in velocity(average acceleration * time), velocity(initial velocity + average acceleration), average velocity(first velocity + second velocity / 2), ∆x(average velocity * time), and x(initial distance + ∆x). Then we change the time to a smaller number, therefore, we can have a more precise result.

Excel with t=1s

Excel with t = 0.1s

Conclusion:

This excel method is very useful. We set up a model and we can vary the value of each variable. Excel will do the calculation for us. It saves a lot of time. Also, we can change the changing factor to a smaller number when we want to find more precise result. 

09/07/2016 : Free Fall Lab - Determination of g and some statistic analyzing data

Lab #2: Free Fall Lab - Determination of g and some statistic analyzing data
Name:   Charles Xu,
Partner: Anthony
Date:     09/07/2016

Statment:
It was a experiment that use excel and logger pro to find the g (acceleration) for free falling body.

Theory:
Using the electromagnet to spark dots on the paper tape, then use excel to find the velocity vs time graph. The slope of the graph is the g value we want to find.

Summary:
We use electromagnet and the sparker thing to record dots on a piece of paper tape during free falling. Then we measure the distance between the dots and input into excel. We input time interval as 1/60 s. Then we use excel to calculate ∆x, mid interval time (the time for the middle of each 1/60 interval) and mid internal speed (∆x/mid-intercal time) for us. Then we select the data columns of Mid-interval time and Mid-interval speed to create a chart. Also, we use data columns of Time and distance to create a time vs distance graph.

The set up of electromagnet

Measuring the distance between dots using meter stick. 

The excel with data we collected and the graphs we plot.

Then we use datas from other groups  to calculate the uncertainty of the experiment by using excel again.

First, we calculate the average value of 8 groups. Then, we deviated from the mean and square the deviation. Next, we took the average of 8 numbers we have from last step and square root it to get the uncertainty value.

Datas of 8 groups 

The excel for finding uncertainty

Conclusion

We find the number of 955 for the result, which is within the range of +- 25 uncertainty. I think it is a successful experiment. Some groups have more precise result than us. I think there is uncertainty and human error during the measurement. There are many little dots on the paper tape, we might measure the wrong dot or not precise enough that cause the errors. Also, we didn't consider air residence in this experiment. it could be a factor of error too.

08/30/2016 : Inertial Pendulum - relationship between mass and period

Lab #1: Inertial Pendulum - Relationship between Mass and Period,
Name:   Charles Xu,
Partner: Anthony,
Date:     08/30/2016

Statement:
It was a laboratory that searching the relationship between mass and period using inertial balance and LabPro.

Theory:
Find the equation that relates time and mass by testing unknown mass of the inertial balance. Then, find a equation in a form of y = mx+b to express the relationship between time and mass. Do two experiments and calculations to find unknown mass.  Compare the final answer with the actual reading on the scale to prove your experimen.

Summary:
We used the Logger Pro to measure the different frequency about the movement of the inertial balance when there was different weight on it. We put 100 grams of mass on the inertial balance, and applied same amount of force on the inertial balance to make it start moving in a periodic movement. At the same time, we use Logger Pro measure the period and time. We then add 100 grams more on the inertial balance each time, and did the experiment rapidly. We collected data into a table and calculated the values of period per second for each weight. Then we turned the formula T = A(m + Mtray)^n into y=mx+b form, which is let = n*ln(m+Mtray) + lnA. At this moment, we had three unknown variables: A, n, Mtray. Then, we input data we recorded into Logger Pro and created three sets of data: m+Mtray, lnT, and ln(m+Mtray). Then we plot lnT vs. ln(m+Mtary) graph. After we adjusted the value of mTray that makes the correlation coefficient is close to one. According to the graph, we find the value of lnA, which is the y intercept; the value of n is the slope of the graph. For the second part of the lab, we use two different objects, golf ball and tennis ball. We measure the period of the inertial balance and time. Through calculation, we were able to find the mass of the golf ball and tennis ball.

Data table 

lnT vs. ln(m+Mtray) graph when Mtray= 220

lnT vs. ln(m+Mtray) graph when Mtray= 270

Experiment 1: measuring weight of golf ball

Experiment 2: measuring weight of tennis ball

Calculation to find the mass of golf ball and tennis ball

Conclusion:

This experiment successfully find the relationship between time and mass using LoggerPro. We found out that the relationship between time and mass is liner. It is in y=mx+b form, which is lnT = nln(m+Mtray) +lnA. We were able to find out the three unknown variables using testing pie method. We were also able to test our theory by measuring two unknown-mass objects and calculated the mass with error. The result from calculation is a little different than the exact reading on the scale. It might because when we released the inertial balance with force while golf ball or tennis ball is not static on the trail. It changed the force acting on the inertial balance and might change the data that recorded. Also, we did not include air resistance, which might cause error, too.