STATIC EQUILIBRIUM
Skylur Jameson
2 April 2009
Experiment # 6
Purpose:
The purpose of the experiment is to analyze a system that is in static equilibrium.
Equipment: Rod, clamps, pulleys, string, weights, weight holders, level, and protractor.
Discussion:
The lab is designed to study the system in static equilibrium. In order for a system
to be in static equilibrium it will need to follow the equations:
∑ Fx = 0
and
∑ Fy = 0
By using each of these condition equations, we will be able to calculate the
unknown mass in a system that incorporates three different masses.
Procedure:
To begin the experiment set up three different sets of masses, hanging each at
different heights, using the rods, clamps, and pulleys available. Also, in order to
have a successful experiment avoid the condition where m1 = m2. By eliminating
this case, our equipment will not be more accurate and helpful. To calculate the
angles of theta as well as the third elevators actual mass, use the free body
diagram and the equations:
m2*cosθ2 = m1*cosθ1 and
m1*sinθ1 + m2*sinθ2 = m3
Lastly, in each trial run compare the calculated mass with the actual mass by
computing the percent error where the experiment minus theoretical is divided by
the experimental value.
Observations: The steel rods were touching the ground so that the system could hang below
the table. At times the elevators were quite wobbly. The pulleys were not
always at exactly equilibrium when were measured everything. The angle was
difficult to read because of the strings position to the table. The protractor could
have been read wrong because of the difficulty of reading it using the level. The
elevators were not below the table with the trials. Using the level helped
measure more accurate measurements. If a weight had more weight on it then
the angle was affected and the measure could have varied.
Conclusion:
In conclusion, the experiment was very instructive and successful because it
helped explain how a system involving three different masses can be at static
equilibrium. After measuring the angles and weighing the masses used in the
system, we were able to calculate the theoretical mass as well as the percent
error present in each of the three trials occurring in the experiment. We found
that for each of our calculated masses for the third elevator were within the
range of less than five to the experimental mass for each mass. This led us to
have a percent error of 1.9, .06, and 2.1 percent for each corresponding trial. If I
had to add some criticism for the static equilibrium experiment would be that I
would have like to have done it alongside an experiment involving kinetic
equilibrium. In the end, I concluded that this experiment was one of the more
enjoyable experiments that we have done so far. It helped my understanding of
what exactly the different is between static and kinetic equilibrium.
Trial
1
2
3
Trial
1
2
3
m1 (g)
150
150
100
m1 (g)
150
150
100
theta1 (degree) Radians1
74
1.29
64
1.12
66
1.15
theta1 (degree)
Radians1
74
=RADIANS(C2)
64
=RADIANS(C3)
66
=RADIANS(C4)
m2 (g)
160
420
220
m2 (g)
160
420
220
theta2 (degree)
78
81
78
Radians2
1.36
1.41
1.36
m3 calc. (g) m3 actual (g) % error
301
295
1.93
550
550
0.06
307
300
2.18
theta2 (degree)
Radians2
m3 calc. (g)
m3 actual (g)
% error
78
=RADIANS(F2) =(B2*SIN(D2))+(E2*SIN(G2)) 295
=ABS((I2-H2)/I2)*100
81
=RADIANS(F3) =(B3*SIN(D3))+(E3*SIN(G3)) 550
=ABS((I3-H3)/I3)*100
78
=RADIANS(F4) =(B4*SIN(D4))+(E4*SIN(G4)) 300
=ABS((I4-H4)/I4)*100