• Open the
Logger Pro file
for today. Record the results of the subsequent motion after a
push down the track until you are satisfied that you have a good set of
four graphs: x, v, θ, and ω, all vs. t. The shapes of the curves
should be parabolic or linear.
• As in the past, fit straight lines using the Linear Fit
routine to the v(t) and ω(t) graphs to get a value for the
accelerations of the cart, a
v and α
ω.
Define a range covering
most of the x(t) parabola. Open the Curve Fit routine.
Choose the At
2+Bt+C option for the General Equation, and
click the Try
Fit button, then OK. Note that the “A” in the Logger Pro equation
is not divided by 2, whereas the “a” (or “α”)
in the kinematics expression for
x(t) is. These are the accelerations a
x and α
θ.
Enter the
four experimentally determined values of acceleration into the table in
Question 5 of the worksheet. All the yellow boxes of the table of
Question 5 should now be filled.
• Position the data boxes on your graphs and size the
graphs such that the data themselves and the contents of the data boxes
can be easily read. Copy and paste the graphs into Question
4 of your worksheet.
• Use the expression that you found for Question 2 to find
the acceleration as predicted by Newton, a
N.
• With your knowledge of the relationships among the
translational and rotational variables and assuming that the “no-slip”
condition applies, calculate the translational acceleration a
ω
from
the rotational acceleration α
ω,
and likewise a
θ
from α
θ.
Enter
these into the table.
• You should now have five different values for
translational acceleration in your table, one predicted from Newton’s
Second Law, two from the direct translational measurements, and two
indirectly from the rotational measurements. They are the ones in
the bold cells in the worksheet: a
N, a
v,
a
ω,
a
x, and a
θ.
Average them, find their
standard
deviation and their fractional
uncertainty (standard deviation divided by the average), and enter
these values into the table. Your fractional uncertainty should
be less than 0.100.
• There remain two questions on the worksheet for you each
to answer individually.