PHY 2091 Stetson University Vector Addition and Components Lab Report lab report in physics about Vector Addition and Components.>>>>>>>>>>>>>>>>>>>>>>>>>>

PHY 2091 Stetson University Vector Addition and Components Lab Report lab report in physics about Vector Addition and Components.>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Exp. Title:
Student Name:
Date:
Setup 1
A
B
C
Setup 2
A
B
C
Setup 3
A
B
C
Mass (g)
115
105
160
Mass (g)
135
240
105
Mass (g)
305
205
n/a
Angle (°)
181
271
44
Angle (°)
45
270
163
Angle (°)
359
116
219
Uncertainty (M): Uncertainty (∠):
±10g
±0.5°
Force (N)
Force (N)
Force (N)
Fx (N)
Fy (N)
Total Fx (N)
Total Fy (N)
Fx (N)
Fy (N)
Total Fx (N)
Total Fy (N)
Fx (N)
Fy (N)
Total Fx (N)
Total Fy (N)
|Error Vector| (N)
|Error Vector| (N)
2.7
|Error Vector| (N)
components that point to the right are positive and vector y-components that point to up are
positive. In Figure 6 the x-component A, equals the magnitude (length) of vector-A multiplied
by the cosine of the angle theta. The y-component A, equals the magnitude (length) of vector-A
multiplied by the sine of the angle theta. This is only true because the polar angle theta
(measured counter-clockwise up from the positive x-axis) is used. When an angle is defined
relative to a different axis, one can have x-components associated with the sine of the angle and
so on.
y component: Ay
x-component: A
Figure 6.
We use the word equilibrium a great deal in Physics. The everyday usage of this word is
basically the same in physics. If two vectors are in equilibrium, they ‘balance each other out.
In this case, the sum of the two vectors is zero. The same is true for three or more vectors acting
on an object at the same time. Later, we will learn that when an object has no acceleration, the
sum of all the forces acting on it add to zero. Therefore, equilibrium of forces comes to mean a
situation where the acceleration is zero. An object can have zero acceleration if it is not moving
at all and also if it moves with constant velocity. We distinguish between these two situations by
adding the word static to mean not moving. Hence, static equilibrium means all the forces add
to zero and the object is not moving.
Method
In this experiment, you establish static equilibrium between three, coplanar, concurrent
forces using the Pasco Mechanics Board shown in Figure 1. The forces are exerted on a small
metal or plastic ring via three pieces of sewing thread. The thread runs over pulleys and ties to
small, calibrated weights, which hang from the pulleys. Sometimes a spring scale is used to
apply the force. Static equilibrium occurs when the ring doesn’t move.
The apparatus contains two analog scales (.e. non-digital): a spring scale and an angle
scale. Since you will read each of these scales only once, you cannot compute an average or
standard deviation, so you must estimate the associated error. In this case, a good estimate is
plus or minus one half of the smallest scale division. When the measuring tool has a digital
display, it is common to take the random error in measurement as #1 in the last digit of the
display. The same error arises in reading or setting the zero of a scale. Of course, if you forget
to zero, say a spring scale balance, then this leads to a systematic error in measurement.
2-2
8)
Discuss with your lab partner(s) the major sources of experimental error. Record the
results of these discussions on your data sheet.
9)
Repeat the previous procedures for Figure 2. This time a different lab partner must take
the lead in setting up the board and making the measurements.
10)
Perform a third trial using Figure 3 as the guide. Keep the angle between each force
vector equal to about 120 degrees. If you are working in a group of three, once again a
different lab partner must take the lead in setting up the board and making the
measurements.
11)
Regardless of the size of the lab group, each person must have three vector addition
diagrams by the end of the lab period. Don’t forget to write the names of all students on
all sheets of paper as well as the date and the section number. Before you leave, show
your work to your instructor and obtain his or her signature on each sheet of paper.
12)
Reminder: In your report list and categorize all realistic sources of error. Also, discuss
how they relate to the error analysis performed.
13)
Further Data Analysis: For each arrangement of the mechanics board, resolve all forces
applied to the plastic ring into x and y components. Determine whether adding
components satisfies the condition for equilibrium to within 5%. Describe (in words) the
relationships between the magnitudes and components of the applied forces in Figures 1
and 2. Also, was the magnitude of the error vector drawn on each graph paper less than
the overestimate of the error in the total force acting on the plastic ring?
14)
For Your Discussion: To appreciate how error propagation can sometimes mushroom
into a large chore, consider adding two vectors (A and B) to give a third vector C.
Suppose errors in the x and y components of A and B are known: 0 Ar, Ay, OBx and O By
How does one propagate these uncertainties to obtain the error in the magnitude of
vector-C? The answer follows. Explain which parts of the last line corresponds to which
of the mathematical operations in the second-to-last line. Refer to the large table of error
propagation formulas in Appendix C.
C = A + B = (4. + B* +(4+B.)3
la=|14
, +)’ +(, +BYTE
V|2(4, +B.),po tom} + {{2(4, +B). Jom, +0%,
27
na
2-4
Procedure
1)
First, listen as your instructor delivers a brief introduction to the topic of error
propagation, which is explained more fully in Appendix C.
2)
Set up the Pasco Mechanics System similar to Figure 1.
a) Obtain three long pieces of string from the single dispenser in the room. The black
string is upholstery thread, which is surprisingly strong.
b) For each string, tie a large, loose loop around the rigid plastic ring as shown in Fig. 7.
Make sure the knot does not slip. Do not tie strings tightly to the plastic ring. The
loop should be able to slide along the ring as the string’s position moves.
c) Set-up the mechanics board as in Figure 1. Use different masses in the hangers of at
least 100+ grams. Make certain the string pulls parallel to the plane of the Mechanics
board.
knot
large loose loop
plastic ring
Figure 7.
3)
Establish static equilibrium of the plastic ring by adjusting the masses and moving the
angle scale. Test for equilibrium by nudging the plastic ring. It should return to the
center of the angle scale. Note: Forces should be recorded in Newtons. Remember to
convert all the applied masses into equivalent forces.
4)
Determine the uncertainty in the magnitude of the tensions due to hanging masses by
adding enough extra mass to the hanger to make the plastic ring pull away from
equilibrium. Remove the extra mass and return the set-up to equilibrium. Adding all of
the amounts of extra mass (converted to Newtons) is an overestimate of the error in the
total force acting on the plastic ring. Despite this, add the force equivalents of the extra
masses.
5)
Measure and record the magnitude and angles of all forces.
6)
(Note: This procedure may be completed at home after the experiment has ended.) Using
the graph paper provided, draw a large vector diagram showing how well the three force
vectors add to zero. First, draw a set of x and y axes with the origin near the center of the
page. Then, draw one vector with its tail at the origin and graphically add the other
vectors tail-to-head. Draw the diagram to scale. Pick a round-number scale so the
longest vector is about 4 cm.
7)
If the vectors don’t sum to zero, draw a small vector to close the polygon. Label this the
“error vector”. Determine the length of the error vector (in Newtons).
2-3
2-5

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