VERIFICATION OF PARALLELOGRAM LAW OF FORCES

OBJECTIVE

To verify the parallelogram law of forces with the help of Gravesand’s apparatus

Apparatus Required

Gravesand’s apparatus, paper sheet, weight, thread, pans, set square, pencil, drawing pin, etc.

Theory

“Parallelogram law of forces” states that if a particle is acted by the two forces represented in magnitude and direction by the two sides of a parallelogram drawn from a point then the resultant is completely represented by the diagonal passing through the same point.

PROCEDURE

Refer to Fig. 1.1

• 1. Fix the paper sheet with a drawing pin on the board set in a vertical plane so that it should be parallel to the edge of the board.
     
  2. Pass one thread over the pulleys carrying a pan at each end. take a second thread tie one end to the middle of the first thread, and tie a pan to its other end.
     
  3. Add weights in the pan in such a manner that the small knot comes approximately in the Centre.
     
  4. Displace slightly the pans from their position of equilibrium and note if they come to their original position of rest. This will ensure the free movement of the pulleys.
     
  5. Mark lines of forces represented by thread without disturbing the equilibrium of the system and write the magnitude of forces i.e. Pan Weight + Added Weight.
     
  6. Remove the paper from the board and produce the line to meet at O.
     
  7. Use Bow’s notation to name the force P, Q, R as AB, BC, and CA.
     
  8. Select a suitable scale and draw the line ab parallel to force P and cut it equal to the magnitude of P.

PARALLELOGRAM LAW OF FORCES Graphical Method

Fig. 1.3, cut OA=P and OB=Q in suitable scale. From A draw AC’ parallel to OB and BC’ parallel to OA. R1 represents the resultant of force P and Q. As the system is in equilibrium it must be equal to R. Note that R and R1 are in opposite direction.

PRECAUTIONS

• 1. Pans/weights should not touch the vertical board
     
  2. There should be only one central knot on the thread which should be small
     
  3. While calculating the total force in each case the weight of the pan should be added to the weight put into the pan
     
  4. Make sure that all the pans are at rest when the lines of action of forces are marked
     
  5. All the pulleys should be free from friction
     

or

AIM: VERIFICATION OF PARALLELOGRAM LAW OF FORCES

APPARATUS:-

Gravesand‟s apparatus complete with two freely moving guide pulleys, weights, thread, a small central ring, white paper sheet, three scale pans, tape, a mirror strip, set squares and pencil.

THEORY

The „Parallelogram Law of Forces‟ states that if a particle is acted upon by two forces represented in magnitude and direction by the two sides of a parallelogram drawn from a point, then the resultant is completely represented by the diagonal passing through the same point.

PROCEDURE:

1. Take any point O on the plane of paper and draw a line OA Parallel to forces Z. Similarly draw a line OB parallel to force X.
2. 
   
   Complete the parallelogram OAC‟ B as shown in Fig.. 2
   
3. Join O to C‟ which is the diagonal of the parallelogram OC‟ to the given scale gives the resultant of forces X and Z.
   
4. Draw a line OC equal and opposite to OC‟ which should be equal to the third force Y.
   

OBSERVATIONS:

Mean Value…………………………….

PRECAUTIONS:

1. The board should be perfectly vertical.
2. The pulleys should be moving freely and if not moving freely, lubricate them.
3. The weights should not touch the board.
4. The weights of the pans should be added to the weight in the pan to find the total force in each string.
5. The directions of forces should be marked only after the system has come to complete rest.
6. The direction of forces should be marked with the mirror strip by keeping the eye, string, and its image in the same line.