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Component Method. In the current experiment, students will be examining how the net force acting on an object at rest is zero in regards to the rules of vector addition. In order to confirm accuracy, percent error will be computed using the components calculated from equation 1 as mean and the average of components for GAV. GAV−MeanGAV×100(4)Equilibrium ConditionsBased on Newton’s first law, it is predicted that an object will not accelerate when the net force acting on it is zero. Therefore, if the object is at rest, the resultant force acting on it is zero. For the current experiment, F is replace with vectors, A, B, and C:⃗A+⃗B+⃗C= 0 (5) The above formula can also be written as ⃗C=−(⃗A+⃗B)(6)to express that vector C is equal in magnitude but opposite in direction to the sum of the other two vectors.In order to test if the forces are in equilibrium using the force table apparatus, the mass for objects must be calculated from Force values obtained from vectors and the gravitational constant:m=Fg(7)It is hypothesized that the equilibrium force will be determined through calculating both the magnitude and direction of the resultant force then adding 180°to it. Materials & Methods Equipment: oSlotted MassesoStringoKey Ringo4 hangersoGraph paper The Graphical Method
Vectors are graphed on a (x, y) coordinate system by being repositioned so that each one’s tail coincides with the head of the previous one. The resultant vector (sum of the forces) is drawn from the tail of the first vector to the head of the last. Students will determine the magnitude (length) and the angle of the resultant vector with a ruler and a protractor. The students will record these values and then draw the equilibrium vector. The Component MethodThis method allows for the vectors to be resolved through their x and y components using sines and cosines then simple trigonometry to solve for the resultant vector. Students will project three vectors on a positive (x, y) coordinate graph and then resolve the x and y components of the vectors through their directions using sine and cosine.Students will record the values their calculations yield.