PROJECTILE MOTION
Physics lab report- Rhea Cabral
Contents
Abstract ......................................................................................................................................................... 2
Equipment used- ....................................................................................................................................... 2
Method- .................................................................................................................................................... 3
Calculations-.............................................................................................................................................. 4
Data collection and processing ..................................................................................................................... 5
Raw Data ................................................................................................................................................... 5
Processed Data.......................................................................................................................................... 5
Averaged Data....................................................................................................................................... 5
Calculated Data ..................................................................................................................................... 6
Graph 1- .................................................................................................................................................... 6
Graph 2- .................................................................................................................................................... 7
Graph 3- .................................................................................................................................................... 7
Conclusion and Evaluation ........................................................................................................................ 8
Evaluation ................................................................................................................................................. 8
Improvements ........................................................................................................................................... 9
Bibliography .................................................................................................................................................. 9
http://calculator.tutorvista.com/projectile-motion-calculator.html ....................................................... 9
1
Abstract
The purpose of my investigation is to identify the factors that affect the Range of an object when in
Projectile Motion. To perform this investigation I would be using two methods. The first would be using
an elastic rubber band to project a ping pong ball on an inclined plane at a fixed angle. The second
method is using an inclined plane setup and project a marble using a wedge.
The former method had one challenge, to calculate the initial velocity of the ping pong ball.
I had my result compared with a standard value 5.45ms-1 obtained.
To achieve this,
I used the formula
𝑹=
𝒖𝟐 𝒔𝒊𝒏𝟐𝜽
𝒈
𝑢2
In this formula my independent variable is Sin2θ and my dependent is Range. Thus my slope gives me .
𝑔
By substituting the value of slope and the standard value of gravity I found the value of velocity
and compared it to the standard value 5.45ms-1. To finalize the standard value of velocity I planned
to use the values I obtained in (http://calculator.tutorvista.com/projectile-motion-calculator.html)
Thus the standard value of initial velocity
u = 5.45ms-1
Initial velocity using method 1 gave
u= 8.91ms-1
giving an uncertainty of ± 3.46 ms-1 and percentage uncertainity of ±39%
I wasn’t happy with the results and felt to obtain gravity value to investigate the
reliability of the experiment.
To do this I used method 2.
The results of gravity are as follows.
2
Apparatus required for this experiment
1)
2)
3)
4)
5)
6)
A table tennis ball – ping pong ball.
A protractor (180°)
Measuring tape. (30m)
Elastic rubber band – 5 of the same quality
Inclined plane (adjustable to any angle)
White board erasable marker.
Diagram
Method
 I started by setting the inclined plane in the desired angle.
 I then placed the ball in the rubber band and pulled it backwards and marked the area with
a white board marker.
 I then let the ball go and had a friend mark the spot where the ball first hit the ground.
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 After doing the same thrice for each angle I measured the distances from the inclined plane
to the markings and noted them down.
Calculations1) To find standard value of velocity. I used the values obtained from
(http://calculator.tutorvista.com/projectile-motion-calculator.html) for each angle and range
and then took the average of them.
4.98 + 5.52 + 5.61 + 5.56 + 5.58
5
27.25
=
5
= 5.45 𝑚𝑠 −1
2) To find the value of velocity using the slope of the graph –
𝑢2
𝑠𝑙𝑜𝑝𝑒 =
𝑔
𝑢2
8.10 =
9.81
8.10 × 9.81 = 𝑢2
√79.46 = 𝑢2
8.91 = 𝑢
3) To calculate Sin2θ
𝐴𝑛𝑔𝑙𝑒 = 𝑆𝑖𝑛2𝜃
𝐴𝑛𝑔𝑙𝑒 = 𝑆𝑖𝑛(2 × 25)
𝐴𝑛𝑔𝑙𝑒 = 0.76
4) To calculate average range𝑡𝑟𝑖𝑎𝑙 1 + 𝑡𝑟𝑖𝑎𝑙 2 + 𝑡𝑟𝑖𝑎𝑙 3
3
1.51 + 1.82 + 2.50
𝐴𝑣𝑔 𝑟𝑎𝑛𝑔𝑒 =
3
𝐴𝑣𝑔 𝑟𝑎𝑛𝑔𝑒 = 1.94𝑚
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑛𝑔𝑒 =
4
5) Relative uncertainty
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =
=
𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦
× 100
𝑎𝑣𝑔 𝑟𝑎𝑛𝑔𝑒
0.50
× 100
1.94
= 25.5%
6) Uncertainty
𝑚𝑎𝑥𝑖𝑚𝑢𝑚 − 𝑚𝑖𝑛𝑖𝑚𝑢𝑚
2
2.50 − 1.51
=
2
𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =
= 0.50
Data collection and processing
Raw Data
Angle
Θ
(±1)
Range
Meter
(±0.5)
25 1.51
1.82
2.50
30 2.60
2.56
2.90
35 2.97
3.10
2.99
40 3.40
3.32
2.61
45 4.15
4.40
4.70
Processed Data
Averaged Data
Angle
Sin2θ
(±0.05)
0.76
0.86
0.93
0.98
1
Average
Range
Meter
(±0.5m)
1.94
2.69
3.02
3.11
4.42
5
Calculated Data
Average Range
Meter
(±0.5m)
Maximum Minimum Uncertainty Total
uncertainty
Relative Uncertainty
1.94
2.5
1.51 0.50
1 25.5
2.69
2.9
2.56 0.17
0.67 6.3
3.02
3.1
2.97 0.06
0.56 2.2
3.11
3.4
2.61 0.40
4.42
4.7
4.15 0.28
0.9 12.7
0.78 6.2
Graph 1-
Range Vs Sin2θ
6.00
y = 8.1021x - 4.3052
5.00
Range
4.00
3.00
2.00
1.00
0
0.2
0.4
0.6
0.8
1
1.2
Sin2θ
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Graph 2-
Range Vs Sin2θ
5.00
4.50
y = 7.0833x - 2.9433
4.00
Range
3.50
3.00
2.50
2.00
1.50
1.00
y = 13.583x - 8.8833
0.50
0
0.2
0.4
0.6
0.8
1
1.2
Sin2θ
Graph 3-
Range Vs Sin2θ
6.00
5.00
y = 8.1021x - 4.3052
Range
4.00
3.00
2.00
1.00
0
0.2
0.4
0.6
0.8
1
1.2
Sin2θ
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Conclusion and Evaluation
From the following graph I have found the value of initial velocity using the value obtained by finding the
slope of the graph and also by using the accepted value of gravity in the formula𝑠𝑙𝑜𝑝𝑒 =
𝑢2
𝑔
Where the slope obtained is- m= 8.10
Substituting the value obtained from the graph for slope in the formula along with the accepted value of
gravity 9.81ms-1.
8.10 =
𝑢2
9.81
We get, u= 8.91ms-1. (See in calculations)
Hence our result is 8.91ms-1, I then compared this result to the result 5.45ms-1 found on
http://calculator.tutorvista.com/projectile-motion-calculator.html.
After comparing both the results I noticed that there is a difference of 3.46m. Which is most likely due
to the many errors that occurred while conducting this experiment.
The uncertainty in the gradient can be found by taking the difference in max and min values of the
gradient and dividing them by 2. (See Graph 2)
Maximum value- 13.5m
Minimum value- 7.0m
Uncertainty in the gradient – 3.25m
The final value is 8.91 ± 3.25ms-1.
The accepted value is 5.45m/s.
We can conclude by saying that the value for velocity wasn’t constant as there were many difficulties
while conducting the experiment.
Evaluation
Looking at the graph, I noticed that the points lie near the line of best fit. Also that the error bars differ
for each value in the case of Range. But remain constant for the angle.
This shows that there were some errors during the experiment.
The air resistance can be considered in the case of this experiment as air would have had an effect on
the distance that the ball travelled after release. But may be considered negligible as the line goes
through most of the points and is straight.
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The value of velocity found from the graph when compared to the accepted value 5.45m shows that
there are errors while conducting the experiment.
The random errors that can be noticed in the graph as there are error bars, has had an effect on the final
outcome and could have been solved by taking multiple readings.
Improvements
The method of carrying out this experiment had a lot of flaws. That have affected the final outcome of
this experiment negatively.
Taking the value obtained for velocity from the graph and comparing it to the accepted value of velocity
we can see that there are some errors due to which the value isn’t as precise.
RANDOM ERRORS
Main drawback of the experiment was that it was
difficult to mark the correct spot where the ball
landed and so the value of distance are not as
accurate.
Not pulling the ball back at the same distance.
The angle of the board not being accurate due to
me not using the protractor accurately.
WAYS TO IMPROVE
Dipping the ball in paint or water so it would
leave a mark on the floor thus indicating the
exact point where the ball first hits, giving us an
accurate value for distance.
By marking the board or making sure that the ball
has been pulled back to the same distance before
releasing it.
By using a better protractor or by making sure
that the board is kept at the proper angle with
help of the markings on the protractor.
There weren’t any systematic errors except that of air resistance in the lab, the air resistance affected
the final value negatively and this can be seen as the line of best fit doesn’t go through the last point
properly.
The uncertainty 3.25 ms-1 could be reduced. By methods mentioned above. To avoid such an error it
would be appropriate to take more trials for each reading and to take more readings so as to cancel any
error.
Bibliography
http://calculator.tutorvista.com/projectile-motion-calculator.html
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