8/10/2019 Torsion Discussison
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Discussion:
Part 1:
In part 1, steel rods of vary lengths were subjected to 1, 2, 3,
4 and 5 Newtons of force in
order to induce an angular deflection on the beam. The model
function for thisapplication of force, as previously stated, is
where g is a constant property of the material. In the case of
steel, this is quantified as
79.6GN/m^2. From this relation, we expect the gradient of a plot
of TL vs Jto be g. Theerror associated with the plot can then be
estimated as the deviation of the gradient from
g. A sample calculation is provided for the case of L=0.300
m:
[ ]
Similar calculations were carried out for the other lengths of
the beam to obtain the
following table:
Length (m) Accepted Experimental % error
0.5 79.6 70 12.0603
0.45 79.6 30 62.31156
0.4 79.6 30 62.311560.35 79.6 40 49.74874
0.3 79.6 50 37.18593
it appears that when the rod was adjusted to lengths of 450 and
400 mm that maximum
error was recorded, which may serve as an indication that these
trials involve some sort
of calibration error, which was suspected due to the age of the
apparatus. The best
accuracy was achieved during the first trial of the experiment,
where a fixed length of
500 mm was used for calculations. A source of error associated
with this lab is the
gradual wear of the steel rod that was used. We do not consider
the elastic deformationthat the rod undergoes after each
application of a load, which accounts for the higher
error in subsequent trials. Another point worth noting is while
g was taken to be 79.6 for
steel, each piece of steel has a different composition of
elements that influence the
individual strengths of the steel. Because of this, the value
that was chosen as the
accepted value may vary.
8/10/2019 Torsion Discussison
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Part 2:
From the model function, we observe that the angular deflection,
theta, is directly
proportional to the length of that rod L. From this relation, we
predict that as the length of
the rod increases while T is kept constant, the angular
deflection will increase as well. In
practice, this becomes a point in consideration when designing
structures that are subjectto frequent torsion forces. In order to
minimize the angular deflection associated with the
applied load, a smaller length is desired for the shaft or rod.
This is exemplified by the
vary lengths of the drive shaft in front wheel drive vehicles.
In order to minimize the
effect of the additional applied torque while steering, one
could minimize the length of
the shafts or break it up into more pieces.
Analysis of the model function predicts that a plot of theta vs
L should give a gradient of
T/(gJ). In the case of a constant torque of 0.15 Nm, this
simplifies to:
( )
This value will be used to measure the error the plot of theta
vs L. From the plot, we
obtain a gradient of 0.363 based on trend line calculations. The
error is calculated as
||
This large value confirms previous suspicions regarding the
accuracy of the apparatus.
Due to the errors in the measurements for each length of the
rod, the overall result is a
large deviation from the predicted slope as evidenced by the
high degree of error.
