Vector Addition of Forces Lab

In this lab we studied vector addition by graphical means and also by using vector components. The materials to replicate this lab are as follows:

• Circular Force Table
• 4 pulleys
• Masses
• Mass Holders
• string
• Protractor and ruler

Intro:
Vectors are arrows with a certain length, which describes the magnitude of an object, and direction. In order to add vectors you must have the vector components which describe how far along the x and y axes the magnitude of the vector travel which will give you <i, j> where i is the x direction and j is the y direction. To find the components of a vector that gives you the magnitude as well as the angle of direction you would use basic trigonometry identities.

To find the x component:

cosӨ = V_x /M

McosӨ = V_x 

To find the y component:

sinӨ = V_y/M

MsinӨ = V_y

Once you find your vector components the notation of your vector you will have <V_x ,V_y >. When you have at least two components you can now add them together by adding the x components and the y components to get the components of the two added vectors which will make up a new vector that you can graph.

Another method you can use to add vectors is graphically.

In this picture you can see that in order to find V₃ you would draw it from the tail of the first vector which is V₁ to the head of the last vector which is V₂.

Procedure:
In this lab we are given 3 masses and an angle by our teacher. The 3 masses and angles we were given were:

• 150 g @ 0°
• 110 g @ 70°
• 250 g @ 135°

We were given a conversion to convert the masses into lengths for the magnitude of our given vectors. The conversion was 1cm = 20 g. We used the conversion and found the magnitudes of our vectors:

• 7.5 cm
• 5.5 cm
• 12.5 cm

We graphed the 3 vectors using the head to tail method first to find the magnitude and the direction of the angle.

We measured the length of the resulting vector with a ruler to be 14.0 cm and 87.75° with a protractor. 

Once we found the resulting vector using the graphic method we then solved for the resulting vector by finding the components of the given vectors.

With these components we were able to find the magnitude and angle of the resultant vector.

Data Analysis:

Now that we have a magnitude and direction for our new vector we now convert it to grams by using the conversion 1 cm = 20 g which gives us 280.4 grams for our resultant vector. We then set up our circular force table with the four pulleys. At the center there is a ring with 4 strings tied from it that hung off of the pulleys. The first 3 pulleys were set at the given angles, 0°, 70°, and 135°. The fourth was set 180° opposite the angle we found which was 87.8. This gave us a new angle 267.8° which now makes our vector negative. After having all of the pulleys set we then hooked the massholders to the ends of all of the strings and added the masses onto the massholders:

The center ring was in equilibrium on the circular force table which means the masses hanging at the end of the strings which hung from the pulleys at the correct angles suspended the ring in the center without touching anything.

We showed the direction of all the vectors to understand the direction they are going on the table.

Conclusion:

We calculated our percent error to be 0.14%. It was a low because we were able to control most of our experiment since we were only trying to find one vector from 3 vectors. The one that was more off was when we solved for it graphically only because we were physically measuring rather than working with the components. In this lab we learned how to add vectors by their components and also graphically with the head to tail method.