Non-constant acceleration problem/ Activity

Non-constant acceleration problem/ Activity

Purpose: Use Excel to solve the non-constant acceleration problem numerically and compare the result to the one done by analytic way.

Activity:
Analytic integration:
1. Set up a function for acceleration based on the problem.

2. integrate the acceleration from 0 to t to 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).

4.solve v(t) to find the time at which v=0.

5.use the time derived in 4 and plug that into expression for x(t) to find how far the elephant goes.

Numerical integration:

1.set up the column of t, a, a_avg, delta v, v, delta x, and x with A2=0, E2=25, G2=0.

2.Input the formula =A2+0.1 into cell A3.

3.Input the formula =-400/(325-A2) into cell B2.

4.Input the formula =(B3+B2)/(A3-A2) into cell C3.

5.Input the formula =C3*(A3-A2) into cell D3.

6.Input the formula =25+D3 into cell E3.

7.Input the formula =

8.Input the formula =G2+F3 into cell G3.

9.Fill down the contents of Row 3 to the rest of the spreadsheet and determine when and where the elephant comes to rest. 

The distance is close to 248.69.
10.Change the time interval to 0.05s instead of 0.1s and see if it makes a difference.

The distance is close to 248.69.
11.Change the time interval to 1s instead of 0.1s and see if it makes a difference.

The distance is close to 248.67.

Conclusion:
1.Both analytic and numerical integration give us the similar result.
2.In the numerical integration, the smaller time interval, the more accurate result we will get.

Free Fall Lab

Free Fall Lab--determination of g

Purpose: 
To examine the validity of the statement: In the absence of all other external forces expect gravit, a falling body will accelerate at 9.8 m/s^2.

Experiment:
1.set up the apparatus as shown below
2.Turn the dial hooked up to the electromagnet up a bit
3.Hang the wooden cylinder with the metal ring around it on the electromagnet
4.Turn on the power on the sparker thing
5.Hold down the spark button on the sparker box.
6.Turn the electromagnet off so that the thing falls
7.Turn off power to the sparker thing
8.Tear off the paper strip and line up a meter stick to record the position of each dot

Data collection and analysis:

1.In Excel, put in the column of time, distance, delta x, Mid-interval time, and Mid-interval speed.

2.Enter the data collected in the experiment.

3.In cell C2 enter =(B3-B2) to get delta x and drag down the column

4.In cell D2 enter =A2+1/120 to get Mid-interval time and drag down the column

5.In cell E2 enter =C2/(1/60) to get Mid-interval speed and drag down the column

Graphing

1.Select columns D and E. Choose an XY (Scatter) graph with the points not connected.

2.Add Trend line, choose linear. Choose "Display equation on chart" and display R-Squared value on chart.

3.Select columns A and B. Follow the same steps above expect choosing polynomial fit of order 2.

Analysis of Errors and Uncertainty:

1..In Excel, put in the column of g, deviation, abs deviation, and deviation^2.

2.Collect and enter the value of g from nine different groups in column B

3.In cell B11 enter =average(B2:B10) to get the average value of g

4.In cell C2 enter =B2-$B$11 to get deviation and drag down the column.
5.In cell D2 enter =ABS(C2) to get abs deviation and drag down the column.

6.In cell E2 enter =C2^2 to get deviation^2  and drag down the column.

Summary: 

Through this lab we can examine the value of gravitational acceleration without any other external forces expect gravity, and we learn how to use Excel to help us organize the data and calculate the functions in a short time. Also, we learn how to test the errors and uncertainty of the data based on the deviation.

Lab:Finding a Relationship Between Mass and Period for an Inertial Balanc

Lab:Finding a Relationship Between Mass and Period for an Inertial Balance

Purpose: To find a relationship between mass and period for an inertial balance
Data collection

        We set up the apparatus as the pictures show. Record the period with the mass on the tray, which range from 0g to 800g, by adding 100g each time. Also, record the period with the wood and wallet on the tray.

Analysis

        We put our data in excel and get the calculated column lnT and ln(m+Mtray). By adjusting the parameter of Mtray,we get a linear equation from these two column.

Calculation
        By comparing the equation with the lnT=n ln(m+Mtray)+lnA, we can get n, A and Mtray. Therefore, when we plug in the period of the unknown mass, we can calculate the mass of  the object.

Summary

      By collecting the period of a set of known mass, we can find the relationship between mass and period for an inertial balance, and use the equation to determine the mass of a object using the period for an inertial balance.