U.0 and ge concurrent forces) Name muhanad fuaad albdisaccdEquilibrium of Forces (Static Equilibrium) Objectives: 1- Resolving forces in two dimensions to study the static equilibrium situations ona force table. 2- To test whether the forces on a body at rest add to zero. 3- To experimentally verify the parallelogram law of vector addition by using a force table. 4- Addition of forces. S- To determine the mass of an object. Materials/Apparatus: Drawing paper and pencil. flat wood board, three weight hangers. pulleys, mass set, rings with strings, ruler and protractor.Introduction The origin of the topic was the formulation of the parallelogram law in 1586 by the Flemish mathematician, Simon Stevin (1548-1620). The development of vector mathematics by the American physicist. Josiah Willard Gibbs (1839-1903) and the English physicist, Oliver Heaviside (1850-1925), in the last quarter of the 19th century drew on the algebra of quatemions which had been formulated by the Irish mathematician Sir William Rowan Hamilton (1805-1865). Still further development of vectors led to the mathematics used by Albert Einstein (1879- 1955) in his general theory of relativity. A force is the push or pull that one object exerts on another. The essentialFor example, to represent a 50 N force acting at an angle of 30° to the vertical (see figure 1), a line is first drawn to represent the vertical. Then another line is drawn at 30° to the first. The length of the arrow is drawn to scale, For instance, with the +°% _ the arrow could be drawn, as in the following diagram, 0.025 m. 0.005 m Vertical Fig.l. Vectors can be denoted in print in various ways. They can be shown with a small arrow above as F. or they can be shown in boldface type as F. The magnitude can be shown simply as F. or as |F]. The sum of two forces F, and F, is found by drawing the forces according to the scale, with the tail of F,coinciding with the head of F,. The sum. F,, is called the resultant. Then F,= FP, +F, is represented by the arrow drawn fiom the tail ofVectors can be denoted in print in various ways. They can be shown with a small arrow above as F, or they can be shown in boldface type as F, The magnitude can be shown simply as F, or as |F|. The sum of two forces F, and F, is found by drawing the forces according to the scale, with the tail of F,coinciding with the head of F,. The sum, F,, is called the resultant. Then F, =F, +F, is represented by the arrow drawn from the tail ofTheory For an object to be in equilibrium. two conditions must be met. The first condition is that the sum of all forces acting on the object must equal zero (oF = 0). The second condition is that the sum of all torques acting on the object must be zero 37 = 0.Procedures An illustrative diagram of the experiment setup is shown below in fig. 4. Note the masses (m,. m, & m3) suspended from each thread. The aim is to calculate the mass of m, using three different methods: 1- From polygon of forces. 2- Analysis of force components (trigonometry). 3- Cosine law.1- Make sure that the board is vertical. 2+ Each pulley must be at the same distance from the board. 3- Tape a paper of paper onto the face of the board so that the paper is centred behind the centre of three threads. 4- Tie three pieces of thread to each other and pass two of them over the upper pulleys leaving the third to hang free. Tie a loop at the end of each piece of thread and suspend a mass hanger from each loop. $- Load each mass hanger with masses m, and m, (120g for each side). Measure the angles 6, and 6; of the upper two pulleys with respect to horizon.7- Draw force diagrams to scale. For example, 12g = 1 cm. Use whatever scale works best to give you the greatest plotting precision. 8- Draw the force vectors, F,, F,, and F3, for the condition of equilibrium found in step 7 by inserting a piece of paper under the system and tracing the direction of the three cords which connect the ring to m,, m2, and m3. 9- From the vector diagram you obtained, with 3 masses, use the polygon method to draw the resultant vector (on the same sheet of graph paper). Measure the length of the resultant vector. 10- From the vector diagram you obtained, with 3 masses, calculate the resultant vector from the x- and y components of each vector, m, = (Asin@, + B sin @2)s ll- From the vector diagram you obtained, again with 3 masses, calculate the resultant vector by using the cosine law, m, = s JA? + B? + 2AB cos 0 © =180°- (6, + 6) 12- Calculate the average value of the resultant vector found in steps 9, 10 and 11. 13- Calculate the percentage error (the accepted value of m, = 160 g). 14- Each person must submit his or her own paper, stapled to his/her own report.