Vectors Addition 9/24/2014

Chris Coutu

Justin Jones

Rajan Pandya

Quinn Howington

I. Introduction

The intent of this experiment is to add vectors effectively by using experimental, analytical, and

graphical methods; and to estimate random error from an instrument's measured sensitivity. The

method for vector addition includes finding the orthogonal components of each vector and adding

so that the components of the resultant vector R is related to the components of the individua l vectors A, B, etc., in the following way:

Rx = Ax + Bx Ry = Ay + By

The magnitude of the resultant vector and the angle Î¸ between the vector R and the x-axis are as followed:

R = (Rx)2 + (Ry)2

TanÎ= [(Ry) / (Rx)]

The equilibrant vector is the vector E which is in opposite direction to vector R.

II. Materials and Methods

In the experiment, a force table with movable pulleys on its rim was used to determine the sum of

two given forces. Begin by the forces are being exerted on an object by two vectors at angles of

(450) and (1350), and, these forces are each equivalent to the weight of a (150) gram mass

(including 50 gram mass of weight hangers). The value of the resultant vector R and its direction

were calculated using the given formulas. On a graph paper, a scale graph was made of two vector

forces, one resultant vector force, and one equilibrium vector force. The force table was used to

measure the weight needed to exactly offset the resultant of your vectors. Thus, an equilibr ium

vector E with mass (210) gram at (2690) angle can be achieved. By repeating all these steps for

case 2, to add the vectors exerted by a (100) gram mass at (1630) and (200) gram at (2870); another

equilibrium vector E with mass (170) gram at (760) angle can be achieved. In analytical method,

to get the resultant vector R, addition of x-components of vector A and B, and addition of y-

components of vector A and B was done. For case 1, Rx and Ry are (0) and (212) respectively, and

for case 2 Rx and Ry are (-37.16) and (-162.02). The direction of the resultant vector will always be on opposite of the equilibrium vector.

III. Results and Discussion

In this experiment, the intent was to add vectors with graphical, experimental, and analyt ica l

methods. Adding vectors by component method proved to be more accurate than graphical method

because there were known values that were used. The other intent was to estimate random error

from instrument's measured sensitivity. Sensitivity in mass was (5) gram in each case, and

sensitivity in direction was +/- 0.50 in each case.

Questions-Answers

1. There is only one equilibrant vector E which balances other vectors, that is, there is only one

mass and angle which balances the resultant. It's because there are no errors in ideal world. In real world, because of number of errors, we can get more than one equilibrant vector.

2. Estimated random error in angle = +/- 0.50

Estimated random error in mass = +/- 5 gram

Pulleys and centering ring with three strings could cause this range in angles and masses that do not seem to affect the balance.

3. Instrumental error = 0.50

4. A "tug-of-war" can't be conducted with a pair of steel pipes welded to a wheeled safe to keep

the pipes' angle Î¸ constant because it will keep moving the wheel in the direction of the resultant force. To stop that, it will need a equilibrant force to stop wheel from moving.

5.

100(Rexp - Rana)/Rana 100(Thetaexp - Thetaana)/Thetaana

Case 1 -0.9% -0.4%

Case 2 2.3% -1.4%

- I. Introduction
- II. Materials and Methods