Lab 4: Vector Addition of Forces

Purpose: To study vector addition by:
                          1) Graphical means
                          2) Using components.
              A circular force table is used to check results.

Equipment: Circular force table, masses, massholders, string, protractor, four pulleys.


Part 1:

Our data:

a: 200grams, 0°
b: 100grams, 55°
c: 200grams, 135°

Our scale:  1cm = 20 grams

The magnitudes (length) of vectors:

a: 200grams x (1cm/20grams) =10cm
b: 100grams x (1cm/20grams) = 5cm
c: 200grams x (1cm/20grams) =10cm

Vector diagram:

We find "d" is the resulant force. Then we use ruler and protractor to determine the magnitude (length) and direction (angle) of "d".

The magnitude (length) of "d": 12.5 cm (equal to 250 grams)
The direction (angle) of "d": 62°


Part 2:

Vector components:

a: Ax=10 × cos(0°) =10
    Ay=10 × sin(0°) =0
a= 10i  + 0j

b: Bx=5 × cos(55°) =2.87
    By=5 × sin(55°) =4.1
b= 2.87i + 4.1j

c: Cx=10 × cos(135°) =-7.07
    Cy=10 × sin(135°) =7.07
c= -7.07i + 7.07j

d: Dx= Ax+Bx+Cx =20+5.74-14.14 =5.8
    Dy= Ay+By+Cy =0+4.1+7.07 =11.17
c= 5.8i + 11.17j

The magnitude (length) of "d": √(5.8^2+11.17^2) = 12.59cm (equal to 251.7 grams)
The direction (angle) of "d": arctan(11.17/5.8) ≈62.6°



Part 3:

Mount three pulleys on the edge of force table at the angles. Attach strings to the center ring so that they each run over the pulley and attach to a mass holder. Hang the appropriate masses on each string:


a: 200grams, 0°
b: 100grams, 55°
c: 200grams, 135°

At this moment, the ring is not equilibrium.

Set up a fourth pulley and mass holder at 180 degrees opposite from the angle you calculated for the resultant of the first three vectors.

d: 251.7 grams; 62.6°+180° =242.6°

When we place a mass on fourth holder equal to the magnitude of the resultant, the ring turns to equilibrium.

The ring is in equilibrium after we the fourth mass

Part 4:

We confirmed our result via simulation:

The simulation of our data

We found the simulation data of the resultant are really close to our resultant data (62.6°), that means our data are convincing.

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.
     This experiment proved that force has direction, and a resultant force consists several vector forces. 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:
            1. Some magnitude of vectors are decimals, but we only have the masses with whole numbers.
            2. Some masses are rusted, so their mass may be higher or lower than the standard.
            3. Our table is not horizontal, so our directions of vectors are little biased.