VERIFICATION OF TRIANGLE LAW OF FORCES

OBJECTIVE

To verify the triangle 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

The “triangle law of force” states that if three coplanar forces acting on a particle can be represented in magnitude and direction by the three sides of the triangle taken in order, the force will be in equilibrium.

This law can also be stated as: If two forces acting on a particle are represented in magnitude and direction by the two sides of the triangle taken in order then their resultant will be given by the third side of the triangle taken in the opposite direction.

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. Please 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 center 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.
  4. Mark lines of forces represented by a thread without disturbing the equilibrium of the system and write the magnitude of forces i.e. Pan Weight + Added Weight.
  5. Remove the paper from the board and produce the line to meet at O.
  6. Use Bow’s notation to name the force P, Q, and R as AB, BC, and CA.
  7. Select a suitable scale and draw the line ab parallel to force P and cut it equal to the magnitude of P.

From b draw the line bc parallel to force Q and cut it equal to the magnitude of Q (Fig. 1.2). Calculate the magnitude of ca i.e., R1 which will be equal to the third force R which proves the triangle law of forces.

If R1 differs from the original magnitude of R, the percentage error is found as follows: Percentage error =(R−R1)/R∗ 100

TRIANGLE LAW OF FORCES Graphical Method

Fig. 1.2(b), draw AB parallel to force P in suitable scale with the use of set square, and then from b draw bc parallel to force Q. The closing side of the triangle represents the force R1 which should be equal to force R.

Note, the difference in R1 and R shows the graphical error.

Analytical Method

Measure angles α, β, and γ, and by using Lami’s theorem check the following relation

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 TRIANGLE LAW OF FORCES

APPARATUS:-

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

THEORY:

The triangle law of forces states that if two forces acting on a particle can be represented in magnitude and direction by the two sides of a triangle taken in order then their resultant will be given by the third side of the triangle taken in the opposite direction.

PROCEDURE:

1. Fix the paper sheet centrally on the board.
2. Take suitable length of thread and pass it over two pulleys, the ends of thread are to be attached to pans which are to carry weights.
3. Take another piece of thread and tie it to the middle of the first thread which is to carry another weight.
4. Place the weights in the pans in such a way that the knot comes nearly in the middle of the paper.
5. For ensuring free movement of pulleys, displace the pans from their original positions.
6. 
   
   Mark the directions of the strings on the paper sheet with the help of a strip of mirror which is put under the string lengthwise one by one to get points for the purpose.
7. Note the magnitude of forces and mark the lines of forces.
8. Remove the paper from the apparatus and produce the force line to meet at point O.
9. Name the forces, X, Y, and Z, according to the Bow‟ ‘s Notation as PQ, QR, and RS.
10. Choose a suitable scale and draw the line Pq parallel to force X and cut it equal to the magnitude of X according to the scale chosen. Now from point q draw the line qr parallel to force Y according to the same scale. Find the magnitude of rp i.e. R which should be equal to the third force Z which proves the triangle law of forces.
11. If the magnitude of r pvaries from that of the forces QR, then
12. percentage error = (Q𝑅−𝑟𝑝 ) × 100 / Q𝑅
13. Repeat the above procedure at least two times more by varying the loads and tabulate the results.

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.