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
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.
