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Analyzing The Motion of a Rolling Ball
Hlaing Phyo Han
Royal Academic Institute, Mandalay, Myanmar
SPH4U: Physics
Dr. Su Su Yee Mon
August 25, 2023
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Contents
Introduction ................................................................................ Ошибка! Закладка не определена.
Method ....................................................................................... Ошибка! Закладка не определена.
Results......................................................................................... Ошибка! Закладка не определена.
Discussion.................................................................................... Ошибка! Закладка не определена.
Inconsistency and Limitation ........................................................ Ошибка! Закладка не определена.
Conclusion ................................................................................... Ошибка! Закладка не определена.
Reference ........................................................................................................................................ 10
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Abstract
This experiment aims to discover the relationship between the angle of inclination and final
velocity, acceleration and net force. Books and wooden plates are used to create an inclination, roll
down the ball on it, and repeat it five times with three different inclinations. Using Newton’s law of
motion, it can be predicted that as the inclination increases, the final velocity, acceleration and net force
increase. Throughout the experiment, our predictions were true, and we concluded that the variables
above are all directly proportional, and the Average time taken is inversely proportional to the angle of
inclination.
Introduction
This experiment aims to determine whether the angle of inclination affects the ball's final
velocity and net force while rolling on the inclined plane. Newton said that when a body is acted upon
by a net force, the body’s acceleration multiplied by its mass is equal to the net force that is parallel to
the incline. The ball rolls down the inclined plane due to acceleration from position 1 to 2, and the ball
will go with constant velocity while going from 2 to 3 as there is no inclination. This is due to the inertia
as there is no external net force on the ball; it will continue with a constant velocity (Brunei &
DiGiuseppe, 2012). We will investigate the final velocity, acceleration and force on the ball. It can be
predicted that the final velocity and acceleration will increase as the incline angle increases. During this
kind of experiment, air resistance is negligible due to their small magnitude.
Method
Smartphone, ruler and marker are used for all the measurements in this experiment. A wooden
plane is used for the inclined plane, and books are used to change the incline angles. To measure the
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incline angle of the plane, we used a smartphone app to get a more accurate measurement. The
measurement and the set-up looked like this:
Figure 1. Software used (Bubble Level, Spirit Level, 2021)
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Figure 2.
Position 3
Position 1
Position 2
Firstly, we combined all the books and wood planes to create the inclined plane. Then we draw
a small mark to identify positions 1, 2 and 3. After that, we measured the distance of these positions and
the incline angle of the plane. We then also measured the mass of the ball. Finally, we rolled the ball
down from position 1 to position three, measured the time taken of it and repeated it five times. We
then put more books under the wooden plate to increase the incline angle and repeat the process.
The distance of the positions and the ball's mass are all constant throughout all the
experiments, but the incline angle is a controlled variable. The dependent variable will be final velocity,
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acceleration and net force. We have used three different incline angles. Static friction, kinetic friction
and air resistance will be ignored in the experiments.
Results
The distance from position 1 to 2 is 0.29m, while position 2 to 3 is 0.16m. The mass of the ball is
0.065kg. In all these results, SI units are being used.
Table 1
Time taken for position 1 to 2
Angle (-°)
5.1
11.4
16.1
0.97
0.61
0.49
0.88
0.54
0.44
1
0.56
0.53
0.9
0.62
0.44
1.07
0.56
0.51
0.964
0.578
0.482
5.1
11.4
16.1
0.5
0.3
0.24
0.43
0.27
0.22
0.52
0.27
0.23
0.45
0.3
0.25
Time Taken for
each trail
(sec)
Average time
taken (sec)
Table 2
Time taken for position 2 to 3
Angle (-°)
Time taken for
each trial (sec)
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0.54
0.29
0.24
0.488
0.286
0.236
Average time
taken (Sec)
Tables 1 and 2 show all the data collected and calculated average time taken of the ball in
different positions. We can calculate final velocity, net force, and acceleration during positions 1 to 2
with the average time taken.
Table 3
Calculated variables that are affected on the ball from position 1 to 2
Angle (-°)
Average time
Final velocity
Acceleration(m/s
Net Force (N)
taken (sec)
(m/s)
^2)
5.1
0.964
0.602
0.624
0.058
11.4
0.578
1.003
1.74
0.128
16.1
0.482
1.203
2.495
0.180
Table 3 shows the calculated results of the kinematic of the ball. The initial velocity would be 0.
We can clearly see that the angle of the incline is directly proportional to the ball's final velocity,
acceleration and net force.
Table 1
Table Title
Angle(-°)
Average time
Average Velocity
taken (sec)
(m/s)
5.1
0.488
0.328
11.4
0.286
0.559
8
16.1
0.23
0.678
Table 4 shows the ball's average velocity from position 2 to 3. As there is no inclination from 2
to 3, there will be no acceleration or net force.
These Free-Body diagrams will give you further understanding:
Figure 3.
𝑓𝑁
Acceleration
𝑓𝑔𝑦
𝑓𝑔
Θ
𝑓𝑔𝑥
Θ
The following equations are used for all the calculated variables:
𝑣𝑓 + 𝑣𝑖
𝛥𝑑 = (
) ∙ 𝛥𝑡
2
𝑎=
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 =
𝑣𝑓 − 𝑣𝑖
𝛥𝑡
𝑇𝑜𝑡𝑎𝑙 𝑜𝑓 𝑇𝑖𝑚𝑒 𝑇𝑎𝑘𝑒𝑛 𝑓𝑟𝑜𝑚 𝑒𝑎𝑐ℎ 𝑡𝑟𝑎𝑖𝑙
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𝐹𝑛𝑒𝑡 =𝑠𝑖𝑛 𝑠𝑖𝑛 𝜃 ∙ 𝐹𝑔
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
∆𝑑
∆𝑡
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Discussion
According to the results, the prediction is right. We can see that the angle of inclination affects
final velocity, acceleration, and net force from position 1 to 2. According to Newton’s second law, as the
wood plate gets steeper and steeper, the time taken from position 1 to 2 gets lower and lower, which
means that the velocity of the ball increases. Since acceleration is the rate of change of velocity, the
acceleration also increases, which means that the force increases. This is due to the net parallel force of
gravity.
With Newton’s law of inertia, from position 2 to 3, there will not be any acceleration, and the
ball will go with constant speed because of no net force.
Inconsistency and Limitation
According to Newton’s law of inertia, the final velocity of positions 1 to 2 should equal the
average velocity of positions 2 to 3. However, they are not equal in this experiment due to the:
-Human Reaction Time Error
-Kinetic friction
-air resistance
Conclusion
Throughout the results, it can be seen that the angle of inclination is directly proportional to
acceleration, final velocity and net force of the ball. As the inline angle gets greater, these variables also
increase, and these variables also do not change while going from position 2 to 3 due to no inclination.
This means that the prediction is true. For further experiments, it would be easier to collect the time
taken if we use the longer distance of the positions.
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References
Bruni, D., & DiGiuseppe, M. (2012). Nelson Physics 12: University Preparation.
Bubble level, spirit level (3.31). (2021). [Software]. NixGame.
https://play.google.com/store/apps/details?id=org.nixgame.bubblelevel