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How the Angle of a Ramp Affects the Speed of a Cylinder Moving Down It

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How the Angle of a Ramp Affects the Speed of a Cylinder Moving Down It


Ø Aim: To see how the angle of a ramp affects the speed of a cylinder
moving down it.


Ø Preliminary Work

I carried out some preliminary tests to see any problems, which could
occur and anything, which could be improved. I first tried timing the
cylinder with a stop watch timer, although this may be slightly
inaccurate because of the result being reliant on the timers
reactions, we felt this to be most efficient. By setting at 5° we got
a result of 1.39s. The results of the experiment with the stopwatch
are shown below. The weight of the cylinder in the set of results
below is 198.18g. Here, we are testing how long the cylinder takes to
reach the end of the ramp - i.e. not the time it takes to completely
stop

Preliminary Experiment

Angle (°)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Average (s)

5

1.59

1.42

1.69

1.50

10

0.98

0.91

1.02

0.97

15

0.77

0.78

0.73

0.76

20

0.53

0.61

0.64

0.59

[IMAGE]

Ø After the 20° angle we found it was becoming difficult to time the
cylinder and also to support the ramp. So we decided to change the
range from 5°- 45° to a more suitable range of 3° - 30° and also to
carry out the experiment 5 times instead of the 3 allowing us to get a
better average. We had previously decided that all the cylinders
should be rolled from a height of 30cm to begin with, although this
could be used as a variable later on.

Ø One can clearly see from this set of results that a trend develops
in the average time in seconds. That is to say that apparently the
steeper the angle of the ramp, the less time the cylinder takes to
leave the ramp. This means that, in my preliminary and most simple
results there is no direct proportion between x and y as the line on
the graph a) is a curve, and b) does not pass through the origin as
demonstrated on the next page. However, what it does show is
satisfactory enough to make a calculated prediction for the
experiment.

Ø Hypothesis: my prediction in its most simple form is that in the
experiment, the general trend of the results is that when y is big, x
is smaller, and when y is small, x is bigger. This trend should stay
intact through the experiment even if we change the variables quite
considerably. For example, if we change the weight of the cylinder
then the trend will still be as mentioned. Later, I will work out the
potential energy of the cylinders using the formula E = m.g.h, where m
is the mass of the cylinder, g is gravity, and h is the heightof the
ramp. We can work out the height of the ramp by using trigonometry. In
the diagram below we know that the hypotenuse of the triangle is 30cm
long, and that the angle is defined.

[IMAGE]

The equation for x is: Sin (whatever the angle is, example 10°) x
hypotenuse (0.3m)

= Sin10° x 0.3 = 0.05cm (3 s.f.).

Ø Using this information we can now work out the PE of the cylinder.



E = m.g.h
=========

= 0.19818 x 9.8 x 0.05

= 0.10J

Factors

Ø Angle of ramp: The experiment could be affected by the angle of the
ramp for example a 10° angle could have a higher amount of potential
energy than a 3° angle.

Ø Surface type of ramp: The surface of the ramp may affect the outcome
of the results because any type of grip on the surface could slow it
down and also such things as lubricants on the ramp could make the
ramp slippery in effect speeding up the ramp.

Ø Weight/mass of cylinder: The mass of the cylinder affects the
results because the weight could either slow it down or even speed the
cylinder up, as there will be a greater amount of potential energy
pulling on the cylinder.

Ø Surface of cylinder: The surface of the cylinder could affect it
because just like the 'surface type of the ramp' the cylinder's
surface could slow it down.

All these factors contribute to the overall performance of the
cylinder and indeed the result takings. It is imperative therefore
that fair testing is incorporated into the method. For example,
variables like the weight of the cylinder need to be kept constant
where necessary: picking up a different cylinder that looks similar is
no good.


Fair test

The experiment will be a fair test as there will only be one variable
factor: the angle. All the other factors will stay the same such as
the material used and the cylinder used: this means that there will
not be any bias issues in this experiment. Later on to broaden the
variety of results we could change the weight of the cylinder to
compare speeds, times and angles.


List of apparatus required for experiment beginning 24/1/02
-----------------------------------------------------------


 Metal/wooden cylinder
-----------------------

 Ramp

 Metre stick

 Angle measurer

 Stopwatch

The stopwatch must be reliable and have a clear screen to prevent
confusion, which could seriously jeopardise the results of the
experiment. As well as this, the metre stick used for measuring must
be very accurate and with clear incisions as to where the markings
are. The angle measurer (or protractor) must be used with great
diligence and readings should be double checked at all times. Each
time the ramp is used in a practical lesson, the same ramp must be
used next time in order to maintain consistency throughout. Lastly,
the metal cylinder must be used each time, also to endorse fair
testing and continuity.

Diagram

In the diagram shown on the next page, I have shown exactly how I
planned this experiment to work. It was a success in my opinion, as it
was fair, safe and reliable in equal measure.

[IMAGE]

SECTION O: OBTAINING EVIDENCE

Method

Ø Collect the apparatus

Ø Set-up as shown in the diagram

Ø Set the angle of the ramp at 3°

Ø Place the cylinder at the top of the ramp and let go

Ø Get partner to start timer at this point

Ø Stop the timer when cylinder reaches end of ramp

Ø Put the result into the result table and repeat experiment 5 times

Ø Add 3° to the angle and repeat the experiment

Ø The mass of the cylinder here was 0.19818kg

Ø The distance from the bottom here is 30cm, or 0.3m (i.e. the
distance it rolls).


Results

Final tests

Angle (°)

Time 1 (s)

Time 2 (s)

Time 3 (s)

Time 4 (s)

Time 5 (s)

Average (s)

3

1.95

2.10

2.18

2.32

1.96

2.10

6

1.40

1.51

1.48

1.35

1.30

1.41

9

1.02

1.01

0.94

0.98

1.01

0.99

12

0.98

0.99

0.89

0.94

0.98

0.96

15

0.80

0.77

0.76

0.79

0.82

0.78

18

0.65

0.67

0.63

0.64

0.59

0.64

21

0.62

0.54

0.61

0.60

0.50

0.57

24

0.44

0.48

0.46

0.46

0.51

0.47

27

0.42

0.38

0.41

0.37

0.45

0.41

30

0.34

0.41

0.38

0.33

0.35

0.36

From this set of data, using the formula Speed (m/s) = Distance (m) /
Time (s), we can ascertain the speed of the cylinder on its way down
the ramp. Using the average time for each angle (shown above in red)
we can put these results in a table (remembering the distance is
always 30cm)

Angle (°)

Time (s)

Speed (m/s)

3

2.10

0.14

6

1.41

0.21

9

0.99

0.30

12

0.96

0.31

15

0.78

0.38

18

0.64

0.47

21

0.57

0.53

24

0.47

0.64

27

0.41

0.73

30

0.36

0.83

From this, we can successfully conclude that the steeper the angle
becomes, the speedier the cylinder becomes, in a graph looking like
this:

[IMAGE]

SPEED IS PROPORTIONAL TO ANGLE SIZE AS THE LINE OF BEST FIT PASSES
THROUGH THE ORIGIN

We can also now work out the potential energy of the ramp by using the
formula. PE=m.g.hFor example, if we take the formula: h = sin θ x
hypotenuse and use it row one of the above table then we can work out
the height. In this case it is Sin3Ëš x 0.3m =0.02m. Taking this figure
into account, and knowing what the weight of the cylinder is and also
knowing gravity is 9.8, then we can work out the PE of the cylinder
for all angle sizes.

Example: PE = m.g.h

0.19818 x 9.8 x 0.02= 0.03J

Therefore I will predict that the PE of the cylinder grows as the
angle gets steeper. This is because I believe that as the height is
the only changing variable then it is obvious that when this figure
increases it will also increase the product of the three figures that
are multiplied. It is also noteworthy that by using this rule when
keeping height constant and varying the mass of the cylinder, then the
heavier the cylinder the more PE it has.

Angle sizeËš

Mass of cylinder kg

Gravity

Equation for height

Height (m)

Potential energy (J)

3

0.19818

9.8

Sin aËš x 0.3

0.02

0.03

6

0.19818

9.8

Sin aËš x 0.3

0.03

0.06

9

0.19818

9.8

Sin aËš x 0.3

0.05

0.1

12

0.19818

9.8

Sin aËš x 0.3

0.06

0.12

15

0.19818

9.8

Sin aËš x 0.3

0.08

0.16

18

0.19818

9.8

Sin aËš x 0.3

0.09

0.17

21

0.19818

9.8

Sin aËš x 0.3

0.11

0.21

24

0.19818

9.8

Sin aËš x 0.3

0.12

0.23

27

0.19818

9.8

Sin aËš x 0.3

0.14

0.27

30

0.19818

9.8

Sin aËš x 0.3

0.15

0.29

My previous theory was correct. As the angle size increases on the
ramp, the potential energy of the cylinder also increases in a graph
looking like this:

[IMAGE]

PE IS PROPORTIONAL TO ANGLE SIZE AS THE LINE OF BEST FIT PASSES
THROUGH THE ORIGIN

Now we can experiment by using different masses for cylinders and also
by measuring the distance the cylinders take to stop

1) Change mass of cylinder to 0.055kg as opposed to 0.19818kg before,
with the length from which it is released remaining at 0.3m

Angle size

Mass of cylinder (kg)

Time 1

Time 2

Time 3

Average time (s)

Average speed (m/s)

3

0.055

2.18

2.12

2.22

2.17

0.14

6

0.055

2.01

2.05

2.02

2.03

0.15

9

0.055

1.96

1.99

1.95

1.97

0.15

12

0.055

1.77

1.85

1.8

1.81

0.17

15

0.055

1.69

1.72

1.69

1.72

0.17

18

0.055

1.23

1.4

1.29

1.31

0.23

21

0.055

1.02

0.97

1.01

1

0.3

24

0.055

0.89

0.86

0.92

0.89

0.34

27

0.055

0.75

0.75

0.76

0.75

0.4

30

0.055

0.58

0.54

0.52

0.55

0.55

[IMAGE]


Here is a graph demonstrating the relationship between speed + angle
size for where the mass is 0.055kg:

We can therefore work out the potential energy of the lighter
cylinder. I predict using both knowledge from previous work and by
using logic that the lighter cylinder will have less potential energy
because it is the only variable that changes. In this way, when the
mass increases this will cause the product of the three variables
(mass, gravity and height) to increase and vice versa.

Angle sizeËš

Mass of cylinder kg

Gravity

Equation for height

Height (m)

Potential energy (J)

3

0.055

9.8

Sin aËš x 0.3

0.02

0.01

6

0.055

9.8

Sin aËš x 0.3

0.03

0.02

9

0.055

9.8

Sin aËš x 0.3

0.05

0.03

12

0.055

9.8

Sin aËš x 0.3

0.06

0.03

15

0.055

9.8

Sin aËš x 0.3

0.08

0.04

18

0.055

9.8

Sin aËš x 0.3

0.09

0.05

21

0.055

9.8

Sin aËš x 0.3

0.11

0.06

24

0.055

9.8

Sin aËš x 0.3

0.12

0.06

27

0.055

9.8

Sin aËš x 0.3

0.14

0.08

30

0.055

9.8

Sin aËš x 0.3

0.15

0.08

Again, as predicted, the potential energy of the cylinder increases as
the angle of the ramp grows steeper. It shows clearly in comparison
with the graph for when the mass of the cylinder is 0.19818kg that
there is a considerably less amount of PE when the mass is less. This
is due to the fact that the equation for PE (PE = m.g.h, where h is a
changing variable and the m & g are constant) is dependant on both the
angle size (translated using trigonometry into height) and the weight
of the cylinder because as one cannot change gravity in a physics room
easily then the totals of the other variables determine the result.

For the next stage of my experiment, I have decided to change one of
the variables, namely the hypotenuse length from which the cylinder is
dropped. Beforehand, it was 0.3m and has remained so throughout the
recent tests. Now however I will change it to 0.6m to investigate
whether this will affect the PE attained by the cylinder. This is the
table of my results.

Angle sizeËš

Mass of cylinder kg

Gravity

Length of hypotenuse

Height (m)

Av. Time (s)

Speed (m/s)

3

0.19818

9.8

0.6m

0.02

2.11

0.28

6

0.19818

9.8

0.6m

0.03

1.87

0.32

9

0.19818

9.8

0.6m

0.05

1.45

0.41

12

0.19818

9.8

0.6m

0.06

1.25

0.48

15

0.19818

9.8

0.6m

0.08

1.14

0.52

18

0.19818

9.8

0.6m

0.09

0.99

0.61

21

0.19818

9.8

0.6m

0.11

0.76

0.79

24

0.19818

9.8

0.6m

0.12

0.63

0.95

27

0.19818

9.8

0.6m

0.14

0.51

1.18

30

0.19818

9.8

0.6m

0.15

0.45

1.33

We can see clearly once again that the speed increases steadily as the
angle gets steeper and the length of the hypotenuse grows. If we put
these results in comparison with when the length of the hypotenuse was
0.3m then these results emerge:

[IMAGE]


It seems that the speed of the cylinder changes quite a bit when the
angle of the ramp is quite low, but then the two sets of results
become more equal as the angle size increases.


SECTION E: EVALUATION

From looking at the results it is clear that both my aim and
predictions were achieved and that the prediction was correct. I also
found that the speed was increased and that the potential energy
increased with the angle. Looking at the graphs shows that the results
were mainly affected by the angles between 3° - 15°. The second graph
shows a positive correlation between the angle and the speed.

I felt that the experiment was done to the best of my ability and went
well overall. I did all that I could to ensure that the investigation
was fair except for the fact that we used a stopwatch instead of a
ticker timer. Although another negative side being that the table that
we used to hold up the ramp could have one of two effects. One that
they could alter the angle slightly, which affects the results. Two it
may allow the wood to slip or even tilt to one side, which may affect
the results too. Using the table and the stopwatch were both not
scientific which meant that the results could be possibly bias. To
improve the investigation I would redo the experiment in the same
fashion but use the ticker timer and a better material to hold the
ramp in place. Although I still feel that my results were accurate
enough to draw a firm conclusion as I had repeated the experiment 5
times and found an average which gave the desired result.

In most cases my predictions were 100% correct, as I related them to
the results of my preliminary work and used scientific knowledge and
logic to make a calculated hypothesis. I also feel that my results
were as accurate as possible in a situation where one is under
considerable time pressure and in a busy environment. If I had been
given more time I would have probably tested the distance a cylinder
rolled after it left the ramp, although these results are
circumstantial once one has worked out the speed and PE of a cylinder.
I did not include these results into my analysis as I felt
investigating time made for a more interesting investigation where it
would be easier to plot graphs that aided my showing of results. Also,
I may have measured the diameter of the cylinders, although this might
not have proven anything. This concludes my investigation.

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"How the Angle of a Ramp Affects the Speed of a Cylinder Moving Down It." 123HelpMe.com. 24 Apr 2014
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