vector addition of forces

Purpose:

To study vector addition by:

1) Graphical means and by

2) Using components.

A circular force table is used to check results.

Equipment:

Circular force table, masses, mass holders, string, protractor, four pulleys.

circular force table / four pulleys

protractor

Procedure:

1. Your instructor will give each group three masses in grams (which will

represent the magnitude of three forces) and three angles. Choose a scale of

1 cm = 20 grams, make a vector diagram showing these forces, and

graphically find their resultant. Determine the magnitude (length) and

direction (angle) of the resultant force using a ruler and protractor.

2. Make a second vector diagram and show the same three forces again. Find

the resultant vector again, this time by components. Show the components of

each vector as well as the resultant vector on your diagram. Draw the force

(vector) you would need to exactly cancel out this resultant.

3. Mount three pulleys on the edge of your force table at the angles given

above. Attach strings to the center ring so that they each run over the pulley

and attach to a mass holder as shown in the figure below. Hang the

appropriate masses (numerically equal to the forces in grams) on each string.

Is the ring in 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. Record all mass and angles. If you now place a mass on this

fourth holder equal to the magnitude of the resultant, what happens? Ask

your instructor to check your results before going on.

figure 1

figure 3

figure 2

figure 4

Vector Calculations:
Rx = (100Cos(0)) + (200Cos(71)) + (160Cos(144)) = 36.1
Ry = (100Sin(0))  + (200Sin(71))  + (160Sin(144))  = 283
ø = 82.7°              R = sqrt(283^2 + 36.1^2) = 285.3  



The simulation confirmed the results as correct. *Note: scale to 1=10.

The diagram shows vectors A, B, C and D as the sum. (1 cm = 20 g)

figure 8

conclusion:during our lab experiment we learned that in order to get three forces that where given. to be in equilibrium a forth force would be necessary to counter- balance the other three forces this force would have to be negative and would be the sum of all 3 forces.