SAMPLE LAB REPORT – PHYSICS 105
Lab Partners: Josephine Physics
Mad Max
Sept 15, 2013
ACCELERATION AND FORCE DUE TO GRAVITY
ABSTRACT
The objective of this lab was to demonstrate Newton’s equations for gravitational
acceleration and force. We measured these factors by dropping apples from a specified
height and measuring the time necessary to fall to the ground as well as the instantaneous
force when the apples hit the ground. Our experimental acceleration values were all
within 2% of the expected value of 9.8 m/s2. Our experimental force values were all
within 4% of the values expected by Newton’s 2nd law of motion.
INTRODUCTION
Tradition has it that Isaac Newton developed his theory for
gravity after being hit on the head by an apple falling from a
tree. (Figure from Ref. 1) While he may not have actually
been hit on the head there is some truth that watching apples
fall did help inspire his theory.2
"After dinner, the weather being warm, we went into the
garden and drank thea, under the shade of some apple
trees...[Newton] told me, he was just in the same situation, as when formerly,
the notion of gravitation came into his mind. It was occasion'd by the fall of
an apple, as he sat in contemplative mood. Why should that apple always
descend perpendicularly to the ground, thought he to himself..."
Comments
About
Format
Abstract:
- objective
- method
- key results
Should be short
and concise
Introduction:
Discuss the
science
that is being
explored in
the lab.
Reference
citations
needed for
anything taken
from elsewhere,
including
literature values
and artwork.
Newton’s 2nd Law of Motion says that force depends on mass (m) and acceleration (a)
F = m*a
(1)
Therefore the force of the apple striking Newton’s head depended on the mass of the
individual apple that fell from the tree.
(2)
You should
number the
equations so
you can refer
to them by
number later.
(3)
Make sure to
define all
variables in the
equations.
On the other hand, his theory of gravity says that the acceleration that contributes to
gravitational force is the same for all objects irrespective of mass. This acceleration is
the gravitational constant (g)
a = g = 9.8 m/s2
The general equation of motion is:
x(t) = xo + vo*t + ½ a*t2
where x(t) is the position at some time t, xo and vo are the position and velocity at
time=0, and a is the acceleration. If we define xo=0 and vo = 0 for the apple initially at
rest, and it takes time=t to fall from a height h, then the acceleration is given by:
a = 2h / t 2
Gentry, 2013
Introduction
should also
present key
equations.
(4)
PROCEDURE
In this experiment we mimicked Newton by dropping apples with different masses.
We kept the starting height constant at a value of 0.50m. For Part A we used a
DataStudio motion sensor located above the apple to measure the location of the apple
as a function of time as the apple fell to the ground. We did this analysis three times
for each apple, and then repeated the overall procedure for a total of 3 different apples
with different masses. For Part B we replaced the motion sensor with an impact sensor
which measured the force of the apple when it hit the ground. As with Part A, we
measured each of the three apples three times, all at the same height of 0.50m.
RESULTS
Part A. Acceleration Due to Gravity
Our first apple weighed 0.215kg. The graph below shows the results that we
obtained when we dropped the apple from a height of 0.50m.
215g Apple Dropped from 0.5m
0.6
Procedure:
Need enough
details for
reader to be
able to
understand
what you did,
but you do not
need to
provide details
on how to run
DataStudio
equipment.
Results:
- raw data
- how you
analyzed the
data
- your calculated
results
- discussion
about
implications of
your results
Time To Fall = 0.42 - 0.12 = 0.30 s
Position (m)
0.5
If instructor so
instructs then
you can show a
representative
graph rather
than every
single graph that
you collected.
0.4
Apple
Hits Ground
0.3
0.2
Apple
Dropped
0.1
0
0
0.1
0.2
0.3
0.4
0.5
Time (s)
From an analysis of the DataStudio data we determined that it took 0.30 seconds to
fall to the ground. This analysis required first removing the data at the beginning
before the apple had been allowed to fall, and then the data at the end when the apple
had hit the ground but the computer was still logging additional data points.
Table 1 shows the results obtained when the three different apples were dropped
multiple times from a height of 0.500m. The experimental acceleration values were
obtained by substituting a value of h=0.500m and our average times into Eqn. 4.
Need to
describe how
you calculated
results from
your raw data.
Can refer to
earlier
equations by
Eqn. number.
Table 1: Time as a Function of Varying the Mass of the Apple
Mass
Apple
(m)
Time
Trial #1
(s)
Time
Trial #2
(s)
Time
Trial #3
(s)
Average
Time
(s)
Experimental
Acceleration
(m/s2)
Theoretical
Acceleration
(m/s2)
0.215
0.286
0.335
0.34
0.28
0.32
0.29
0.33
0.35
0.34
0.345
0.3
0.32
0.32
0.32
9.6
9.9
9.7
9.8
9.8
9.8
Make sure to
include proper
units on all
tables.
According to Newton, all of the trials should have had a theoretical acceleration of
9.8m/s2 irrespective of mass. The data demonstrate that all of the samples had
experimental accelerations very similar to the expected value -- varying the mass of
the apples had no effect on acceleration. Differences from the theoretical value may
have been due to frictional forces for the apple falling through the air. There may
also have been instrumental errors in that the apple might have hit the ground inbetween sampling points, thus giving the wrong falling time.
Make sure you
discuss the first
set of results
before going on to
the next part of
the experiment.
Don’t just give the
numeric results.
Discuss what the
numbers mean.
Part B. Force of Impact
In the second part of this experiment we replaced the motion sensor that was measuring
position with an impact sensor to measure the instantaneous force when the apple
struck the ground. We did this with the same 3 apples used earlier. The experimental
values for the impact force were taken directly from DataStudio.
Table 2 presents the data that were obtained by dropping each apple from the same
height of h=0.500m. The theoretical forces were calculated using Eqn. 1 and an
acceleration of a=9.8m/s2.
Table 2: Force of Impact as a Function of Varying the Mass of the Apple
Mass
Apple
(m)
Force
Trial #1
(N)
Force
Trial #2
(N)
Force
Trial #3
(N)
Average
Force
(N)
Theoretical
Force
(N)
0.215
0.286
0.335
1.86
3.12
3.26
2.25
2.76
3.11
2.43
2.85
3.25
2.18
2.91
3.21
2.11
2.80
3.28
Newton’s 2nd Law of Motion (Eqn. 1) says that the force at impact depends on mass and
acceleration. The data in Table 2 demonstrate good correlation between the
experimentally determined impact forces and Newton’s theoretical impact forces.
Deviations may be due to the apple not striking the center of the impact sensor and hence
the instrument not measuring the correct force. Errors in the data may also have been due
to the apple not being a hard sphere when it hit, but instead was a soft, deformable object.
CONCLUSION
Our experimental results successfully demonstrate that the gravitational acceleration of
a falling object is a constant value of 9.8m/s2 independent of the mass of the object.
That is not to say that the mass is not important. The second part of the experiment
demonstrates that while acceleration is constant, the force of impact of a falling object
does increase with the mass of the object. These observations are entirely consistent
with the laws of motion predicted by Isaac Newton in the 17th century and experienced
by his head when the apple hit it.
Conclusion:
Should discuss
overall success
of experiment,
and come back to
the broader
implications of
the science and
physics involved.
Also discuss
sources of error
if not already
addressed
earlier.
REFERENCES
1. http://www.aps.org/publications/apsnews/200908/zerogravity.cfm (accessed 9/15/13).
2. http://www.newscientist.com/blogs/culturelab/2010/01/newtons-apple-the-realstory.html (accessed 9/15/13).
Give reference
citations for any
material taken
from elsewhere.
This includes
literature values
and artwork.