# Composition and Resolution of Vectors Lab

Document Sample

```					                                                           Forces Lab
Source: Zober and Zober

One report per group is required. Each group member should complete part of the lab work and everyone should review the final
product before it is turned in.
Due one week after lab is performed.

Introduction:
Scalar quantities are those that may be completely described by giving the magnitude of the quantity, such as length, mass, or density.
To completely describe a vector quantity such as velocity, force, or displacement a direction as well as a magnitude is needed. The
question “What direction?” is as important as the question “How much?” A vector may be represented by a straight line segment
drawn from some origin, with the length of the line proportional to the magnitude of the vector and the direction of the line
represented by the tip of an arrow pointing in the direction of the vector.
Vectors maybe combined graphically or analytically. The operation of adding vectors graphically consists of drawing one vector with
appropriate length and direction, and from the head of this vector, another vector is drawn with appropriate length and direction, and
so on, for as many vectors as are present. The straight line drawn from the origin to the head of the last vector represents the sum of
the vectors and is called the resultant.
y

C
R
B
A
x

The best way to add vectors analytically is to break each vector into its x and y components. Using sin, cos, tan or their inverses will
be helpful. Once all the x and y components for each vector have been calculated, add all the x’s to create a final x component. Do
the same with the y’s. Once a final x and y component have been created, add them head to tail and use the Pythagorean Theorem to
resolve the resultant vector.

Materials:
 Force table
 String
 Weights

Procedure:
Note the following tables. Force units are dependent upon the system in use. In the SI, the unit is the Newton, N. The English unit is
the pound, lb. In this experiment we are going to invent a force unit called the gram force that we will abbreviate as g-force. We
define the force unit as the force produced by a one-gram mass.

Table 1: Two Forces
Problem Number                       F1                                    F2
No                                   g-force                               g-force
1                                    200@ 0 degrees                        150@ 75 degrees
2                                    150@ 0 degrees                        250@ 300 degrees
3                                    150@ 20 degrees                       150@ 120 degrees

1.   You will be working in groups of 3. One report per group.
2.   Choose two problems from Table 1.
3.   Apply the weights in grams (g-force) as the problem states. For example, if the problem states “200@ 0 degrees and 150@
75 degrees” then place a 200g weight at the end of one string lined with the 0 degree mark and place a 150g weight at the end
of another string lined with the 75 degree mark. Set the center ring on the pin in the middle of the force table. You should
have 3 pulleys, two for the known forces from Table 1, and one for the equilibrant/balancing force. Remember that the
equilibrant will “balance” the known forces. We say that if the forces and equilibrant balance then the system is in a State of
Static Equilibrium.
4.   You will notice that the center ring which holds the strings is not in equilibrium. This is because the two weights are not
equal and opposite. The goal of this lab is to bring the center ring into equilibrium. Starting at 0 degrees, move and position
the pulleys in a counterclockwise manner. Set and “lock” each pulley at the given angle.
Groups on the hall side of the room:
5.   To bring the center ring into equilibrium, you first need to find the resultant g-force vector created by the two strings/g-forces
F1 and F2. To do so, make an x y coordinate on a sheet of paper and draw the g-force vectors F1 and F2. Use the analytical
method to find the resultant vector (xy-table).
6.   The resultant vector is telling you the direction and magnitude affecting the center ring. Thus to balance the center ring, you
need to add a weight/magnitude equal to the resultant vector but in the opposite direction. This is your equilibrant vector.
7.   After analytically calculating the equilibrant vector, test it experimentally to see if it causes the center ring to enter a State of

Groups on the window side of the room:
5. Place the table g-forces on the force table and experimentally determine the
equilibrant vector (the g-force that allows the ring to be centered over the center
pin). Note the angle and mass of your equilibrant vector.
6. To check your experimental finding, calculate the equilibrant vector by first
adding the g-force vectors in an xy-table to determine the resultant vector.
Determine the equilibrant vector by keeping the magnitude of the resultant vector
and adding 180o to the direction. This is the calculated equilibrant vector.
All groups:
8. Make sure all your work is done neatly on a sheet of paper.
9. Repeat the procedure for your second problem from Table 1.
10. After completing two problems from Table 1, pick two problems from Table 2. Find the equilibrant force for these problems
as well, switching your method from the one you used for Table 1.

Table 2
Problem Number               F1                          F2                             F3
No                           g-force                       g-force                      g-force

1                            200@ 0 degrees                200@ 60 degrees              150@ 120 degrees

2                            250@ 0 degrees                150@ 100 degrees             200@ 210 degrees
3                            200@ 20 degrees               200@ 90 degrees              200@ 150 degrees
4                            200@ 30 degrees               200@ 135 degrees             250@ 220 degrees

Include an Introduction section to your lab-write up. Mention the purpose of this lab, the physics concepts involved, how this
information can be used in practical applications and a brief procedure summary. Provide at least 2 examples of balancing forces.
Also, include a Data section. It should include diagrams (on paper, well-labeled) of your force diagrams. For your Conclusion