Experiment 5

FORCES & VECTORS

ANALYSIS

Exercise A:

 
1.  GRAPHICAL METHOD: On a plain sheet of graph paper, pick an origin in the middle of the sheet and lay out the +x-axis. Draw FORCE A to scale with its tail at the origin, along the +x-axis (0°). You should choose a convenient scale such as 1 N = 2 inches.

2.  Next, draw FORCE B to the same scale with its tail at the origin. Use a protractor to reproduce its angle from the +x-axis. Then draw FORCE B again, without changing its orientation, with its tail at the tip of FORCE A.

3.  Draw a vector from the origin to the tip of FORCE B--this is the RESULTANT. It has the same magnitude as and is oriented 180° opposite to the EQUILIBRANT. Carefully measure the magnitude and the angle of the RESULTANT and record them in cells B15:B16 on the Worksheet. Enter the same magnitude for the EQUILIBRANT in cell C15. Make sure you convert from the inches scale back to newtons.

4.  If the RESULTANT’s angle is less than 180°, add 180° to it and enter the result as the EQUILIBRANT DIRECTION in cell C16. If the angle is greater than 180°, subtract 180° from it and enter the result in cell C16.

5.  Compare the experimental (D10:D11) and graphical (C15:C16) values of both the magnitude and the direction of the EQUILIBRANT. Find the percentage difference between the two values in each case, and enter them in cells D15 and D16.

6.  COMPONENT METHOD: Compute the x- and y-components of FORCE A, FORCE B, and the EQUILIBRANT (cells B10:D11), and record them in cells B20:D21 on the Worksheet. BE CAREFUL about the algebraic signs of the components.

7.  Add up the components of FORCE A and FORCE B (separately in the x and y directions) to obtain the x-component and the y-component of the RESULTANT, and enter them in cells E20:E21.

8.  Copy the magnitude of the EQUILIBRANT from cell D10 to cell D23.

9.  From the components of the RESULTANT, calculate the MAGNITUDE and enter its value in cell E23.

10.  Compare the MAGNITUDE that you calculated (E23) with the MAGNITUDE of the EQUILIBRANT (D23). Find the percentage error and enter it into cell E24.
 
Exercise B:
1.  GRAPHICAL METHOD: On another plain sheet of graph paper, pick an origin in the middle of the sheet and lay out the +x-axis. Draw FORCE A to scale with its tail at the origin, along the +x-axis (0°). You should choose a convenient scale such as 1 N = 2 inches.

2.  Next, draw FORCE B to the same scale with its tail at the origin. Use a protractor to reproduce its angle from the +x-axis. Then draw FORCE B again, without changing its orientation, with its tail at the tip of FORCE A. Repeat the same procedure for FORCE C, putting its tail at the tip of FORCE B.

3.  Draw a vector from the origin to the tip of FORCE C--this is the RESULTANT. It has the same magnitude and is oriented 180° opposite to the EQUILIBRANT. Carefully measure the magnitude and the angle of the RESULTANT and record them in cells B34:B35. Enter the same magnitude for the EQUILIBRANT in cell C34. Make sure you convert from the inches scale back to newtons.

4.  If the RESULTANT’s angle is less than 180°, add 180° to it and enter the result as the EQUILIBRANT DIRECTION in cell C35. If the angle is greater than 180°, subtract 180° from it and enter the result in cell C35.

5.  Compare the experimental (E29:E30) and graphical (C34:C35) values of both the magnitude and the direction of the EQUILIBRANT. Find the percentage difference between the two values in each case, and enter them in cells D34 and D35.

6.  COMPONENT METHOD: Compute the x- and y-components of FORCE A, FORCE B, FORCE C, and the EQUILIBRANT, and record them in cells B39:E40 on the Worksheet. BE CAREFUL about the algebraic signs of the components.

7.  Add up the components of the three individual forces (separately in the x and y directions) to obtain the x-component and the y-component of the RESULTANT, and enter them in cells E45:E46.

8.  Copy the magnitude of the EQUILIBRANT from cell E29 to cell D48.

9.  From the components of the RESULTANT, calculate its MAGNITUDE and enter the value in cell E48.

10.  Compare the MAGNITUDE that you calculated (E48) with the MAGNITUDE of the EQUILIBRANT (D48). Find the percentage error and enter it into cell E49.

11.  Hand in the Worksheet and the two vector plots with your lab report.