Name: ______________________
Partners: _______________________________________
Date: __________
Period: ________
bjm9/07
Force Table Vectors
Purpose: To learn how to add vectors, quantities dependent on both size and direction, by the
diagram method. Question: Does our method show a cancellation of forces?
Each lab table has three force scales pulling on three strings. Since the strings aren’t moving, we will assume the
three forces exerted by the three scales are canceling out. That is; Total Force = zero
Slide an 8.5”x11” piece of paper under the central knot where the three strings join. Mark spots under each
string near the knot and near the edge of the paper under each string. Make sure the paper does not move while
you do this. You’ll use these dots to draw lines representing each string.
Disconnect a string from one of the scales so that the strings are slack. If the scales do not read zero, calibrate
them by turning the white dial. Now you’re ready to take force measurements.
Record the force reading in Newtons (N) from each scale next to the mark(s) representing each string, near the
paper edge.
The diagram with its numbers is your data. EACH PERSON SHOULD HAVE A COPY (in your book, of
course). You’ll turn in this piece of paper as a team, with your lab.
Draw three vectors on top of the marks representing the three strings. This lines
should extend almost to the end of your paper. They represent the directions of
the forces the springs were exerting OUTWARDS on the knot. Measure the angles
between the lines. The sum of the three angles should be 360°.
B
C
A
Why should the sum equal 360°?
Select the middle-sized force (not length of line, Force!) as A. Label the three vectors A, B, and C, with B and
C labeled in a clockwise fashion from A as shown above. Note: The length of the line on your small paper is
NOT important. The force reading is.
Get a large piece of paper (one for each team). Construct a copy of the three vectors with the intersection point
in the approximate middle of the large paper. Vectors B and C should be drawn in with the proper angles
relative to vector A and oriented clockwise from A as before. It is important to get the angles between the
vectors accurately constructed. If the drawing does not look just like the one above, that is OK, your angles are
likely to be different.
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Extend the lines to lengths proportional to their force values. To do this you must establish, and record, a scale
factor, similar to the scale on a road map. For example: You might let 2.0 cm represent 1.0 N or perhaps 4.0 cm
for 1.0 N. You must pick your own scale which should satisfy three conditions:
1. The diagram should be reasonably big, the smallest force should be represented by more than 10 cm if
possible.
2. However, the entire diagram should fit on the page. It may take some judgment and visualization to satisfy
both criteria.
3. The scale should be easy to use. Don’t do something weird like 1 cm = 7.34 N etc.
Show here your calculation of the length of force A. Show using the factor-label method (required ! ! !).
Draw a new vector B, using the same scale, so that it is
parallel to the old vector B. However, draw it starting at the
other end of vector A (adding tip to tail) (see the diagram to
the right).
B
B
Note in the diagram where the measured angle is used to
make vector B on the big diagram parallel to the original
vector B. Many people do this incorrectly so think!
Imagine that you have simply picked up vector “B” on your
diagram and moved it from the "tail" or start of vector A to
the "head" or end of vector A. The original vector “B” and the
new vector B should be parallel.
Draw in a new vector that starts at the beginning of the first
vector (A) and ends at the head of the second vector (B). This
represents the “vector sum” or “resultant” of these two
vector forces:
( A + B ) which is defined here as vector R.
C
A
B
C
R = Resultant
B
A
“R” stands for “Resultant” or vector sum.
If everything has worked out right, this represents a combined (Resultant) force that the third force (C) must
cancel (since the whole thing remained stationary). That means it must satisfy two conditions:
1) Our resultant force R = A+B must be the same size as the third vector (C), and
2) must point in the opposite direction from the third vector (so that A+B will cancel out C).
PUT ALL YOUR NUMBERS ON THE BIG SHEET: Angles, scale, force in Newtons
Force Table Vectors Lab
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Q1: From the length in centimeters of vector R, calculate the Resultant force in Newtons using your scale
factor. Show here using the factor-label method (required).
Q2: Calculate the percent difference between this and the third force in Newtons (vector C). This is calculated
by subtracting the two values (in this case, Force R minus the third force C) and dividing by the average of
the two values (R and C). Then multiply by 100 to convert to %. Take the absolute value. It is customary
to round up,droping all digits to the right of the decimal (15.24% becomes 16% and 7.34% becomes
8% for example) unless the value is less than 1% (then round up to one digit so 0.521% becomes
0.6%).
Put this % difference formula in your notes.
Q3: Draw a detailed sketch of the diagram on the big paper here, including all data. Measure and record here
(and on the big paper) the angle between vector R and vector A. Measure and record the angle between
vector “A” and vector “C”. Show in the diagram below how you would use these angles to show that
vector R and the vector C are colinear, but opposite directions, to each other. Use percent error to show
how close your numbers are to a perfect situation (what angle would they be to each other directly
opposite?) Include labels!
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Conclusion: Do our three measured vectors cancel out? How do you know? Summarize the logic and
quote the necessary numbers to back up your conclusion. Remember, do not expect ‘exact’ results.
DO
THIS IN YOUR LAB BOOK AS WELL AS THIS SHEET.
By the way, note how this question repeats the question or problem stated in the Purpose at the beginning of the
lab. I won’t always put a clearly worded conclusion question at the end since I expect YOU to read the purpose
and respond to it in the conclusion !
Turn in the 8.5”x11” paper and the large paper with these lab instructions (and answered questions).
Fold the large paper so that it is about the same size as this page, and write your names on the outside! This will
make it easier for me to grade (and a happy graders gives better grades)!
Force Table Vectors Lab
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