Venger
Experiment Nathan 5:
Acceleration
Date Experiment Conducted : 02/22/12
PHY121 Course 23252
Abstract
The acceleration of the marble with a mass of 0.06 kg is calculated by the recording of time as it
passes a designated distance on an inclined plane. Acceleration is calculated from a = v/t.
Additionally the lab report concludes that the greater the degree above the horizontal (creating a
steeper incline) is the greater the velocity will be for the travelling object. This is explained with
F = mg(sin ). Lastly, the experiment explains unbalanced force, and why it causes objects to
travel down inclined planes.
This lab report focuses on the acceleration of a marble ball while it travels down on an
inclined plane. To understand why an object will travel on an inclined plane, it is important to
discuss Newtons First Law of Motion and the normal force.
Regarding the observations
observed for this lab Newtons First Law of Motion notes that an object will remain at rest unless
acted on by an unbalanced force. For this experiment the unbalanced force Newton is referring
to is due to the incline. To understand why an incline will result in an object having an
unbalanced force it is important to discuss normal force and what it is.
If the same marble is placed on a flat surface without an incline, it will not have travel in
any direction. The marble moves down the inclined plane because of a change in its normal
force. The normal force is the force that a surface exerts on an object with which it is contact
namely, the component that is perpendicular to the surface. Simplified the normal force is the
force acting or pushing against an object. Mathematically the normal force is expressed as:
Fn = mgcos()
For a horizontal surface the normal force is equal to the objects weight. This is because the
angle (expressed as ) is zero degrees, and the mass is multiplied by the acceleration of gravity
(mass multiplied by gravity is the objects weight). For an object on an inclined plane this is not
the case. For an inclined plane the acceleration of gravity is less than magnitude of gravity
acting upon the object; thus, as the incline of a plane increases the magnitude of the gravitational
force will decrease (upon reaching an incline of 90 degrees the object will be in free-fall). A
visual representation of this is found on Observation 1 (found in the Additional Graphs section).
It is this decrease in the magnitude of the gravitation force that results in the unbalanced force
Newton refers to in his First Law of Motion.
In addition to explaining why an inclined plane will cause an object to leave its state of
rest, Newton also rationalized what acceleration truly is. If the magnitude of gravity and the
normal force are at equilibrium the object is a rest; however, if the forces are unbalanced the
object is in motion and acceleration. Newton defined acceleration with this understanding in his
Second Law of Motion. Newtons Second Law of Motion states that the force of an object is
proportional to the mass of an object multiplied the objects acceleration. Mathematically this is
expressed as:
F = ma
This formula can be revised in concern to an object on an inclined place. The constant force
pulling all objects downward on Earth is gravity. The magnitude of gravitys force on an object
can be found through force being proportional to the mass of an object multiplied by the
acceleration gravity multiplied by sin(angle of the inclined plane).
Mathematically this is
expressed by:
F = mg(sin )
If an object is laying on a horizontal surface the angle of the incline (expressed as ) is zero
degrees. Sin(0) is zero. This states that the force of gravity on the object is nonexistent. If the
incline is greater than zero degrees, but less than 90 degrees, the force of gravity will directly
affect the acceleration of the object. Based on the above formula, as an object gets closer to 90
degrees its will travel at a greater acceleration. This experiment will help explain why.
Two tests were performed in this experiment. The first test performed concerned the
acceleration of an object as it travelled across an inclined plane. The object was a marble. The
inclined plane was a wooden bench. One end of the wooden bench was raised 0.79 meters (m).
The degree of the benchs incline was measured using a protractor at 30 o. Lengths of 0.5 m,
1.0 m, and 1.5 m were measured on the wooden bench using a measuring tape. The lengths were
delineated with duct tape at all measured points. The marble was placed at the starting point
(zero meters) and released from a static position. Upon release a stopwatch recorded the time it
took for it to reach each designated length. Five trials of this experiment were conducted.
When released the marble reached 0.5 m in 0.783 s, 0.671 s, 0.731 s, 0.768 s, and 0.639 s
respective to each trial. The average time it took the marble to travel 0.5 m was 0.7186 s. The
velocity of the marble as it crossed 0.5 m was calculated by distance divided by time. For each
trial the marbles velocity was 1.28 m/s, 1.49 m/s, 1.37 m/s, 1.30 m/s, and 1.56 m/s, with an
average velocity of 1.4 m/s.
The acceleration was calculated from this collected data.
Acceleration can be derived from an object velocity divided by the time it took to reach a
distance. From this calculation the acceleration of each trial was 1.63 m/s2, 2.22 m/s2, 1.87 m/s2,
1.69 m/s2, and 2.44 m/s2. The marbles average acceleration for this test was 1.97 m/s 2. The
results of this test as the marble travelled to 0.5 m is shown on Table 1 (shown below).
Table 1 - Test One
When released the marble reached 1.0 m in 1.231 s, 0.944 s, 1.126 s, 1.120 s, and 1.120 s
respective to each trial. The average time it took the marble to travel 1.0 m was 1.0792 s. The
velocity of the marble as it crossed 1.0 m was 1.62 m/s, 2.12 m/s, 1.77 m/s, 1.79 m/s, and
2.05 m/s, with an average velocity of 1.856 m/s. From this calculation the acceleration of each
trial was 1.32 m/s2, 2.25 m/s2, 1.57 m/s2, 1.60 m/s2, and 2.10 m/s2. The marbles average
acceleration for this test was 1.768 m/s2. The results of this test as the marble travelled to 1.0 m
are shown on Table 2 (shown below).
Table 2 - Test One
The final phase of this test concerned the time it took for the marble to travel 1.5 m at the
noted incline. When released the marble reached 1.5 m in 1.463 s, 1.311s, 1.432 s, 1.448 s, and
1.280 s respective to each trial. The average time it took the marble to travel 1.5 m was 1.3868 s.
The velocity of the marble as it crossed 1.5 m was 2.05 m/s, 2.29 m/s, 2.09 m/s, 2.07 m/s, and
2.34 m/s, with an average velocity of 2.168 m/s. From this calculation the acceleration of each
trial was 1.40 m/s2, 1.75 m/s2, 1.46 m/s2, 1.43 m/s2, and 1.83 m/s2. The marbles average
acceleration for this test was 1.574 m/s2. The results of this test as the marble travelled to 1.0 m
are shown on Table 3 (shown below).
Table 3 Test One
The second test performed was identical to first expect the degree of incline was at 23 o,
not 30o. This angle was measured with a protractor. Because of the different degree of the angle
the height was different as well. The height from reach the marble was released was 0.59 m.
When released the marble reached 0.5 m in 1.223 s, 1.056 s, 1.192 s, 1.041 s, and 1.072 s
respective to each trial. The average time it took the marble to travel 0.5 m was 1.1168 s. The
velocity of the marble as it crossed 0.5 m was 0.82 m/s, 0.95 m/s, 0.84 m/s, 0.96 m/s, and
0.93 m/s, with an average velocity of 0.9 m/s. The acceleration was 0.67 m/s2, 0.90 m/s2,
0.70 m/s2, 0.92 m/s2, and 0.87 m/s2. The marbles average acceleration for this trial was
0.812
m/s2. The results of this test as the marble travelled to 0.5 m is shown on Table 4 (shown below).
Table 4 Test Two
When released the marble reached 1.0 m in 1.688 s, 1.615 s, 1.750 s, 1.520 s, and 1.600 s
respective to each trial. The average time it took the marble to travel 1.0 m was 1.6346 s. The
velocity of the marble as it crossed 1.0 m was 1.18 m/s, 1.24 m/s, 1.14 m/s, 1.32 m/s, and
1.25 m/s, with an average velocity of 1.226 m/s. From this calculation the acceleration of each
trial was 0.70 m/s2, 0.76 m/s2, 0.65 m/s2, 0.87 m/s2, and 0.78 m/s2. The marbles average
acceleration for this test was 0.752 m/s2. The results of this test as the marble travelled to 1.0 m
are shown on Table 5 (shown below).
Table 5 Test Two
The final phase of this test concerned the time it took for the marble to travel 1.5 m at the
noted incline. When released the marble reached 1.5 m in 2.151 s, 2.039 s, 2.160 s, 2.032 s, and
2.056 s respective to each trial. The average time it took the marble to travel 1.5 m was 2.0876 s.
The velocity of the marble as it crossed 1.5 m was 1.39 m/s, 1.47 m/s, 1.39 m/s, 1.47 m/s, and
1.46 m/s, with an average velocity of 1.436 m/s. From this calculation the acceleration of each
trial was 0.65 m/s2, 0.72 m/s2, 0.64 m/s2, 0.72 m/s2, and 0.71 m/s2. The marbles average
acceleration for this test was 0.688 m/s2. The results of this test as the marble travelled to 1.0 m
are shown on Table 6 (shown below).
Table 6 Test Two
Using the methods detailed above test one and two were able to successfully calculate the
acceleration of the marble as it travelled on an inclined plane.
For test one the average
acceleration was 1.77 m/s2. For test two the average acceleration of the marble was 0.75 m/s 2.
As the averages indicate the acceleration of the marble increased as the incline of wooden bench
increased. This is due to the acceleration of gravity becoming true to its actual rate of 9.8 m/s 2 as
the angle of the incline increased. The greater the degree of incline the closer the acceleration
gets to the acceleration of free-fall. With this in mind it can be stated if the incline were to reach
90 degrees than the force of gravity would no longer be diminished by the marble (or any object)
travelling over an inclined plane, and the objects downward acceleration would equal its
maximum acceleration the constant force of gravity. Furthermore, this experiment it is also
possible to recreate one of Galileos famous insights.
During the 16th century Galileo conducted multiple experiments to the find velocity at
which objects fall to the ground. To slow down the process of an object falling Galileo had an
object travel down an inclined plane. Through multiple experiments Galileo hypothesized that
the distance an object fell was proportional to the time it took falling squared or d = t2. Although
conducted over a distance between 0 to 1.5 meters, this experiment helped to confirm Galileos
observations.
Even though the results of test one do not exactly match Galileos observation of d = t 2, it
is a close representation his of observation. The same can be said for test two of this experiment.
For test one the average time it took for the marble to roll one meter was measured at 1.0792
seconds. According to d = t2 to fall one meter would take one second. Additionally, a close
observation was found for test two. During the experimental phase of test two it was observed
that the average time it took for the marble to travel 1.5 meters was 2.0876 seconds. Using d = t 2
the time required for an object to fall 1.5 seconds is 2.25 seconds. Tables 7 and 8 show how
numerically close the experiments data from test one and two were to d = t 2. These nearly
identical results help to confirm Galileos insight that the distance covered by a falling object is
proportional to the time it travelled squared. Graphs 3 and 4 provide visual representations of
test one and two and how close each came to confirming d = t 2 are found below (in the
Measurement and Observation Data Section). Reasons for why the results of the experiment
Table 7 d =t 2 compared to results found from test one
Table 8 d =t 2 compared to the results found from test two
are not identical to Galileos insight may have to do with friction or human error. This will be
discussed later regarding the results of the entire experiment.
Using these two tests it is also possible to demonstrate how an unbalanced force is
created by the inclined plane. An unbalanced force, as noted above, will result in force being
applied to an object causing it to change its current state (whether at rest or in motion). To
calculate whether a force is balanced or unbalanced the magnitudes of the two forces (in this
example the force of gravity and the normal force) acting on an object need to found.
For a force to be balanced the two magnitudes need to equal one another. An example of
this comes from a box laying on a horizontal surface. Suppose the boxs mass is 50 kg, and the
acceleration of gravity is 9.81 m/s2. By multiplying the boxs mass and the acceleration the
downward force pressing against the box is 490.5 N. What is keeping the box from falling past
the surface it is resting on is the normal force. Newtons Third Law states that for every action
(or force) there will be an opposite and equal reaction. This reaction is the normal force. Using
the formula found above the normal force pushing against the downward force is
((50 kg)(9.81 m/s2)(cos(0)). From this the normal force is 490.5 N; thus, the force pushing
downward is 490.5 N and the force pushing upward is 490.5 N. Both forces are applying an
equal amount in opposite directions causing the box to remain on the surface. This is not the
case for an object on an inclined plane.
When an object is on an inclined plane the forces are unbalanced. Prior to the experiment
the mass of marble was measured at 0.06 kg. This measurement was found with aid of a spring
scale. When measured on a spring scale the marble weighed 0.6 N. Assuming the force of
gravity is 9.81 m/s2, the mass of the marble is 0.06 kg. The mass of the marble was calculated
through a revision of what a Newton mathematically is. A Newton is expressed by the formula:
Newton = mass(gravity). Mass, therefore, is: mass = Newton/gravity. The downward force
applied to the marble throughout the experiment was 0.5886 N. The normal force, for test one,
was 0.5098 N. When applied to test two the normal force was 0.5418 N. Neither normal forces
for test one and two equaled the downward force 0.5886 N. Due to this a net force of 0.0788 N
and 0.0468 N (for each respective test) remained. With the downward force remaining greater
than the normal force the marble was still being pushed downward. This resulted in it continuing
toward the center of the Earth until it reached a horizontal surface where it obtained a balanced
force keeping it from further plummeting.
From this experiment the velocity and acceleration of a marble as it rolled down an
inclined plane was calculated. From these calculation it was shown that the greater the incline
the greater the velocity (and thus the greater the acceleration). The average velocity for the
marble at 30o above the horizontal was 1.808 m/s. Its acceleration was 1.77 m/s 2. When released
on a surface 21o above the horizontal the average velocity was 1.187 m/s. For the second test the
average acceleration was 0.75 m/s2. What is interesting to note is throughout the experiment the
velocity increased while the acceleration decreased as the marble travelled further down the
incline plane. Velocitys increase is consistent with Galileos observation of d = t 2. It is
consistent because velocity is proportional to the distance travelled divided the time it took to
travel the distance. Because d = t 2 the distance is always the time raised to the second power;
thus, the distance will always be an ever increasing number while the time will always be the
square root of this. This has tremendous implications for the velocity of an object in free-fall or
on an inclined plane (with friction being a negligible factor). The distance of the velocity
travelled will always be greater than the time it took to travel the distance. This results in a
larger number always being divided by an ever increasing smaller number, or simply put, a
velocity that is indefinitely increasing during its free-fall or travel downward down an inclined
plane. Unfortunately, acceleration did not follow suit.
As previously noted acceleration is proportional to velocity over time. Because velocity
is ever increasing, it would have been assumed that acceleration would have been increasing as
well. This was not the case, and may have been a result of friction or human error.
Friction is caused by the irregularities between two surfaces in contact with one another.
The contact between the two surfaces with irregular surfaces forces the object to slow down.
Because of friction the acceleration of the marble may have slowed down. A second possibility
for this may be due to human error. The time it took the marble to travel the designated distances
were recorded by a stopwatch. The time it took for the object to be recorded as it passed each
length in spite of human reaction time was not calculated. These two possibilities may account
for why the acceleration decreased as it travelled down the inclined plane.
The rate of velocity and acceleration of an object is related to degree (above the
horizontal) of the inclined plane it is travelling on. The greater the incline, the greater its
velocity and acceleration. Furthermore, by using Newtons Laws of Motion it was possible to
understand why an inclined plane would cause marble (or any object) to change its state of
motion. This experiment provided proof of Newtons conclusions, and how an incline is directly
proportional to the velocity and acceleration on object travels at.
Measurements and Observations Data
Graph 1 Average Rate of Distance and Time for Test One
Graph 2 Average Rate of Distance and Time for Test Two
Graph 3 Average Velocity for Test One compared to d= t2
Graph 4 Average Velocity for Test Two compared to d = t2
Observation 1 The relationship between gravity, the normal force, and acceleration
Acceleration
Height of ramp: __.79 m;
DATA TABLE 1:
TRIAL No.
Angle of incline = _30
o
1
Distance (x)
m
.50
Time (t) seconds
0.783
Velocity (v)
m/s
1.28 m/s
Acceleration
(a) m/s2
1.63 m/s2
2
.50
0.671
1.49 m/s
2.22 m/s2
3
.50
0.732
1.37 m/s
1.87 m/s2
4
.50
0.768
1.30 m/s
1.69 m/s2
5
.50
0.639
1.56 m/s
2.44 m/s2
Average
0.7186
= Average =
1.4 m/s
Average =
1.97 m/s2
1
1.0
1.231
1.62 m/s
1.32 m/s2
2
1.0
0.944
2.12 m/s
2.25 m/s2
3
1.0
1.126
1.77 m/s
1.57 m/s2
4
1.0
1.120
1.79 m/s
1.60 m/s2
5
1.0
0.975
2.05 m/s
2.10 m/s2
Average =
1.0792
Average =
1.856 m/s
Average =
1.768 m/s2
1
1.5
1.463
2.05 m/s
1.40 m/s2
2
1.5
1.311
2.29 m/s
1.75 m/s2
3
1.5
1.432
2.09 m/s
1.46 m/s2
4
1.5
1.448
2.07 m/s
1.43 m/s2
5
1.5
1.280
2.34 m/s
1.83 m/s2
Average =
1.3868
Average =
2.168 m/s
Average =
1.574 m/s2
Calculations: Notice that your data consists of times (t) and distances (x). In order to
calculate acceleration you must use the four equations of motion. First work with
Equation 2:
Equation 2:
x = (v/2)t
Rewriting to isolate v, the equation becomes:
Equation 2:
v= (2x)/t
You already know the distance, x and the time, t. Now you can solve for velocity, v, by
using Equation 2 in this form. Fill in v for each trial on your data sheet. Use Equation 1
to find acceleration, but first it must be rewritten to isolate the variable (a).
Equation 1:
v=at
divide both sides of the equation by (t):
a= v/t
With Equation 1 rewritten in this way it is easy to solve for acceleration, a using time, t
from your data sheet and velocity, v that you already calculated. Fill in the value for
acceleration in each trial on your calculation table.
Questions
A. Newtons first law says a body at rest will remain at rest unless acted upon by an
outside force, and a body in motion will continue in motion at the same speed and in
the same direction unless acted upon by an outside force. What forces were acting
on the marble as it traveled down the ramp?
B. Did the velocity of the marble increase as it traveled down the ramp?
C. Did the acceleration of the marble increase as it traveled down the ramp?
D. What would happen to the velocity and acceleration of the marble if the ramp
were steeper? How about if the ramp were vertical? If you have trouble answering
this, repeat the experiment with a steeper ramp.
E. As you are riding in a car your body is at rest relative to the car but in motion
relative to the street. What might happen to the passengers in a car during a sudden
stop or crash if there are loose objects stacked in the rear window of the car?
a. If a vehicle were to come a sudden stop loose objects in the rear window
(assuming they are unsecure) would continue to travel at the velocity they
were originally travelling at. The objects would only come to rest due to
other forces acting upon it. One vertical force would be gravity. Due to
gravity the object would not change its horizontal velocity but would
eventually come to a rest because gravity would eventually bring the
objects to the ground (and upon reaching the ground the objects would
come to a rest). Another force acting upon it is air-resistance. Due to airresistance for the objects would act as a kinetic frictional force. Because
of this the objects would require additional force in the horizontal to
continue moving at a constant velocity. The car had come to a stop, and
because of this there is no more horizontal force pushing the objects.
Without this force the objects would eventually come to a stop.