FORCE TABLE

OVERVIEW
All measurable quantities can be classified as either a scalar or a vector. A scalar has only magnitude while a vector has both magnitude and direction. In this lab we will use a force table to determine the resultant of two vectors
LEARNING OBJECTIVES:
At the end of this module, you should be able to:1. Use the force table to determine the sum of two vectors.2. Compare experimental values with calculated values for the magnitude and direction of the resultant.
WHAT IS A FORCE TABLE?
The image on the right is a force table. As shown, it is a circular platform supported by a tripod stand. The tripod's three legs each include a leveling screw that may be adjusted in order to level the circular platform. The surface of the spherical platform is marked with angle measurements in degrees. Anywhere along the platform's edge, two or more pulleys may be clamped. The number of pulleys to be used will depend on the number of vectors to be balanced. For example, you need to balance three vectors, then three pulleys are to be used, and so does three strings. These strings are attached to a central ring and then each string is passed over a pulley. Hanging masses are then attached to the other end of these strings as can be seen in the photo. These masses will produce a tension force in the string. When, the forces are balanced, the center ring will be positioned at the exact center of the table. Note that it is unbalanced once the center ring rests against one side of the central post. The force due to each hanging mass will simply be mg or the mass times the acceleration due to gravity.
FORCE VECTORS
It is known that vector quantities are quantities that possess both magnitude and direction. A force has both magnitude and direction, therefore, a force is a vector quantity. Force is equal to mass times acceleration due to gravity. However, in this laboratory experiment, we ignored the acceleration due to gravity since it is constant and common to all vectors. Henceforth, the force is equal to the mass. Its unit will be in terms of grams (g) instead of Newton (N). Furthermore, resultant is defined as the vector sum of two or more vectors. If we had resultant displacement in the previous laboratory experiment, we have resultant force in this one. This resultant force is the single force that represents the vector sum of two or more forces.
EQUILIBRANT
When the different forces acting on an object is balanced, it is considered to be in equilibrium. The balancing of force in a system occurs when leftward force balances the rightward force and upward force balances the downward force. But when the forces are unbalanced, there must be a force to be added to balance the system. This force is called the equilibrant. The equilibrant of a set of forces is the force needed to keep the system in equilibrium. It is equal in magnitude with the resultant force but with opposite direction as shown in the figure. The red vector is the equilibrant while the blue one is the resultant. In this experiment, the goal is to find the equilibrant of two known forces using the force table. Shown below is the laboratory report for this experiment.
Salazar_BSCE2B_LR#2_Force Table.pdf
Unlike the force table shown, we conducted this experiment without using the pulleys. Instead, we directly hung the strings on the edge of the circular platform. As stated in the procedure, we first designated two masses for the first two vectors then computed their vertical and horizontal components to be used in determining the magnitude and direction of the equilibrant represented by R in the laboratory report. Then, we positioned the third vector based on the computed mass and angle for the equilibrant. We did minor adjustments to position the middle ring exactly in the center and noted these adjustments to be compared on the computed values. In order to compute the vertical and horizontal components of each of the vectors, I used y = msinθ and x = mcosθ, respectively, where m is the displacement and θ is the direction or angle of the vector. To determine the magnitude of the resultant force, use the formula R = √(x2 + y2), where x and y are the summations of the x's and y's of the previously computed horizontal and vertical component. Furthermore, to compute the direction of the resultant, use tan θ = y/x. Note that it is not the resultant force but the equilibrant force that will balance the system. Henceforth, the direction to be used should be opposite to that of resultant force.
The direction of the resultant force that I obtained was ( - , + ) which is located on the second quadrant. Its opposite location is in ( + , - ) or in the fourth quadrant, hence, I positioned the equilibrant on this location to balance the system. The computed magnitude of the equilibrant was 39.69 grams with an angle of 65.89°. On the force table, the mass used to balance the system was 40 grams with an angle of 66°. Observing these numbers, it can be inferred that the experimental values were just the rounded numbers of the theoretical values. They only differ in few decimal places. Numerically, the calculated percentage errors were 0.78% for the magnitude or mass and 0.17% for the angle. These less than 1% error means that the force table is an effective and efficient way of determining the vector sum of some given vectors. The experimental values were 99% correct and the reason for the 1% discrepancy is the estimation that has to be made in balancing the system. Furthermore, since the system was balanced despite the less than 1% error, it can be said that percentage error is already negligible. Lastly, the equilibrant is the force needed to balance the system and is always with opposite direction to the resultant force but with the same magnitude.



REFLECTION
This laboratory experiment introduced to me the physics lab apparatus, force table. Yes, it was my first time to see such equipment and knowing its use amazes me more. The force table is used to determine the sum of two or more vectors. One should keep in mind that the middle ring should be at exactly center of the circular platform before saying that the forces are already balanced. Once the middle ring rests on one side of the central pole, the forces are unbalanced. Furthermore, I also learned that the force needed to balance two or more forces is called the equilibrant. The equilibrant should always have the same magnitude as the resultant force but in opposite direction. For example, if the resultant lies on the second quadrant, then the equilibrant should lie on the fourth quadrant. Since we utilized the calculated values as the theoretical values, I have realized that it is always the analytical method that is considered to yield the most accurate result since a careful computation will always give a perfect or almost perfect result. This is in comparison to the actual values obtained during the lab experiment which was considered as the experimental values. Moreover, the experiment proved to me that when the forces acting on an object are balanced, the system is said to be in equilibrium.



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