Name: Connie Chen Class: Grade 9B Date: Nov, 8 th
, 2019
Qualitative Data:
The aim of this experiment is to investigate and determine how can different inclination angles of a tilted ramp affect the velocity/acceleration of a marble rolling down from the inclined plane. The angles of inclination of a ramp are switched from shallow to wide when three trials of the experiment are completed. Furthermore, the ramp with a total length of 4.8m was also separated into four identical portions: 1.2m, 2.4m, 3.6m and 4.8m. Each portion was marked with a sign to make it clearer for students to calculate the change of velocities after stopping a timer from running whenever the marble went pass a sign. Both the velocities and the accelerations are calculated from the time taken recordings for a marble to roll down a ramp with two types of inclinations. Eventually, the final result of this experiment was concluded by comparing the different calculations of the two inclination angles of the ramp.
According to the observations during the experiment, the marble seemed like rolling down faster on the plane when it had a wider angle of inclination. On the contrary, only seen by naked eyes, the speed of the marble didn’t look like it was changing when the marble was rolling down from a shallow angle. Also, while using a book at the end of the ramp to resist the marble from keep on running, the force that the marble generated of bumping into the book seemed to be greater when the marble was rolling down from a wider angle of inclination.
Data Collection:
Table 1: Raw data of the time taken recordings (s) a marble rolled down from a tilted ramp with two types of inclination angles (degree
º
) and four portions of lengths/distance markings (m).
The table below shows the raw data of the time taken for a marble to roll down from a tilted plane with two types of inclination angles: shallow and wide. Four distance markings (1.2m, 2.4m,
3.6m and 4.8m), with students standing by and recording with timers, are labeled with ruler on the plane to clarify the time taken for the marble to go pass each of them. Three trials are completed for each of the inclination of the ramp to ensure the reliability of the experiment.
Distance markings
(meters)
1.2
Timers Angles of Inclination (Degree º )
Shallow Angle Wide Angle
Trial 1 (s) Trial 2 (s) Trail 3 (s) Trial 1 (s) Trial 2 (s) Trial 3 (s)
Timer 1 1.65 2.85 2.66 1.50 1.72 1.78
2.4
3.6
4.8
Timer 2
Timer 3
Timer 4
2.75
3.58
4.50
4.08
4.95
5.93
4.16
4.43
5.91
2.47
2.71
3.94
2.53
3.14
4.00
2.53
3.08
3.94
Data Processing:
1) The average recordings of the time taken for a marble to roll down an inclined plane will be calculated at four distance markings for two types of inclination angles (shallow and wide).
Formula: Average time taken recordings at each distance marking (s) = The sum of time taken for three trials of experiment in the same inclination angle (s) / Number of trials (three)
Sample calculation for the average time taken recordings for all three trials with the shallow

inclination at the distance of 2.4m:
(2.75s + 4.08s + 4.16s) / 3 = 3.66s (approximately)
2) The average velocities of a marble rolling down an inclined plane will be calculated for two types of inclination angles and at four distance markings.
Formula: Average velocity calculations for each inclination and distance marking (m/s) = The overall distance of the marble rolling down (m) / Time taken (s)
Sample calculation for the average velocity when the marble is at 1.2m from the plane with a wide inclination:
1.2m / 1.67s = 0.72 m/s (approximately)
3) The average accelerations of a marble rolling down the tilted ramp is calculated for two angles of inclination and four distance markings.
Formula: Average acceleration of a marble rolling down (m/s²) = Δ Velocity (Final velocity – Initial
Velocity) (m/s) / Time taken (s)
Sample calculation for the acceleration of the marble at 1.2m of the ramp with a shallow inclination angle:
0.50m/s / 2.39s = 0.21m/s²
Data Presentation:
Table 2, Graph 1: The average calculations of the time taken (s) a marble is required to roll down an inclined plane with shallow and wide inclinations (degree
º
) and the four distance markings (m).
The table and the graph below are showing the average time taken recordings (s) a marble rolled down from a tilted ramp with two inclinations. The time taken was affected by shallow and wide inclination angles, and was recorded at four distance markings: 1.2m, 2.4m, 3.6m and 4.8m.
Distance markings
(meters)
1.2
2.4
3.6
4.8
6
5
4
3
2
1
0
Average of the Time Recordings for Different Angles of Inclination (s)
2.39
3.66
4.32
5.45
Marking 1
Shallow Angle (s)
1.67
2.51
2.98
3.96
Marking 2 Marking 3
Distance Markings (m)
Wide Angle (s)
Marking 4
Average of the Time Recordings for Different Angles of Inclination (s) Shallow Angle
(s)
Average of the Time Recordings for Different Angles of Inclination (s) Wider Angle (s)

Table 3, Graph 2: The average velocities (m/s) of the marble rolling down from an inclined plane at four distance markings (m) and two distinctive angles (degree
º
).
The table and the graph below both show the average velocities (m/s) calculated from the average time taken recordings (s) at shallow and wide angles of inclination the ramp has. The velocities are calculated when each timer was stopped at each distance marking (1.2m, 2.4m, 3.6m and 4.8m). The table and the graph are using the second formula in data presentation.
Distance markings
(meters)
1.2
The Calculated Average Velocities of the Marble Rolling Down (m/s)
Shallow Angle (m/s) Wide Angle (m/s)
0.50 0.72
2.4
3.6
4.8
0.66
0.83
0.88
0.96
1.21
1.21
1,4
1,2
1
0,8
0,6
0,4
0,2
0
Marking 1 Marking 2 Marking 3
Distance markings (m)
Marking 4
Average Velocity of the Marble Rolling Down (m/s) Shallow Angle (m/s)
Average Velocity of the Marble Rolling Down (m/s) Wide Angle (m/s)
Table 4, Graph 3: The average accelerations (m/s²) of the marble rolling down from a tilted plane with two angles of inclination (degree
º
) and at four identical distance portions.
Acceleration is known as the rate in which an object is changing its velocity. The table and the graph below are both showing the average accelerations of a marble rolling down from an tilted plane that varies between shallow and wide angles of inclination (degree º ). Each acceleration is calculated at a distance marking on the ramp. Also, the accelerations being calculated below are based on the change in velocities in table 3 and graph 2, using the third formula in data presentation.
Distance markings
(meters)
1.2
2.4
3.6
4.8
0.21
0.18
0.19
0.16
Calculated Accelerations based on Average Velocities (m/s ² )
Shallow Angle (m/s
²
) Wide Angle (m/s
²
)
0.43
0.38
0.41
0.72

0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
Marking 1 Marking 2 Marking 3
Distance Markings (m)
Marking 4
Calculated Accelerations based on Average Velocities (m/s²) Shallow Angle (m/s²)
Calculated Accelerations based on Average Velocities (m/s²) Wide Angle (m/s²)
Conclusion and Evaluation:
The goal of this experiment was to investigate and determine how the two inclination angles
(shallow and wide) of a ramp may affect the velocity and the acceleration of a marble rolling down the ramp. As shown in Table 2 and Graph 1, by observing the two lines, it is obvious that the slope of the line representing the shallow angle is steeper than the slope of the line representing the wide angle. Also, the line of the shallow angle is distinctly higher than the wide angle, which means that it took much more time for the marble to roll down the shallow angle. According to Table 3 Graph 2 and Table 4 Graph 3, the velocities and the accelerations of the marble rolling down the wider angle is obviously greater than the marble does on the shallow angle, the red lines have higher and steeper lines than the blue lines on the graphs. Especially when the red lines are approaching to the end, the slope of the acceleration line surges in a great amount at marking 4s. The data suggests that the inclination of ramps does affect the velocities and accelerations of a marble rolling down. The results of the experiment are likely due to the approaches of the marble to free-fall. When the ramp gets steeper and has a larger inclination angle, the marble rolling down will have a greater gravitational acceleration energy and a larger inertia to push it down the ramp. The acceleration of the marble is accumulating and therefore causing the velocity to enlarge while the it is rolling down. The result of the experiment supports the hypothesis made. This is because the ramp that has a wider inclination angle has greater accelerations and velocities than the ramp with a shallow angle.
Evaluation and Improvements:
Weakness/Source of Error Possible effect on data and magnitude of weakness/error
Independent Variable: The inclinations of the ramp.
During the experiment, it wasn’t ensured that the ramp was staying at the exact same position all the time. The ramp moved slightly and might
This won’t affect the actual result widely, since it was ensured that the inclinations of ramp were keeping the same for each three trials of the
Suggested Improvements
To ensure that the ramp won’t be removed when it is in the same inclination angle, students doing the experiment should be careful and make

cause effects on the final results. experiment. The only factor being slightly shifted was the position the ramp.
Dependent Variable: The accelerations and velocities of the marble. sure that they won’t kick the ramp accidently.
The marble wasn’t pushed down the ramp with the exact same force during the experiment. It would probably cause an effect on the velocity and the acceleration of the marble.
Giving an extra force to the marble will generate more energy to the marble rolling down the ramp. The marble might have a greater velocity or gravitational acceleration energy while rolling down the
To avoid pushing the marble when it is on top of the tilted plane, the student dropping it should make sure that he/she isn’t bringing extra forces. The student should only release the ball during the experiment. inclined plane.
Controlled Variable: The time the students at each distance marking start their timers.
During the experiment, the time that the students at each distance marking start their timers are not controlled accurately. If students were not starting their timer at the same time, it will probably cause effects on the calculations and the final results of the marble’s velocities.
If some students started their timers before the marble released, and others started after the marble started rolling down, the recordings of the time taken of marbles won’t be accurate enough.
To avoid this from happening, the person releasing the marble could give a signal to others who are starting their timers. In this way, everyone could start their timers almost the same time.