The Triangle of Forces - Lab Report Example

The Triangle of Forces (Lab Report) Science Practical Assignment Faculty January 22, 2009 Aim: The aim is to verify experimentally the theorem of the triangle of forces. Introduction: The theorem of the triangle of forces states that “if three forces P, Q, R (See Figure 1) meeting at a point can be represented in magnitude and direction by the three sides of a triangle OB, AO, and BA respectively, taken in order, then the three forces are in equilibrium.” Figure 1: Triangular force diagram In above diagram (figure 1), actually, the converse of the triangle of forces theorem is investigated, that is “ if three forces P, Q, and R meeting at a point are known to be in equilibrium, then their magnitude and directions can be represented by the sides of a triangle taken in order and parallel to the three forces.” Setup (Apparatus): 1. Vertically mounted board with two pulleys (figure 2) 2. Three strings knotted together, two passing over the pulleys 3. Three hangers and set of 100g weights Figure 2: Experiment on three balanced forces Procedure: 1. Attach hangers to the free ends of the three strings. 2. Add different weights to the three hangers (between 50 and 200 grams), and allow the system to come the equilibrium. 3. Place a plain sheet of paper behind the strings, and mark the position of the strings with a pencil. 4. Repeat this procedure for five different combinations of weights placed on the hangers. 5. Draw a vector diagram for each of the five combinations of weights used. Vector and Bow’s Notation Figure 2 on the left shows a space diagram in which only the lines of action of the forces are shown. On the right is the force or vector diagram in which sides of the triangle represent to scale the magnitude and also the direction of the three forces. Forces in the space diagram are designated by capital letters placed in the spaces on each side of the force, e.g. the force labelled ab in the force diagram is called AB in the space diagram. Note that the force AB emanates outward from the node. A force designated BA would be the opposite direction. The small letters a, b, c denotes the ends of the vectors in the force diagram. This system of referring is called Bow’s notation. Experiment (Lab) Results Experiment 1: Weight Combination of 70g, 70g, and 90g Figure 3 on the left shows a space diagram (the position of the strings) in which only the lines of action of the forces are shown. The combination of weights (forces) taken are 70g, 70g, and 90g. On the right is the force or vector diagram in which sides of the triangle represent to scale the magnitude and also the direction of the three forces. The force 70g () is represented by vector in the, the force 70g () is represented by vector in the, and the force 90g () is represented by vector in the. From figure 3, it can be seen that the three forces,, and in equilibrium forms a triangle (approximately). The triangle is not closed because of measurement errors. Figure 3: Combination of 70g, 70g, and 90g weights Experiment 2: Weight Combination of 90g, 70g, and 90g Figure 4 on the left shows a space diagram (the position of the strings) in which only the lines of action of the forces are shown. The combination of weights (forces) taken are 90g, 70g, and 90g. On the right is the force or vector diagram in which sides of the triangle represent to scale the magnitude and also the direction of the three forces. The force 90g () is represented by vector in the, the force 70g () is represented by vector in the, and the force 90g () is represented by vector in the. From figure 4, it can be seen that the three forces, , and in equilibrium forms a triangle (approximately). Figure 4: Combination of 90g, 70g, and 90g weights Experiment 3: Weight Combination of 90g, 90g, and 110g Figure 5 on the left shows a space diagram (the position of the strings) in which only the lines of action of the forces are shown. The combination of weights (forces) taken are 90g, 90g, and 110g. On the right is the force or vector diagram in which sides of the triangle represent to scale the magnitude and also the direction of the three forces. The force 90g () is represented by vector in the, the force 90g () is represented by vector in the, and the force 110g () is represented by vector in the. From figure5, it can be seen that the three forces, , and in equilibrium forms a triangle (approximately). Figure 5: Combination of 90g, 90g, and 110g weights Experiment 4: Weight Combination of 150g, 110g, and 170g Figure 6 on the left shows a space diagram (the position of the strings) in which only the lines of action of the forces are shown. The combination of weights (forces) taken are 150g, 110g, and 170g. On the right is the force or vector diagram in which sides of the triangle represent to scale the magnitude and also the direction of the three forces. The force 150g () is represented by vector in the, the force 110g () is represented by vector in the, and the force 170g () is represented by vector in the. From figure 6, it can be seen that the three forces, , and in equilibrium forms a triangle (approximately). Figure 6: Combination of 150g, 110g, and 170g weights Experiment 5: Weight Combination of 150g, 170g, and 170g Figure 7 on the left shows a space diagram (the position of the strings) in which only the lines of action of the forces are shown. The combination of weights (forces) taken are 150g, 170g, and 170g. On the right is the force or vector diagram in which sides of the triangle represent to scale the magnitude and also the direction of the three forces. The force 150g () is represented by vector in the, the force 170g () is represented by vector in the, and the force 170g () is represented by vector in the. From figure 7, it can be seen that the three forces, , and in equilibrium forms a triangle (approximately). Figure 7: Combination of 150g, 170g, and 170g weights From experiment 1 to 5, we can see that the three forces at equilibrium, taken in order in magnitude and directions can be represented by the sides of a triangle taken in order and parallel to the three forces. Therefore, the converse of the triangle of forces theorem is proved experimentally. Consequently, the theorem of the triangle of forces also proved. Conclusion In conclusion, if the three forces meeting at a point can be represented in magnitude and direction by the three sides of a triangle, taken in order, then the three forces are in equilibrium. Therefore, the theorem of the triangle of forces is correct. Read More