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EXPT NO: 04. LAW OF PARALLELOGRAM OF VECTORS

Aim: To find the weight of a given body using parallelogram of vectors.

Apparatus : A wooden board, two pulleys with clamp ,pan , hanger, slotted weights , string,white plane paper ,drawing pins, a plane mirror,  meter scale unknown weights etc

Diagram :

Formulae:                                       

                

Where                          R         = Unknown weight

                                    P & Q             =Known Weights

                                    q          = Angle between the P & Q

Procedure:

                  Fix the wooden board in a vertical position. Clamp the pulleys on the wooden board . fix a white plane paper on the board with the help of a drawing pins.

                  Pass a long string over the pulleys and tie a hanger at each end. Tie another string at the center of the first string and attach a unknown weight to its free end.

                  Add suitable weights in the hanger so that the system is in equilibrium and the common point 'O' is near the lower position of the paper.

                  Hold the plane mirror on the paper behind the string and mark two points on the paper at the ends of the mirror such that the string and its image in the plane mirror coincide. The straight line joining the two points gives the line of action of the corresponding force. Determine the lines of action of all the three forces in this manner.

                  Remove the paper from the board. Produce the lines of action to meet at a common point 'O'.

                  Take a suitable scale so that parallelogram should be of large size. Mark the points 'A' and 'B' such that the length OA and OB represent the magnitudes of the forces  and  respectively.

                  Complete the parallelogram OACB. Draw the diagonal OC. Measure the length OC and determine the magnitude of resultant  using the scale chosen.

                  Measure the angle AOB (= q) between the forces  and. Calculate the magnitude of resultant  using the formula.

                  Take one more reading by changing the values of forces  and .

 Observations:

S.No.	P gm-wt.	Q gm-wt	Angle q	Unknown weight in gm -wt
				By Geometry	By Calculation
01
02

Calculations :

  

Result :     The unknown weight,     by geometry  =………………..gmwt

                                                            by calculation ==………………..gmwt

 Precautions:

                  The hangers and the string should not touch the wooden board.

                  Friction at the pulleys should be minimum.

                  The common point “O” should be near the lower portion of the paper.

                  A pencil with sharp tip should be used for drawing lines.

J K L