4.Vector Addition of Forces

Purpose: To study vector addition by Graphical means and Using components.

Equipment: circular force table, masses, mass holders, string, protractor, and four pulleys.

Part 1.  Dr. Haag gave us 3 masses in grams which represent the magnitude of three forces and three angles.

	Magnitude	angle
A	100kg	0°
B	100kg	335°
C	100kg	270°

 

We made a vector diagram showing these forces, and find the resultant after adding the three vectors. There is two ways to calculate the resultant:

·         The head to tail vector. This involves lining up the head of one vector with the tail of the other.

·         The parallelogram method to calculate resultant vector. This method involves properties of parallelograms but, in the end boils down to a simple formula.

 

100 cos 0° + 100 cos 335° + 100 cos 270°= 190.631 = X

100 sin 0° + 100 sin 335° + 100 sin 270° = -142.262

Tanθ= 190.631/-142.262

θ= tan^-1 (142.262/190.63)= -36.733 + 180 = 143°

 

 

Conclusion:


When we place a mass on fourth holder equal to the magnitude of the resultant, the ring turns to equilibrium. That means the force of the fourth mass is equal to the resultant force of the first three masses. A vector is a quantity having a magnitude and a direction, and two vectors of the same type can be added.

The sources of error: Some magnitude of vectors are decimals, but we only have the masses with whole numbers.