Lab Report M-2

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Community College of Philadelphia *

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Apr 3, 2024

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Community College of Philadelphia Philadelphia, Pennsylvania Experiment Number: M-2 Title: Force Vectors Written by: Physics 140, Section 003 Lab Instructor: Professor Indu Das Date: February 04, 2022

Experiment M-2 2 Purpose The purpose of this experiment is to determine the vector resultant of several concurrent, coplanar forces and to confirm that this resultant accurately predicts the combined effect of these forces. Procedure * Part I: Force Board 1. Mark the three spring balances F 1 , F 2 , and F 3 in counterclockwise order. Place each balance flat on the table, apply a small tension force, slowly reduce the force to zero, and take a zero reading. Mark the zero reading on the piece of masking tape attached to the balance and use that reading to correct all later readings before entering them on the data sheet. 2. Place the three balances on a piece of plain 8.5" x 11" paper on the force board, and attach the chains into the slots that meet the following 3 conditions: (1) The angle between F 1 and F 2 should be between 30  and 80  for trial I. (2) At least one force should be over three-quarters of the full-scale reading (over 15 N). (3) Each of the other two forces should be over one-fourth of the full-scale reading (over 5 N). 3. Adjust the paper under the balances until the center of the paper is beneath the ring and until the long dimension of the paper is parallel to F 1 . Lift the ring a very small distance from the table to slightly increase the tension force in each balance. Gently lower the ring and release it. 4. Near each balance and near the edge of the paper, write the reading of the balance and show the correction for the zero reading. Draw a dot on the paper directly below the center of the ring. Draw thin dim pencil lines along the long edges of the balances. Write the trial number on the sheet of paper and remove the paper from the force board. Draw thin dim pencil lines from the center dot parallel to each pair of lines for each balance. 5. Draw the three vectors in dark wider lines over the dim lines. 6. Determine graphically the magnitude and direction of the resultant R 12 of forces F 1 and F 2 by using the parallelogram method. Measure R 12 with a cm scale and apply the scale factor to calculate its magnitude in newtons. Use a protractor and measure the

Experiment M-2 3 angles  12 ,  13 , and  1R between F 1 and each of the other vectors. Label each vector near its arrowhead with its letter symbol and magnitude. Show with an arc where each angle is measured. Label each angle with its letter symbol and its magnitude. 7. Record the various force magnitudes and angle for trial 1. The percent difference in magnitude and the percent error in angle will be calculated. 8. Repeat steps 2 through 7 for different magnitudes and angles of the forces. Make the angle  12 between 100 and 150  for trial II. This angle should be less than 90  for at least one trial and more than 90  for at least one trial. In all three trials at least one force should be greater than 15 N and the other two forces should each be greater than 5 N. * Part II: Force Table 1. Set one pulley at the zero-degree position and place 50g on its weight holder for a total mass of 55g. Set up a second pulley at 75  and place a mass of 200g on its weight holder. Set up a third pulley at 210  and add 150g to its weight holder. All angles are measured counterclockwise from +x. 2. Set up the fourth pulley and a weight hanger to experimentally keep the ring in equilibrium at the center of the force table. Make small adjustments in the weight and angle for the fourth force so as to reach the equilibrium condition as closely as possible. The ring should remain in the center. It may be appropriate to make slight adjustments on the three original pulleys so that the threads are at the correct angles. It may be appropriate to slide some of the threads along the ring to help make them head toward the center of the ring and the center of the disk. 3. Record the four masses in grams and in kilograms. 4. Calculate each of the four forces in newtons by using F = w = mg. 5. Calculate the magnitude and angle of the resultant R 123 of F 1 , F 2 , and F 3 by using the method of rectangular components and trigonometry. 6. Calculate the percent difference in magnitude and the percent error in angle.

Experiment M-2 4 Data Sheets * Part I: Force Board Trial F 1 F 2  12 Calculated Resultant Measured Equilibrant Percent Difference in Magnitude Percent Error in Angle R 12  1R F 3  13 N N degrees N degrees N degrees % % 1 11.5 8 64 16.6 25.6 17 154 2.38 -0.22 2 10 8 88 13 37.8 14 147 7.4 2.67 3 10 12 52 19.8 28.6 22.5 155 12.8 2 * Part II: Force Table Masses: (Include the 5 g mass of the hanger in addition to the mass on each hanger.) m 1 = 55 grams = 0.055 kg m 2 = 205 grams = 0.205 kg m 3 = 155 grams = 0.155 kg m 4 = N/A Forces: (Weights of the masses) F 1 = 0.539 N F 2 = 2 N F 3 = 1.52 N F 4 = 1.19 N Angles: (Measured counter-clockwise from +x)  1 = 0   2 = 75   3 = 210   4 = 102.6 

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