Essay Example on Vector Summation

Published: 2019-11-04
Essay Example on Vector Summation
Type of paper:  Essay
Categories:  Mathematics
Pages: 2
Wordcount: 476 words
4 min read

Purpose and Introduction

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The main purpose of this experiment is to verify vector addition and to examine several static force configurations using the tabletop apparatus called a force table. As per Newton's second law, an object that is not accelerating must have no net force, i.e. the summation of the vectors of the forces on that object must be zero. This method for vector summation entails calculating the orthogonal components of every vector then adding; consequently the components of the resultant vector R is related to the components of the individual vectors A, B, etc., as per shown below:

Rx = Ax + Bx + ... + Nx

Ry = Ay + By + ... + Ny,

N is the total number of forces acting on the object. The magnitude of the resultant vector is the angle th between the vector R and the x-axis is

The equilibrant vector is therefore vector E which when added to R returns zero


Three masses were applied in exerting measurable forces on a ring at the center of the force table. These were then placed at measurable angles; the components of the force vectors could be easily evaluated. A forth mass was then placed so that the net force on the ring was zero, i.e. the ring was centered on the table


The forces applied to the ring and the calculated and measured equilibrant forces are shown in the table below:

Forces Magnitude Angle X component Y component

Force 1 400 30 346.4102 200

Force 2 200 -60 100 -173.2051

Force 3 300 135 -212.1320 212.1320

Sum of components 234.2781 239.9270

Resultant Force R 334.62267 45.56 Equilibrant Force E 334.62267 225.6 Measure Force 350 227 % Difference 4 1 Forces Magnitude Angle X component Y component

Force 1 400 45 282.8427 282.8427

Force 2 200 -45 141.4214 -141.4214

Force 3 500 270 -9.1886E-14 -500

Sum of components 424.2641 -358.5786

Resultant Force R 555.498 -40.2 Equilibrant Force E 555.498 -139.8 Measure Force 550 140 % Difference 1 0 Forces Magnitude Angle X component Y component

Force 1 350 20 328.8924 119.7070

Force 2 200 315 141.4214 -141.4214

Force 3 500 250 -171.0100 -469.8463

Sum of components 299.3037 -.491.5606

Resultant Force R 575.5124 -58.66 Equilibrant Force E 575.5124 121.3 Measure Force 570 118 % Difference 1 3 Forces Magnitude Angle X component Y component

Force 1 300 25 271.8923 126.7854

Force 2 200 310 128.5575 -153.2089

Force 3 250 200 -234.9231 -85.5050

Sum of components 165.5237 -111.9284

Resultant Force R 199.8176 -34.07 Equilibrant Force E 199.8176 145.9 Measure Force 200 143 % Difference 0 2 Results/Conclusions

The results of this experiment are as shown in the table above. All the measured forces are just within 4 percent difference of the total calculated forces; therefore the conclusion is that the method used in the calculation of vector addition was accurate.

The first source of error is failing to ensure that the assorted weights and hangers are exactly the weight they are said to be having. It is imperative to ensure each and every weight and hanger is weighed precisely just like the machine that is being used to weigh them. The second source of error is failing to ensure that the force table is as level as it ought to be. More time should be used in testing the force table with marble while the strings attached are not attached.

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