Experiment 5: Vectors and Static Equilibrium of Forces
In physics, the subject of statics deals with the description of conditions of force system that is necessary to maintain the state of equilibrium of engineering structure. When a body is in equilibrium, the resultant of all forces acting on it is zero. Main condition for static equilibrium is that the vector sum of all the forces acting on a body must be zero. In this report equilibrium was discussed by carrying out an experiment. For an analysis of a vector quantity like force vector operations like vector addition and subtraction are required and in this experiment this vector operation was also discussed.
THEORY AND OBJECTIVE:
Many quantities studied in physics are vector such as velocity, acceleration, force, momentum etc. For analysis and study of vector quantities it is vital to have knowledge about Vector operations such as Vector addition and subtraction. One of the objects of this experiment was to use vector addition and subtraction. Another purpose of this experiment was to be familiar with static equilibrium. When a number of forces act on a body and there is no movement of that object, the object is in static equilibrium. Same condition is applicable if that body moves without any acceleration.
When a body of mass m hangs from a support, force exerted by it on the support is the weight. The one body on the surface of the earth has a weight W. Now W = m.g, where g is equal to 9.81m/sec2. From Newton’s Universal Law of Gravity, g = GM/r^2, where G is the Universal constant of gravitation, M is the mass of the earth and r is the radius of the earth.
At first exercises related to Vector Arithmetic such as Vector Addition, Vector Subtraction and Vector Components were carried out. Then experiment was initiated with setting up the Pasco Mechanics System similar to following figure.
The apparatus contains two analog scales – a spring scale and an angle scale.
In the above mentioned system, three forces were arranged and it was ensured that all the forces had roughly similar magnitudes. Static equilibrium was established by adjusting the weights and moving the angle scale and the equilibrium was tested by nudging the plastic ring or the knot. Then magnitude and angles of all forces were measured and recorded. After this, those forces were resolved into x and y components. It was determine whether adding components satisfied the condition for equilibrium. In the next step a half-page vector diagram was drawn on a sheet of graph paper. In that diagram, it was shown how the three force vectors sum to zero.
In the next step the extruded, L-shaped, piece of black, anodized aluminum was mounted on the Mechanics board. The plane was tilted, so it made a shallow angle as indicated by the attached plumb bob. The mass of the aluminum cylinder and the angle of incline were measured. Then aluminum cylinder was placed on the incline. A paper clip was hooked to the frame on the cylinder and a thread was tied to the paper clip. It was made sure that the thread was parallel to the inclined plane, and its loose end was run around a pulley. The loose end of the thread was tied to the spring scale. It was made sure that the length of the string running from the pulley to the spring scale was vertical. Then the second arm enclosing the cylinder was rotated so that it made a 90 degree angle with the incline. A thread was tied from that arm over a pulley and the loose end was tied to a weight hanger. Enough weight was added to the hanger, so the cylinder just started to lift off of the incline. The incline was then removed to test whether static equilibrium had been achieved. A force vector diagram i.e. free body diagram of the cylinder was drawn and all the forces acting on the cylinder were labeled. Then the perpendicular i.e. normal force and the force parallel to the incline were recorded. The Normal and parallel force were rewritten in terms of the mass of cylinder and angle of the incline using the free body diagram. Then theoretical value was calculated and compared with experimental values.
But from vector diagram the percentage error was found as 54%.
The experiment was carried out safely. From the result of the experiment, it was found out that the percentage error is considerably high. Possible source of error may be due lack of care during experiment, taking wrong measurement of magnitude and angles of the forces. However, theoretical value of percentage error and the percentage error obtained by graphical method were almost equal. By performing this experiment knowledge about vector operation such as vector addition and subtraction, drawing free body diagram as well as knowledge about static equilibrium was obtained. So, it can be concluded that objective of this experiment was fulfilled.