Analysis and Conclusions:  By subtracting the height of the hook of the hanging mass above the lab table from the height of the bar above the lab table, we can calculate the vertical displacement of the suspended mass. By dividing the distance between the sliding clamps in half, we can calculate the horizontal displacement of the suspended hooked mass. These measurements will give us the tangent of the angle between the bar and the spring scales.

 

Once we know the tangent value, we can calculate the angle and any other required trig values.

 

Examination of the hanging mass reveals the following freebody diagram centered on the hook at the top of the suspended mass.

 

 

Since the position of the mass was adjusted until the tensions on the two spring scales were identical, the horizontal components, T cos(q), cancel each other. The equation for vertical equilibrium based on our freebody diagram is shown below.

 

 

In our experiment, the tension, T, was the dependent variable while the angle, q, was the independent variable. The final equation shown above represents the theoretical equation for our line.

 

Open the EXCEL file 1-staticequilibrium.xls and enter your data recorded in your data table.