12-Sep-2016: Lab 3 Non-Constant Acceleration Problem/Activity

1. Title: Lab 3 Non-Constant Acceleration Problem/Activity
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler
    Date: 12-Sep-2016

2. Purpose
To used excel to solve problem by using the numerical approach because some physic problem are extremely difficult to solve analytically if it is even possible at all. 

3. Introduction
A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a fill and arrives on level ground. At that point a 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.

Find how far the elephant goes before coming to rest.

4. Apparatus/Experimental Procedure

To figure out how far the elephant goes before coming to rest we can use calculus to integrate the acceleration function into a velocity function and further integrate that to come up with a position function. Though the functions were able to be integrated, which is not always the case, we are now left with an incredibly hard function to solve. Using calculus we can solve for the time when the velocity of the elephant equals zero. We then plug that time into our position function to come up with x=248.7 m, and the time is 19.690575 second.

5. Data

Used the Excel spreadsheet and enter the following:

6. Calculated Results 
Here is the data that we entered into Excel spreadsheet by changing the time interval in order to  in order to find where was the elephant stopped.

1) the time interval in 1 second

2) the time interval in 0.1 second

3) the time interval in 0.05 second

Here is the data about changed the mass into 7000 kg, the fuel burn rate is 40 kg/s, and the thrust force is 13000 N.

7. Explanation/Analysis

Even though we changed the time interval from 1 second to 0.1 second and to 0.05 second, we still got the same distance that the elephant stopped and its stopped time is around 19 to 20 second, the distance that the elephant stopped is around 248.6 m. However, when we changed the fuel burn rate and the thrust, but keep the same mass, the distance of stopping is became 164 m and the time became 13 second. 

8. Conclusion

In this experimental, we learned how to use the Excel to solve problems numerically. The error percent of the time is 0.65%, the error percent of the distance is 0.01018%. For a complication problem, we can use the Excel by entering the equation that we can get more values in order to analysis the results easily. Also, this method is a great alternative to solve the difficult integration problems. 

07-Sep-2016: Lab 6 Propagated uncertainty in measurements

1. Title: Lab 6 Propagated uncertainty in measurements
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler
    Date: 7-Sep-2016

2. Purpose
In this lab, we studied the propagated uncertainty by measuring the Density of Metal Cylinders. To find density of different cylinders along with the propagated error.

3. Theory/Introduction
The reason we worried about propagated uncertainty was we didn't know what the accepted value was. The equation to find the total density and differential of uncertainty is

4. Apparatus/Experimental Procedure
We started by choosing two cylinder made of different meals which are Al and Tin. Measured the masses by using a scale, then measured the heights and radius using a measuring instrument called a fractional caliper. The fractional caliper allows us to take precise measurements that we calculated an accurate volume. The pictures show the cylinders and the measure machine.

5.Data

Here is the values that we got from the scale by measure the Tin and Al of height, diameter and mass.

6. Results/Graphs

We took the data from the table above and solved for the density of Tin and Al. After we solved the density, we got the propagated error of our calculated density.

The calculation of the density of Tin:

The calculation of the density of Al:

7. Analysis

Through the calculation, we calculated the propagated error in each of density measurement. We found that the experimental uncertainty of the density of the Tn is 11.32+/-0.62 g/cm^3; the experimental uncertainty of the density of the Tin is 2.79+/-0.23 g/cm^3. Compared to the theoretical value of the density, Al is  2.7 g/cm^3, and Tin is 7.31 g/cm^3. 

8. Conclusion

In this lab, we studies how to measure the density of the metal cylinders in order to do the propagated error calculation. We used the equation of calculating the propagated uncertainty that we learned in the class, and tried to determine the density of the metal cylinders. Through this lab, it made me more clearly to understand the concept of the propagated uncertainty. 

31-Aug-2016:Free Fall Lab - Determination of g (and learning a bit about Excel) And Some Statistics For Analyzing Data

    Title: Free Fall Lab - Determination of g (and learning a bit about Excel) And Some Statistics For                     Analyzing Data
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler
    Date: 31-Aug-2016

Part 1
-- Purpose:
In this lab, we will show that an object under the influence of gravity alone accelerates at a constant rate. We will also measure this acceleration and compare with the actual value of 9.8m/s^2. We will also learn techniques of Excel and analyze data.

-- Theory/Introduction:
Free fall is the motion of a freely falling body, it is determine by gravity. If a net force acts upon a body, then that force caused the body to accelerate. If the force is constant magnitude, then the acceleration of the body will also be constant. Use sturdy column to provide a constant distance for studying free fall. When the free fall body held at the top by an electromagnet, it released and is recorded by a spark-sensitive.

-- Apparatus:
Use sturdy column provide a long 1.5m falling distance for an accurate reading. Through the spark-generator to record the fall, and the marks made at intervals on the spark-sensitive tape attached to the column give us a permanent record of the fall. We can measure the distance in the paper in order to get time and velocity.

-- Data:
Use a Excel Function to enter data.

-- Result/Graph:

Mid-Interval Time vs. Mid-Interval Speed

Time vs. Distance

-- Analysis:
The velocity in the middle of the a time is the same as the average velocity for that time interval, because for constant acceleration, any speed for interval is equal to speed at the middle of the time.
We can get the acceleration due to gravity from Velocity vs. Time, the equation of acceleration is a=(Vf-Vi)/(t2-t1). Through the equation of position and time, we can do the second derivative to get the acceleration.

-- Conclusion:
This lab proved very helpful to understand free fall. I learned that when an object falls under the influence of gravity, its velocity increases at a regular pace and the average of this pace is known as g= 9.8. We were able to prove this within an error of    % which is still good considering the equipment. I also learned that use Excel to build up table and analyze data. Overall, this was a great learning experience and an awesome lab.


Part 2 - Errors and Uncertainty
-- Purpose:
In this lab, we used Microsoft Excel to study the standard deviation. Generally, We used the last class lab's values (from free fall) and use Excel functions to fill down the data in order to find the relationship between the average deviation of the mean and the standard deviation of the mean. Also, we learned how to use the Excel functions of sum, count, average, power, square and absolute cell reference in order to analyze our data.

-- Theory/Introduction:
There are two forms of error (not including human error), random error and systematic error. Random error is scatter in date that people can not "blame" on anything particular. Systematic error comes from assumptions that people made which are not true and consistent equipment problem. The average deviation of the mean is to take the average of the absolute value of all of the deviations from the mean. We write this as:

Standard deviation of the mean is a very popular way of describing the spread of data, assuming the spreads around the average value are "random". the  People make all of the deviations positive is to square them, average the squared deviations, then take the square root. We write this as:

-- Apparatus/Experimental Procedure

Use a Mac book and open a new file in Microsoft Excel to enter the last class lab's values from each groups. Then, followed the lab guild line to set up a worksheet. 

-- Data:

Here is the data that we used from last lab's values:

Here is the guild line that how to enter the data into Excel:

-- Results/Graphs:

Here is what data look like in Excel, we entered last lab's values from cell A2 to A11. Then, we entered the formula "=average(a2:a11)" in cell A12 to get the average. We entered the formula "=a2-$a$12" in cell B2. After that, highlight the cells Ba through B11, enter the Edit menu select the option Fill Down. We can get all the deviation of the mean in each g. 

The pictures below is with the outline of 880:

This one is without 880, the number of 880 is the lowest value in those data, therefore, we removed the lowest value to calculate in order to get a more precision results.

-- Explanation of graph/Analysis:

The first picture in the results/graph shows that the average of those g is 935.9 and standard deviation of the mean is 28.2717173, it means that the propagated uncertainty in this case is 935.9+/-28.2717173. Without of 880, the average is 942.11111; the standard deviation of the mean is 21.262382, and the propagated uncertainty is 942.111111+/-21.262382. Compared to both results, we found that the second results is more close to the values that we want. 

-- Conclusion:

Our average value plug the standard deviation of the mean is close to the accepted values of g. Air assistance and offset or zero setting error may cause difference between the average value of our measurements and those of the class. Air assistance is the random error; offset or zero setting error is the systematic errors. In this lab, we practice use Excel to analyze data, and Excel is very helpful to compare the different date in different conditions. 

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

1. Title: Finding a relationship between mass and period for an inertial balance
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler
    Date: 29-Aug-2016

2. Purpose
To use an inertial balance to measure mass, and find relationship between T and m for inertial pendulum equation that predicts well. We calibrate the balance using known masses, and use the balance to find the mass of unknown objects.

3. Theory/Introduction
The concept of inertia originated from Newton's First Law of Motion. Mass is measured by comparing the fore of attraction due to gravitation between earth and the object and that between earth and comparing masses.
Here is, Power-law type of equation:

T=A(m+Mtray)^n

If we take the natural logarithm of each side we can get,

ln T=n ln (m+Mtray) + ln A, which looks like y=mx+b

therefore,

y: ln T       slope: n        x: ln (m+Mtray)         y-intercept: ln A 

4. Apparatus/Experimental procedure
Use a C-clamp to set up the inertial balance on the tabletop. Put a thin piece of masking tape on the end of the inertial balance. Then, set up photogate and LabPro like those picture one.

In the picture two, we tape on the end of the tray in order to pass through photogate to measure period. Add 0 to 800 gram to the tray, 100 gram at a time, to measure period each time.

5. Data

Here is a date table for recording each period by 0 to 800 gram. According to power law type of equation, we have three unknown values - A, Mtray, and n. We use above data in order to make a plot of ln T vs. ln (m+Mtray).

6. Results/Graphs
This is a graph about ln T and ln (m+Mtray). We use "Linear Fit" to make our graph become a beautiful straight line.

Here is a process that we adjust our data:

225g  correlation   0.9994

240g  correlation   0.9995

250g  correlation   0.9995

270g  correlation   0.9995

295g  correlation   0.9994

240g

250g

270g

Also, through the above equation, we can find the mass of two other unknown objects by measuring their periods of oscillation.

the period of staple = 0.340s

the period of pencil case = 0.422s

Therefore, the mass of staple is 88.72g, and the mass of pencil case is 88.29g.

 7. Analysis
In that graph, we can get constants A and n:

ln A= -4.767 , A= e^-4.767       and        n= 0.6316

So, the equation is:

T = e^-4.767 (m+Mtray)^0.6316

We can see that ln T increasing when ln (m+Mtray) increasing. It means that with the mass of objects increasing, the period of the object will be increased.
By finding two unknown objects of masses, we can know that if we have object's periods, we will get a mass of objects.

8. Conclusion
In this lab, the relationship between mass and period was found using an inertial balance and a photo gate. We calculated the period(T) and compared it the measure period(T). The values also allowed for the mass of 3 "unknown" objects to be calculated and compared to the measured masses. When comparing the period and masses with the calculated and compared, the differences between them were less 10%. Before we even performed any calculations, we made an assumption that when mass increasing, the period will increasing. We had measured the period of different mass and notices that assumption is correct. Also, by the power law equation, we can get the mass of unknown object through its period.