Rotational Equilibrium: 
      A Question of Balance

Student Worksheet:

 Materials

•	Student Resource Guide and Student Worksheet
•	1/4 x 1/4 by 36-inch balsa wood stick, one per mobile.
•	Pennies or similar objects of uniform weight, eight per mobile.
•	Sewing thread or light string.
•	Material on which to mount the pennies: e.g. construction paper, cardboard or poster board.
•	Marking pen.
•	Cellophane tape or glue.
•	Scissors.
•	Ruler marked in millimeters and centimeters or a meter stick.

 Step One: Prepare the materials

The horizontal members of the mobile are made from ¼ x ¼ inch balsawood.  Cut three pieces thirty-one centimeters (or 310 mm) long.  For convenience, mark the center point of each horizontal member and, beginning in the center and going in each direction, mark each centimeter and half centimeter along the length of the horizontal member. The spacing between weights will in all cases be 30 centimeters or 300 millimeters.

Make each weight from a poster board or cardboard cutout.  Tape or glue a single penny to each cutout.  Use only pennies were that were minted after 1983 in order to ensure uniform weights of the pennies.  Use lightweight string or thread to suspend the cutouts from the horizontal members.

 Step Two: Team Predictions

Predict the total force, F, and the position of the balance points.

Before building the mobile, estimate the dimensions X1, Y1, X2, Y2, X3 and Y3 and estimate the forces, F1, F2 or F3 in the main supporting strings in terms of “W.”  Ignore the weight of the horizontal members and of the string or thread in making these preliminary estimates.  Draw free-body diagrams for each level and show all work.  Enter your estimates in the table.  The solutions for "X" and "Y" involve a set of two simultaneous equations.  Check your answers for each level of the mobile by plotting on the graph paper provided the linear function defined by each equation.  The solution is given by the coordinates of the intersection of the two lines that represent the two equations.

      Rotational Equilibrium: 
      A Question of Balance

Student Worksheet: (continued)

 Step Three: Build Your Mobile

Build the mobile and adjust the points of suspension until the mobile is balanced.  

 Step Four: Record Your Actual Results

Measure and record in the table the actual values of dimensions X1, Y1, X2, Y2, X3 and Y3.

 Step Five: Analyze Your Results.

Compare the actual to the predicted values of dimensions X1, Y1, X2, Y2, X3 and Y3.  Calculate the differences, expressed in percentages of the predicted values, between the predicted and the actual measured dimensions X1, Y1, X2, Y2, X3 and Y3.  Show all work.  Explain the differences.  Would you expect your predicted and actual lengths to be closer or father apart if the weights were heavier?  Test your answer by adding a second penny to each of the cutouts and repeating your measurements.  Record your new results in the table. 

     
           
      Rotational Equilibrium: 
      A Question of Balance

Student Worksheet: (continued)

 Data and Results

Table - Results				
	Level 1	Level 2	Level 3	
Predicted X
				
Predicted Y
				
Predicted force, F
				
Single penny results				
Measured X
				
Measured Y
				
Difference X, %
				
Difference Y, %
				
Two-penny results				
Measured X
				
Measured Y
				
Difference X, %
				
Difference Y, %

Record all dimensions to the nearest whole millimeter.

      Rotational Equilibrium: 
      A Question of Balance

Student Worksheet: (continued)

 Graph of Equations for Level 1

          

      Rotational Equilibrium: 
      A Question of Balance

Student Worksheet: (continued)

 Graph of Equations for Level 2

      Rotational Equilibrium: 
      A Question of Balance

Student Worksheet: (continued)

 Graph of Equations for Level 3