Vector Addition of Forces Edwin Gonzalez

Introduction

The purpose of this lab was to study vector addition by graphical means and by using components.
The results were checked with a circular force table. Equipment used consisted of a
circular force table, masses, massholders, string, protractor, and four pulleys.


Calculations

Rx=(magnitude*cos(angle))+(magnitude*cos(angle))+(magnitude*cos(angle))
Rx=(400 cos 34°)+ (300 cos 56°)+(100 cos 21°)
Rx= 592.7

Ry=(magnitude*sin(angle))+(magnitude*sin(angle))+(magnitude*sin(angle))
Ry=(400 sin 34°)+ (300 sin 56°)+(100 sin 21°)
Ry= 508.2

R=[(Rx^2)+(Ry^2)]^(1/2)
R=[(592.7^2)+(508.2^2)]^(1/2)
R=780
Data

Vector Diagram with ruler and protractor

  1 cm = 20 grams
 A=100 (m) 0°
  B=200 (m) 71°
   C=160 (m) 144°
  D=284 (m) 83°

Vector Diagram

Rx=(100 cos0°)+(200 cos71°)+(160 cos144°)= 36.1

Ry=(100 sin0°)+(200 sin71°)+(160 sin144°)=283

θ= 82.7°

R=[(36.1^2)+(283^2)]^(1/2)=285.3

Vector Components

Ax=(100 cos0°)=100           Ay=(100 sin0°)=0

Bx=(200 cos71°)=65.1         By=(200 sin71°)=189

Cx=(160 cos144°)=-129        Cy=(160 sin144°)=94

Rx=36.1                      Ry=283



Confirmation of Results

 Results

Here the weights are shown hanging by the string

 An aerial view of the Circular force table with the weights

Here the center ring is shown in equilibrium

Conclusions

In conclusion, we learned how to solve a problem where there are multiple forces acting on a  single entity. The vectors are first calculated individually in respect to the Y-axis and in respect to the X-axis (sin & cos). Then the resultant vector is found by treating those as vectors also. So the square root of Rx^2+Ry^2 is taken then the resultant vector is found.  You basically take the components of the small vectors and combine them into a bigger vector, after that you those 2 bigger vectors and add them to find the resultant vector. Sources of error include the circular force table, the weights are attached by string through a pulley. The string could absorb some of the weight because it goes through elastic elongation we also did not take in to account the mass of the string because it would add to the masses hanging. The pulleys also add friction that was not accounted for.