name____________________ period _______ lab partners___________________________________
Purpose
The purpose of this experiment is to 1) provide a physical realization of vector addition by applying three forces to a central ring that is free to move as part of the force table, and 2) use this to experimentally determine the force which balances two other forces (so that this addition of three force vectors
= 0.) This result is checked by adding the two forces--first graphically, then using their components.
Background / PreLab (fill in the blanks below)
A quantity, such as displacement, velocity or force, which has both an associated number and direction is called a vector. Physical quantities, like speed, time, or temperature, that are not vectors--meaning they can be specified with a number only, no direction is needed--are called ___________. This experiment works with forces--directed pushes or pulls. If you haven't already, as directed by your instructor read the relevant portion of your text about vectors--specifically about adding vectors by
1) the graphical method, and 2) by the components method. Identify where in your text the rules for graphically adding two or more vectors are located: __________. Identify where in your text the procedure for adding two vectors or more using their components is located:_________________.
After doing this reading, you should realize that two vectors of the same length but pointing in
____________ directions add up to zero. This experiment starts with physically representing two vectors, vector F
A
and vector F
B,
on the force table. The resultant of adding these two vectors--called vector F
R
--is then found by three methods: experimentally, by components, and graphically. This vector, and another called the equilibrant F
E
, add up to zero. The figure below illustrates the relationship between these vectors.
Background / The Force Table
The forces in this lab will be read from spring scales calibrated in grams. There are two reasons why we will not use this unit: 1) grams are not actually force units, and 2) if we stick with grams we'll end up using unmanageably big numbers. So will we convert them to a true force unit--the Newton, abbreviated N--by multiplying the grams by the following conversion factor: .00981 N / g to change to
Newtons, or equivalently dividing by 102 g / N. The directions of these forces will be limited to particular directions: each quarter circle = 90 o quadrant is divided up into 10 o positions where there are

notches to hold (or latch) the springs which apply the forces.
Procedure
Assemble the force table and place the three springs so that the ring is in the center of the table. Always latch Spring #1 at 0 o
. This will represent Force A. Latch Spring #2--which will represent Force B-- at
120 o
. To get started, aim for having these springs provide pulling forces of roughly 600 to 800 grams
(for Spring #1 / Force A) and twice that--1200 to 1600 grams (for Spring #2 / Force B). The pull of
Spring #3 (Force E) latched in positions generally opposite those of the other two springs--will provide the third force that achieves equilibrium / balance. You'll know you have this when you have the ring centered in the center of the force table. Record the readings in grams and the angles in degrees for all three springs (in Data below). Convert the readings in grams to Newtons using the conversion factors.
Data Force A = ______ grams x .00981 N / g = ________
Force B = ______ grams x .00981 N / g = ________
Force E = ______ grams x .00981 N / g = ________ angle = ________
To determine theoretically what spring force F
E
(we need both its magnitude and direction) should be applied to restore equilibrium / balance after the first two forces are applied (force vectors F
A
and F
B which add to give resultant vector F
R
), we find the magnitude and direction of the equilibrant F
E
1) by the graphical method and 2) by the component-method.
Graphical Method
On a separate piece of paper, construct a tail-to-head diagram of the Force A and Force B vectors.
Don't rush into this! Establish an appropriate scale (1 cm = some number of Newtons). Choose this
scale so that your diagram will fit on the sheet of (polar coordinate style) graph paper provided. Use a
metric rule and protractor (if needed) to measure the magnitude and direction of the resultant vector F
R
.
Record the results in Table 1. Remember to record the direction of the equilibrant vector F
E
, which is
opposite in direction to the resultant.
Component Method
On as separate piece of paper, add the vector components of Force A and Force B vectors to determine
the magnitude of the equilibrant vector F
E
. Use trigonometry to find the direction (remember, the
equilibrant F
E
is exactly opposite in direction to the resultant F
R
). Record the results in Table #1.
Table #1 Results--Of Three Methods of Vector Addition
Method Equilibrant Force F
E
direction
Experimental
Equilibrant Force F
E
magnitude
Graphical
Component F
R x comp =_____
F
R y comp = _____
Questions
1) How do the theoretical values (graphical and component methods) for the magnitude and direction of
the equilibrant F
E
compare to the actual magnitude and direction? (Hint: compute percent errors!)
2) With respect to your answer to question 1) above, identify possible sources of error and discuss.