Gravity acting on a load of mass exerts a force on the spring which causes a displacement of the lower end of the spring from its no-load position. Here we determine the no-load scale position and the stiffness constant of the spring. Both will be used in the subsequent parts of the experiment.

PROCEDURE

1.   Measure the ruler position of the bottom edge of the pan with only the pan (mass 50 g) hanging from the spring. Tip: Tape your measuring stick to the top of the stand to facilitate reading off your ruler measurements.

2.   Place additional 20 gm masses on the pan, one at a time, and read the pan positions directly off the ruler. Do not take the difference from the starting position. You will take a total of 10 measurements with different masses.

3.   Record your data into the Lab 2, Part 1 Excel sheet. As you enter the data, Excel will compute for you: the load, uncertainty of the load, and uncertainty of the mass. A plot of the load versus the pan position (in meters) will also be generated as you enter data.

Note: Be mindful of what units Excel and the report is asking you to record.

4.   Fit a straight line to the data in Excel. To do this:

a. Click on a data point on your graph. This should highlight all of your data points.

b. Right click, which will open a window, and select ‘Add Trendline.’ From the pop-up window, select ‘Linear’ as well as ‘Display Equation on Chart’ and ‘Display R-squared value.’ The value measures the correlation coefficient which represents the goodness of fit. It tells you how well your data is fitted by a straight line.  If your value is close to 1, this means your data is well-fit by a straight line.

5.   Ensure that your plot has descriptive axis titles. Also ensure that your axes are properly scaled so that your data fills the chart, including room to extrapolate the x-intercept. If your axes do not scale automatically, you can change the bound by right-clicking on the axis in question, select ‘Format Axes’ and then change the bounds appropriately. Copy your plot and data into your Lab 2 Report.

***Warning*** Your graph must have correct axis labels, and a plot title in order to receive full marks for it. You will be penalized if you do not include these in your graphs from this lab onwards.

6.   Determine the magnitude of the stiffness constant of the spring from the slope of the line and Equation (1). The intercept of the line with the position axis is the pan position when the displacement is zero (). Determine this position before going on to the next part of the experiment.

Answer the following questions in the Lab 2 report, Discussion section:

Question 2.

Determine the value of using the trend-line in the graph. Explain what is in this scenario, referring to Equation (1). Hint: What is another way that you can determine in the lab, aside from using your graph?

CHECKPOINT

(Show your  value to the TA to ensure that it is correct before moving on.)