Lab Report Instructions
Lab reports are an effective way of communicating important information, and their use is stressed in this course. There is little point in doing a wonderful experiment with great results if you cannot effectively communicate your method and findings to others. Although you have some freedom in preparing your lab report, make sure to include the following sections:
· Cover Page
· Introduction - Provide a concise theoretical background.
· Procedure - Describe your procedure in your own words.
· Pictures - Include clear pictures of your setup.
· Data - Organize and present the data you collect in the experiment. Also provide a description of the behavior and apparent trend of the collected data.
· Analysis and Discussion - Give clear and detailed analysis of your data as described in the manual. Make sure to include sample calculations, especially for newly calculated columns in data tables. You may also need to produce graphs and perform appropriate fits. E
or analysis and a discussion of measurement uncertainties should be provided.
· Conclusion - Present a
ief summary of your findings and results.
· Questions - Provide detailed answers to the questions at the end of the lab.
Lab #3: Projectile Motion
· Need to use this software to do data analysis
· https:
physlets.org/tracke
PHYS 200 – Introductory to Physics 1
Lab 3: Projectile Motion
Athabasca University
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Introduction
The main focus of Lab 3: Projectile Motion is to examine the projectile motion of an object in
two dimensions while observing the parabolic motion of the projectile under the influence of
gravity. A projectile is an object given an initial velocity, after which only moves under the
influence of gravity. Projectile motion can be subcategorized as accelerated motion in the
vertical direction and the constant velocity motion in a horizontal direction. Within this lab, the
assumption is made that the acceleration will be that ay = 9.80m/s^2 downwards. The
kinematics equations which will be used within this lab are as follows:
1. y =y +v t−1gt2
2. x=x0 +vxt
Materials
• Medium/large ball
• Measuring tape
• Digital camera
Procedure
As stated in the Lab 3: Projectile Motion lab manual
1. Located an empty room where there is a large area
2. Identified a location of known length with a measuring tape
3. The measuring tape is placed in a position where it is perpendicular to the objects plane
of motion
4. The ball was thrown from a position near the floor at an angle θ between 40 and 75 above
the horizontal plane
5. Recorded the objects projectile motion using a digital camera for the data to be analyzed
y Tracker software
6. Analyzed the trajectory of the ball through Tracker software
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Figure 1: Procedural set-up. This includes a known vertical length demonstrated by the tape
measurer (1.39m) and the ball used.
Analysis
To properly collect and analyze data during this lab, frame-by-frame video captures are required.
Data that was collected from the Tracker software is provided below.
Figure 2: A collection of data points every 0.034s while portraying the graph of time vs.
distance (y-axis)
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Figure 3: The time vs. vertical position graph portraying the velocity of the ball over 24 data
points and the co
esponding fit parameters
Analyzing figure 2, it is evident the time vs. vertical position of the graph demonstrates a
parabolic form. When examining this graph, select data points have a slight deviation, being
either slightly above or below the parabolic line. These data points are still within proximity of
the parabola’s margins. This is due to the inaccuracy of the software used to analyze the position
of the object throughout the lab. During the lab, it was challenging to pinpoint the middle of the
all in each frame during the 0.80s. Although the data is slightly inaccurate, the graph from
figure 2. can still be interpreted. The graph above displays the projectile motion of the ball under
the influence of gravity with a slight margin of e
or. To examine the parameters in the fit
equation, the kinematics equation y = y + v t − 1 gt2 can be used. The value A is represented as (-
g), the value B is represented as the velocity of the y-direction (v 0y), and the value C is
epresented as the initial y position (y 0). The parameter value of A is equal to –2.476m/s 2.
Through using the gravity constant of 9.80m/s 2 (½), the parameter value is not in proximity of
the kinematics equation value of –4.90m/s 2 but is relatively close. The initial position of the
object is a little below 0. Although this is inaccurate, the object lies within an acceptable margin
(only 1.0m below the y-axis). Taking these inaccuracies into consideration, the data within
figure 2. supports the idea of the object moving with a constant acceleration in the vertical
direction.
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Figure 4: A collection of data points every 0.034s while portraying the graph of time vs. distance
(y-axis)
Figure 5: The time vs. Horizontal position graph portraying the velocity of the ball over 24 data
points, the values of the fit equation parameter values, and the co
esponding fit equation
It is important to solve for the object’s velocity in two components. The acceleration of g = 9.8
m/s 2 is acting downwards on the object, only the vertical component of the object will be
affected. The object’s horizontal velocity will remain constant over time. When analyzing
figure 3, since the object is under constant velocity it can be assumed the rise over run of the
graph (slope) is equal between each data point. This creates a straight line that goes through
each data point. When examining this graph, select data points have a slight deviation, being
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either slightly above or below the parabolic line. This is due to the inaccuracy of the software
used to analyze the projectile motion of the object throughout the lab. Despite the slight
inaccuracy of the data collection through the Tracker software, the graph is still interpreted to
display a constant velocity with a slight margin of e
or. The fit equation parameter can be
explained using the kinematics equation, x=x0 +vxt. The A value is represented as the velocity in
the horizontal direction, the B value is represented as the ball’s initial position, and the x value is
the ball’s final position. The B value should equate to 0, but due to inaccuracies when trying to
align the ball’s position perfectly with the bottom of the cali
ation stick and choosing the
middle of the ball in the initial frame capture it deviates.
Figure 6: A graph representing the distance on the x-axis vs distance on the y-axis
Lastly, a comparison was made between the distance on the x-axis and the distance on the y-axis
during the projectile’s trajectory.
Conclusion
In conclusion, while conducting this lab, the data collected demonstrates the ball moved at a
constant acceleration during its trajectory. Refe
ing the figure 3, the parabolic graph and data
points within a close margin portray a constant acceleration. If the ball was not moving at a
constant acceleration, the parabolic curve would not be even on both sides of the apex, it would
e more present in one direction. The graph from figure 5 demonstrated the time vs horizontal
distance has an equal slope of line with a minimal margin of e
or. Through this data, it is
evident that the velocity was constant in the x-direction. The total distance travelled in both the
x-axis and y-axis are reasonable in comparison to the known length. This concludes that the
graphs presented within this lab accurately demonstrate the vertical and horizontal distances
travelled, the time, and velocities in both directions of the projectile motion of the ball.
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Questions
1. Through the analysis we can understand the A value in the fit equation represents the
acceleration of the object due to gravity. When substituting the fit-equation with the
kinematic equation y = y + v t − ½gt2. we can observe that gravity (g) must be multiplied
y ½. This results in a g value of 4.90m/s2 downwards. The parameter values in figure 3
demonstrate that the value A equals 2.746m/s 2, which is 2.154m/s 2 from the expected
value of 4.90m/s 2
2. The velocity in the horizontal direction can be solved by using the kinematics equation
with the parameter values mentioned in figure 5.
x=x0 +vxt
− 2.546x 0 + v x (1.45)
− 2.546m = 1.45v x
− 1.75m/s = v x
The horizontal velocity of the ball during the lab was 1.75 m/s (left)
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