BH19500541

0 College of Engineering Math & Science Department PHYS501 – Section : MG Laboratory Experiment Force Table and Vector Addition of force Ahmed Mohamed Elnourag BH19500541

1 Introduction Vector quantities are both magnitude and direction quantities. A force consequently has both magnitude and direction: the force is a quantity of the vector; its units are newtons and N. Forces can induce movement; forces can work alternately to hold (a) objects still. Objective The purpose of this experiment is to get knowledge of the power table, and to get a key idea of how to use it for vector calculations. Using the methods of graphical and analytical solving for the resulting power. And to balance by determining the relationship to the resulting force. Theory Only scalars (temperature, volume and time interval) are physical quantities that may be entirely defined by magnitude. The quantity and direction of certain physical amounts. These vectors are known as vectors. Example: Example (velocity and force) Physics is a science of math. There is a mathematical underpinning for notions and principles. During our physics research, we will find a number of ideas that are connected with them on a mathematical foundation. While we typically focus on the conceptual nature of physics, we focus on its mathematical element considerably and constantly. Object motion can be expressed using words. Even an individual without a background in physics is able to explain moving things using a combination of words. Going quickly, stopping, slowing down, speeding up, and turning are just a few of the words and phrases that may be used to describe the motion of objects. These and other terms are used in physics. Words like distance, displacement, speed, Velocity, and acceleration will be added to this vocabulary list. These terms are linked with mathematical numbers that have rigorous meanings, as we will see shortly. There are two types of mathematical quantities that are used to explain the motion of things. Experimental Procedure andApparatus first step is to attach an object onto a pulley and then hang a 350 g at the 30o mark on the table and another weight of 250 g off the 130 degree on the force table. The third pulley is then adjusted to be opposite to the other pulley forces, giving 70 & 420g weight.

2 Apparatus: 1. Pencil 2. Ruler 3. Ring 4. String 5. Mass holder Results Mass (g) Mass (Kg) Force (N) Direction Force 350 0.35 3.43 30 250 0.25 2.45 130 F1 420 0.42 4.12 250 F2 Equilibrant F1 Resultant 420 0.42 4.12 70 FR1 Table 1 Experimental solution

3 Force Mass (g) Mass (Kg) Force(N) Direction 350 0.35 3.43 30 F1 250 0.25 2.45 130 F2 393.44 0.393 3.85 Equilibrant 248.7 F1 68.7 Resultant 393.44 0.393 3.85 FR1 Table 2 Graphical solution Analytical solution calculations: F1X=350cos (30) =303.1g F1Y=350sin (30) =175g F2X=250cos (130) = -160.7g F2Y=250sin (130) =191.5g =301.1+(-160.7) =142.4g =191.5+175=366.5g R=x2+y2=393.2g tan-1(366.5/142.5) =68.7

4 Force Mass(g) Mass (Kg) Force (N) Direction X Y component component F1 350 0.35 3.43 30 303.1 175 F2 250 0.25 2.45 130 -160.6 191.5 Equilibrant 393.4 0.393 3.85 248.7 -142.5 -366.5 F1 Resultant 4 0.393 3.85 68.7 142.5 366.5 FR1 393.4 4

5 Table 3 Analytical solution Error Calculation: [ (Experimental- Analytical) / Analytical] *100% (0.42-0.393)/0.393*100%=6.87% [ (graphical - Analytical) / Analytical] *100% (0.393-0.393)/0.393*100%= 0%

6 Discussion & Conclusion First, we calculate the masses of the two forces (F1 = 350g, F=250g). The force with the gravity acceleration (9.81m/s2) to convert the force by newton. Then we apply force so that (350 and 250) equals (R=420 and angle=70). To determine the real value of the equilibrium force, add the x- and y-components. We obtain the real value of (R = 393.44g and angle = 67) by computation. Finally, calculate the percentage error for the magnitude experiment and compare it to analytical data (6.879 percent). And the graph's percentage was (Zero), because the two magnitudes were the same. We then graph it. Finally, we determined that the goal of this lab was to get expertise dealing with vector computations. When working with vectors, the most important thing to know is that they must be split down into horizontal and vertical components before any computations can be performed. The differences between the graphical, experimental, and analytical conclusions are minor, with the biggest difference occurring between the calculations from the analytical and graphical analyses. The analytical answer is the most precise since it was computed using vector formulae, whereas the graphical method included drawing free hand lines in the hopes that they would be parallel to the original vectors. Further sources of error may have included the bulk exclusion from strings, although the masses are unlikely to affect our conclusions. Friction is another problem, although it is doubtful that the results will have altered dramatically.

7 References ▪ https://www.physicsclassroom.com/class/1DKin/Lesson-1/Scalars-and- Vectors ▪ https://physicslabs.ccnysites.cuny.edu/labs/207/207-force- tables/forcetables.php ▪ http://www.physics.smu.edu/~ryszard/1313fa97/1313-Force_t_.PDF