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In these graphs, we initially graphed acceleration versus mass
in order to find the relationship
between both. In order to get a linear trend, we then took the
log of both acceleration and mass
and then graphed the log (acceleration) versus the log (mass),
which finally linearized the data.
In order to show the relationship between them both, we them
graphed Acceleration versus the
inverse of mass.
Mass (kg)
0.002
Acceleration (ms-2)
T1 T2 T3 Avg.
0.521 0.5118 0.5340 0.5120 0.5193 0.0111
1.521 0.1678 0.1812 0.1697 0.1729 0.0067
1.669 0.1286 0.1402 --------- 0.1344 0.0058
1.866 0.1401 0.1427 0.1434 0.1421 0.0017
2.866 0.0614 0.0641 0.0627 0.0627 0.0014
This is the final data table which shows the mass of the cart
and then the acceleration which it
showed. In order to collect this data, we used the Video
Analysis part of Logger Pro and created
points on which it could track and take the data for us.
Evaluation:
There were many limitations that could have halted our results
from being perfect. The
first was the timing of when the car finally reached the end of
the track, which could have
skewed the average acceleration. After that when we were
measuring the weights, although they
were already written on their, some of them were hollow and
contained space for metal beads
which gave the weight; weight! If some of these metal beads were
not in the container, then the
weight of the cart could be partially messed up. Other than
that, maybe when we were tracking
the cart on logger pro we may have missed the ball by a few
marks.
In order to improve this lab, the first thing that we could have
obviously done was taken
more experiments. Unfortunately, we did have a time constraint,
and did not have a large amount
of time (which was fine). Also, maybe using consistent types of
weights and a much more
precise ruler could have helped. Since the weights as I stated
above were a little bit varied, using
the same type that were all metal would have made the data much
more consistent. Also, the
meter stick in the background may have been tilted or angled,
and may not have given a true
impression of what exactly the meter was (on the video
analysis).
In order to find the relationship Fnet = MA, we had to find the
inverse of mass. Finding
the inverse of the mass showed that the relationship between the
net force and the mass times the
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acceleration was inversely proportional. This can also be proved
by what exactly a Newton of
force is:
Also, since Newtons formula F = ma can also be re written to
equal acceleration like so:
So, in order to get to this step it is necessary to multiply the
force (net) by m-1
or simply
1/m. The third graph that we plotted is simply doing this with
the linearized data, and is the clear
evidence of this relationship. This finally shows that the
larger the force on the smaller mass of
something leads to more acceleration being applied. The smaller
the force on the more massive
of the object leads to less acceleration being applied to the
object.
