Experiment # P205 General
College Physics I
Dr. S.F. Ahmad
Force Table and Vector Addition
Name:
Group Names:
Object: To demonstrate that forces
can be represented by vectors and that when equilibrium is achieved the vector
sum of all the forces acting on an object is zero.
Apparatus: Force Table with three pulleys, ring, string
and weights.
Theory:
We will be applying
different forces to the center ring by means of weights attached to
strings. The magnitude of each force on
the string is given by the weight attached and the direction is the as the
direction of the string. At equilibrium
the ring is stationary and at the center of the round table.
Observations:
Part I: Observations
to be recorded in Table I:
1. Place a pulley at the 10o mark
on the force table and attach a
total mass m1 of 0.100 kg at the end of the string. Record this as force F1
= m1g.
1.
Place a second pulley at the 100o mark and attach a total
mass m2 of 0.200 kg at the end of the string. Record this force as F2
= m2g.
2.
Place a third pulley at an angle
J and attach a mass M to
it. By trial and error adjust
J and M such that the ring is
in equilibrium. The ring is in
equilibrium when it is centered on the table and a small amount of displacement
by hand will always bring it back to the center. Record
J, and the resultant force R = Mg.
4. Check the angular uncertainty by observing how large a
change you can make in the position of a pulley without detectably upsetting
the equilibrium. Record this uncertainty
DJ.
TABLE
I
|
m1
= |
F1
= |
R sinJ
=
|
|
|
m2
= |
F2
= |
R
cosJ = |
|
|
M = |
R =
|
|
|
|
J = |
|
R
sin(J +
DJ)
= |
|
|
DJ = |
|
R
cos(J +
DJ)
= |
|
Part I Calculations:
Graph I: Draw the three force vectors obtained F1,
F2, and R, nose to tail according to the rules of vector addition.
Note any discrepancy and comment.
Graph II: On a graph paper draw rectangular coordinates with the origin
assumed to be at the center of the force table. From Table I plot the x and y
components of the three forces. You may take F1 to be along the
x-axis, and F2 to be along the y-axis. Then you will have to resolve only R along
the two axes. Keep track of the signs of
the components.
Q.1. Is the vector sum equal to zero.
Look at Graph 1 and also evaluate the deviation from zero by calculating
(m1 – m3 sinq) and (m2 – m3 cosq)
from your table. These quantities are
proportional to the x and y components of the resultant force.
Q.2. Compute
(m3 sin(q +Dq) – m3 sinq)
and (m3 cos(q
+Dq) – m3 cosq). Can these uncertainties account for the
non-zero values of the components of the resultant force?
Part II:
Observations to be recorded in Table II:
1.
Arrange the force table as shown in Fig. Determine the values of the angles
a
and
b that give equilibrium. Enter values and other information required
in Table II below. Note that the masses
given should include the weight-holders.
|
.300 kg
|
|
.200 kg |
|
.400 kg |
|
X |
|
Y |
|
a |
|
b |
|
a = |
b = |
|
0.200 (9.8) sin
a = |
0.300 (9.8) sin
b = |
|
0.200 (9.8) cos
a = |
0.300 (9.8)cos
b = |
|
Da = |
Db = |
|
0.200 (9.8) sin(a +
Da) = |
0.300 (9.8) sin(b
+
Db) = |
|
0.200 (9.8) cos(a +
Da) = |
0.300 (9.8) cos(b
+
Db) = |
RESULTS: Report
your results in a brief statement.
Sources of
Error: Write down the sources of error in this experiment.