verification of parallelogram laws - practical

• Law of parallelogram of forces


  If two forces act on a body or if two forces act on a point, the resultant of the two forces can be found by completing a parallelogram with the two forces as adjacent sides and measuring the diagonal of the parallelogram
• Verifying the law of parallelogram of forces

  1. Fix a vertical wooden board with two pulleys

  2. Tie three known weights (m1, m2, m3) to strings that go over the pulleys

  3. Observe the equilibrium of the system

  4. Draw lines proportional to the tensions (t1, t2, t3)

  5. Complete the parallelogram

  6. Measure the diagonal of the parallelogram

  7. Verify that the force indicated by the diagonal is equal to the middle weight (m3g)
• Determining an unknown mass using the law of parallelogram of forces

  1. Replace the middle weight (m3) with an unknown mass (m3')

  2. Repeat the process of drawing the parallelogram and measuring the diagonal

  3. The force indicated by the diagonal will be equal to the unknown mass (m3'g)
• Assumptions for the experiment

  • The strings are light and have negligible weight
  • The pulleys are smooth and frictionless
• Possible errors in the experiment
• Conditions for verifying the law of parallelogram of forces
• Purpose of using a set square or mirror strip
• Purpose of the three-beam balance
• Importance of the step to pull and release the middle weight
• Experiment to verify the law of parallelogram of forces

  1. Remove load w2

  2. Place given body not w2 w3 on the middle one

  3. Place given body the unknown load

  4. Repeat the experiment

  5. Use same or different scale
• If middle weight w3 is very small, then w1 and w2 have to be changed as well
• Construct the parallelogram


  1. Draw the diagonal OC'

  2. Measure the length of the diagonal
• Reduce the mass of the given body in accordance with the theory
• The apparatus required includes: drawing board with pulleys, white paper, meter ruler, threads, known weights, unknown weight, mirror or set square, pencil
• Set up the experiment

  1. Fix the drawing board vertically

  2. Hang the strings and plates without touching the board

  3. Assume frictionless pulleys
• Adding weights to the system creates an equilibrium where the tension in the strings equals the weight
• To ensure frictionless pulleys, displace the weights and see if the system returns to equilibrium
• Draw the parallelogram


  1. Mark the lines for T1 and T2

  2. Draw the parallelogram proportional to the weights

  3. Measure the diagonal length
• The length of the diagonal multiplied by the scale should equal the unknown weight
• Errors can occur due to pulley friction and weight of plates/chains, leading to a slightly different result from the actual unknown weight
• 5 grams


  1 centimeter
• 16.5 centimeters multiplied by 5 is 82.5 grams
• Actual value used was 90 grams, but the calculated value is 82.5 grams due to experimental errors
• Reasons for the difference between actual and calculated values


  • Pulleys are not 100% frictionless
  • Weight of plates and chains was neglected
  • String may not be completely inextensible and light
• Despite the errors, the calculated value of 82.5 grams is close to the actual value of 90 grams, verifying the parallelogram law
• Finding the mass of an unknown object using the parallelogram of forces

  1. Set up with known weights on two sides

  2. Adjust weights to get a suitable parallelogram size

  3. Draw the parallelogram and measure the diagonal

  4. Use the scale to calculate the mass of the unknown object
• The actual mass of the unknown object may differ slightly from the calculated value due to the same experimental errors
• The scale used was 1 cm = 2 grams
• The length of the diagonal was measured as 20 cm, which corresponds to a mass of 40 grams
• Items needed for the experiment

  • Half-meter ruler
  • Thin mirror strip or set square
  • Method to test for negligible pulley friction (pull weight and check if it returns to original position)
• Steps to verify the parallelogram of forces

  1. Trace the strings on the board

  2. Draw the parallelogram with the traced lines

  3. Draw the diagonal that goes through the intersection point

  4. Measure the diagonal length and multiply by the scale
• Light strings


  Ensure the tension is the same along the string
• If the diagonal is not exactly vertical, it is likely due to friction in the pulleys
• If the scale pans are not light, their weight should be added to the weights or they should be removed and the weights connected directly
• Finding the weight of the stone using the parallelogram of forces


  1. Complete the parallelogram using set square and ruler or compass

  2. Draw the diagonal and measure its length

  3. Use the scale to calculate the weight of the stone
• The scale used was 1 cm = 2 grams, and the diagonal length was measured as 30 cm, corresponding to a weight of 60 grams