Lab 1 – Introduction To Numerical Methods
Purpose: The purpose of the lab is to practice the introduction of analytic techniques, so we can
refer to them throughout both physics labs.
Introduction: In lab 1 we are going to be practicing analytic techniques, that are widely used all
throughout physics. First, we will calculate the volume of a tabletop from the measurements
given, and then create a data table. Once our data table is complete, we will then use this
information to plot two graphs. After the data is plotted on the graphs, we will then analyze the
calculations and apply what we learned to a few questions. Lastly, once we have applied what
we learned we can then make any conclusions that may have developed from this lab.
Reflection:
1. Out of all the three cases, the cases that was affected the most was the height and the
case that was affected the least was the length. This is because the error in height 5.05
cm^3 is less in length which gives it a greater volume and percent error. Whereas the
error in length 150.05 cm^3 is greater in length which gives the volume and percent
error a lesser value than height.
2. For the perfect case the exact volume was 37,500 cm^3 and the rounded volume was
38,000 cm^3, there is a significant volume difference between the two. For the perfect
case the percent error using the exact volume was 0% and the percent error using the
rounded volume was 0%, there is no difference between the two. For the error in length
case the exact volume was 37,512.5 cm^3 and the rounded volume was 38,000 cm^3,
there is a significant volume difference between the two. For the error in length case the
percent error using the exact volume was 0.033% and the percent error using the
rounded volume was 0%, there is only a tiny difference between the two. For the error
in width case the exact volume was 37,537.5 cm^3 and the rounded volume was 38,000
cm^3, there is a significant volume difference between the two. For the error in width
case the percent error using the exact volume was 0.10% and the percent error using
the rounded volume was 0%, there is only a tiny difference between the two. For the
error in height case the exact volume was 37,875 cm^3 and the rounded volume was
37,900 cm^3, there is a significant volume difference between the two. For the error in
height case the percent error using the exact volume was 1.00% and the percent error
using the rounded volume was 0.263%, there is only a slight difference between the
two. I noticed that when not rounding the significant digits for error in height makes the
value of height greater the error in width and length, and the perfect. I also noticed that
rounding the significant digits for the error in height makes the values less than the error
in width and length case, and the perfect case. After observing the data, I feel the best
method is to use the error in height method, because there is less of a difference
between the exact volume and rounded volume, which will give you a more accurate
percent error.
Purpose: The purpose of the lab is to practice the introduction of analytic techniques, so we can
refer to them throughout both physics labs.
Introduction: In lab 1 we are going to be practicing analytic techniques, that are widely used all
throughout physics. First, we will calculate the volume of a tabletop from the measurements
given, and then create a data table. Once our data table is complete, we will then use this
information to plot two graphs. After the data is plotted on the graphs, we will then analyze the
calculations and apply what we learned to a few questions. Lastly, once we have applied what
we learned we can then make any conclusions that may have developed from this lab.
Reflection:
1. Out of all the three cases, the cases that was affected the most was the height and the
case that was affected the least was the length. This is because the error in height 5.05
cm^3 is less in length which gives it a greater volume and percent error. Whereas the
error in length 150.05 cm^3 is greater in length which gives the volume and percent
error a lesser value than height.
2. For the perfect case the exact volume was 37,500 cm^3 and the rounded volume was
38,000 cm^3, there is a significant volume difference between the two. For the perfect
case the percent error using the exact volume was 0% and the percent error using the
rounded volume was 0%, there is no difference between the two. For the error in length
case the exact volume was 37,512.5 cm^3 and the rounded volume was 38,000 cm^3,
there is a significant volume difference between the two. For the error in length case the
percent error using the exact volume was 0.033% and the percent error using the
rounded volume was 0%, there is only a tiny difference between the two. For the error
in width case the exact volume was 37,537.5 cm^3 and the rounded volume was 38,000
cm^3, there is a significant volume difference between the two. For the error in width
case the percent error using the exact volume was 0.10% and the percent error using
the rounded volume was 0%, there is only a tiny difference between the two. For the
error in height case the exact volume was 37,875 cm^3 and the rounded volume was
37,900 cm^3, there is a significant volume difference between the two. For the error in
height case the percent error using the exact volume was 1.00% and the percent error
using the rounded volume was 0.263%, there is only a slight difference between the
two. I noticed that when not rounding the significant digits for error in height makes the
value of height greater the error in width and length, and the perfect. I also noticed that
rounding the significant digits for the error in height makes the values less than the error
in width and length case, and the perfect case. After observing the data, I feel the best
method is to use the error in height method, because there is less of a difference
between the exact volume and rounded volume, which will give you a more accurate
percent error.
