THEORY: Any vector quantity can be represented as a line segment where its length represents the magnitude of the vector, and the angle 9 represent the direction of the vector as shown in figure {1}. A vector can be resolved into two components; x component {at} and y components {a,.), their magnitudes can be determined using the equations: ax=acose... {1} ay=asin B {2) Figure {1) Where a is the magnitude of vector and 9 is the angle the rector makes with the positive 1: - axis counterclockwise. An object Is at static equilibrium If the net force acting on It equal to zero. That means the forces applied on the object is balanced. And the iorces along x axis and along the y axis are balanced , and _ To determine the resultant force for two or three forces when the object at static equilibnum. we can use three different methods: 1. garment\" method usng the force table. The force table contains a black rod In the middle, a white ring as an object attached with four massless strings. each string connected with a hanger so you can hang masses on it. And the surface oi the force table is a protractor, see fIgure [1]. Figure [2| Mding a mass on one of the hangers creates a iorce on the ring. The magnitude of this iorce equal to the weight oi the added masses 1F - mg}J where m is the total mass hanged on the hanger and g is the acceleration due to gravity [3 -1IJ mislt. while the angle that the string points on it is the direction of the force. It the ring touches the rod in the middle, that means the object is not at static equilibnum. acting on the ring F1 and F1 balanced and the system Is _ the static equilibrium .' [Fa] should be added to the For example; If two forces then the forces is not not at equilibrium. To satisfy I~ condition a balancing force force table as shown In figure Figure :3] The magnitude ol the balancing force is equal to the magnitude of the resultant force: and in the opposite direction. where Is the angle [direction] of the resultant lorce with the positive x'axls counterdodiwlse, and is the angle {direction} of the balancing force with the positive x-axis clockwise. When using the force table to [Ind the resultant lorce, a balancing t'orce needs to he added to the force talbe to satlslyI equilibrium condition. Then the resultant force and the balancing force are equal in magnitude and opposite In direction. 2. Analytical method. To determine the resultantvector. each added vector should be resolved Into : and 3,- components. Then solving [or the components of the resultant vector. Rx-Fi.rFal..-13] Rv'Fivi'FIv-u '4] R: mm + Ry\"2)".5 [5i taniaj = Ry! R: [6] Where R: is the x - component of the resultant lorce ,R,. is the v - component ol the resultant force _ F1. and F1\" are the: - components [or the forces and , F\" and F2, are the}.I - components of the [orces. The magnitude and direction of the resultant vector can be calculated using the lormulas shown In :5} and [b] above: 3. Era ical method. In graphical method, the resultant vector is calculated using head to tail method. Starting with drawing the first added vector, then draw the second added vector so that the tail of second added vector is at the head of the preceding one. The resultant vector drawn from the tail of the first vector added to the head of the last vector added. The magnitude of the resultant vector is represented by the length of the lIne segment. While the direction Is the ange the resultant vector made with the positive x-axis counterclockwise. In ligure i4}, plot [a] shows three vectors using Phet simulation, plot [bi shows the method of adding these vectors using head to tail method. PROCEDURE Before you start. visit the Phet interactive simulation using the link below to explore the uses of each part in the simulation. https:thet.coloradoeclua'simsa'htmlJuector-additionflatestivector-acldition en.html THE RESULTANT 0F ADDING TWO FORCES (VECTORS). In this activity consider vectors as force (F: and F1], and vector as force {Fa}; as the resultant vector 1- Click on the I1nk shown above and select equations opt1on Mndow at the bottom of the graph as shown In figure [5]. 2. Drag the origin oi the graph paper to the middle of the graph. a . .H ... . .m . g, 3- Clidr on a . . base vector and selecta... -b,a..-T,b,--3, by -9. Andilxthetalloi the two forces [vector at and I ' [vector In: at the onglnas _ _ ':Z" 1n gure [5]. 4- Write .' ' the magn1tudeand direction of the forces in table 1 c) :1]. n 5. Use head _ to tail method to [Ind the Figure 5 resultant iorce FR. [vector c}. and take a screen shot of your graph. 5- W\"!!! "19 _ .. magnitude and directional / - ' - the resultant force Fit " t I. ' [vector c} In data analysis ' =' I ' ' step i. m cm Figure 4 \f$511115: 1. Ii'I'l'iat is the difference between vector and scalar quantlty? Give 2 examples for hath. 2. What. are the equllibnum mndltions for an object of mass n1? 3. If an object is at equilibrium, therefore the object must be at rest. Is thls statement True or False. lee an explanation to your answer whether it Is true or false. 4_ Two vectors quantlties are said to he equal if and onlyI If