Physics experiment #15: Investigating a bouncing ball Nicolai Solheim 3IBG

Physics 3HL

Physics experiment #15: Investigating a bouncing ball Purpose: Investigate how change in temperature (T) affects the bouncing height of a ball. Equipment: […] for dropping the ball: a ball

a stand a clamp

a ruler gaffer tape […] for digital observation

a remote video camera a laptop/desktop with adequate software […] for change in temperature (T):

a beaker a gas cylinder a stand for warming the beaker a digital thermometer H2O as water H2O as snow/ice

Procedure: 1) First the lab environment was set up as on the illustration above, where the green

arrow represents the video camera and the yellow line represents the ruler.

2). The beaker was then filled with water and heated to temperature Tx. The ball was then left in the beaker for 3 minutes before put in the clamp and dropped from the stand at height d. This was repeated 5 times for each value of Tx, and we let the ball bounce two times. For temperature 1.50 C̊, there was poured ice and snow into the beaker

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Physics experiment #15: Investigating a bouncing ball Nicolai Solheim 3IBG

Physics 3HL

The values of Tx used were: T1) 01.50 C̊ T2) 20.00 C̊ T3) 40.00 C̊ T4) 60.00 C̊ T5) 80.00 C̊

T6) 97.50 C̊ 3) The different bouncing heights were then read of the movie clips in slow motion mode.

Experimental Data:

Throughout the experiment the ball was dropped from a height of 65.0 cm and the uncertainty of the measurements were ± 0.5 cm both for the ruler and the digital observation tool. The uncertainty for the temperature (T) was ±3.00 ̊C as it was difficult to keep the water at a constant temperature. In the table below are the experimental values as read from the video clips in slow motion. The first value represents the height of the first bounce, and the second value the height of the second bounce: {1st bounce} | {2nd bounce}.

Tx Trial 1 ± 0.5 cm Trial 2 ± 0.5 cm Trial 3 ± 0.5 cm Trial 4 ± 0.5 cm Trial 5 ± 0.5 cm 01.50 ±3.00 C̊ 42 cm | 31 cm 45 cm | 32 cm 47 cm | 32 cm 45 cm | 33 cm 47 cm | 32 cm 20.00 ±3.00 C̊ 53 cm | 39 cm 55 cm | 44 cm 53 cm | 41 cm 53 cm | 42 cm 52 cm | 41 cm 40.00 ±3.00 C̊ 54 cm | 43 cm 55 cm | 45 cm 54 cm | 44 cm 53 cm | 44 cm 54 cm | 43 cm 60.00 ±3.00 C̊ 57 cm | 45 cm 56 cm | 44 cm 58 cm | 45 cm 54 cm | 44 cm 57 cm | 44 cm 80.00 ±3.00 C̊ 57 cm | 46 cm 58 cm | 46 cm 57 cm | 45 cm 57 cm | 46 cm 59 cm | 46 cm 97.50 ±3.00 C̊ 58 mc | 46 cm 58 cm | 47 cm 59 cm | 46 cm 60 cm | 46 cm 58 cm | 45 cm Data Processing:

The first thing we want to do is to calculate the average values for each value of Tx: Tx Average ± 0.5 cm 01.50 ±3.00 C̊ 45.2 cm | 32.0 cm 20.00 ±3.00 C̊ 53.2 cm | 41.4 cm 40.00 ±3.00 C̊ 54.0 cm | 43.8 cm 60.00 ±3.00 C̊ 56.4 cm | 44.4 cm 80.00 ±3.00 C̊ 57.6 cm | 45.8 cm 97.50 ±3.00 C̊ 58.6 cm | 46.0 cm When this is done, we want to plot our data collection into a coordinate system, in order to see if there are any recognizable patterns.

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Physics experiment #15: Investigating a bouncing ball Nicolai Solheim 3IBG

Physics 3HL First we plot all the trials individually, giving us the following map:

We may also want to draw lines between the trials, which gives us:

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Physics experiment #15: Investigating a bouncing ball Nicolai Solheim 3IBG

Physics 3HL

From the graphs on the previous page, we may see a pattern which represents the bouncing heights of the ball used in the experiment. The lines that are drawn between the trials are, however, not linked in any way as the trials were done independently of each other. The lines are only there to suggest a pattern. Further we want to add the average values:

We can at this point start to see a pattern: the bouncing height becomes smaller when T goes towards 0 degrees and larger as T increases.

We may in terms of Hook’s Law assume that the elastic of the ball used in this experiment is given by the formula  , where t represents the tension or elastic of the ball. This means that the factors affecting the bouncing height will be given by both k and x, where k is the spring constant and x the amount the ball is compressed when hitting the ground. The spring constant, k, is affected by temperature (T), and we may therefore assume that T affects the bouncing height, which may be supported by the graphs we have made.

The other factor that affects the bouncing height of the ball, in terms of x, is the drop height. As we are using a constant drop height for the first bounce throughout the whole experiment phase, we may assume that x is constant for the first bounce only. It is, however, the “spring constant” k that changes due to change in temperature (T).

If we look away from all independent trial values, and only concentrate on the average values, we obtain the following graphs, as may be viewed on the next page.

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Physics experiment #15: Investigating a bouncing ball Nicolai Solheim 3IBG

Physics 3HL

By using adequate computer software one may also insert an exponential function for a restricted area. This function gives a theoretical model of the bouncing heights in this experiment.

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Physics experiment #15: Investigating a bouncing ball Nicolai Solheim 3IBG

Physics 3HL

  

We may assume that the bouncing height of the ball would follow these models for the different bouncing height. We may also look at these bouncing heights in terms of percentages, and we may use the following formula to find the percentage: 100

.   

For finding the uncertainty in percentages, we do the following: .

100 0.76 %

65.0 

By using the following average values for bouncing heights:

Tx Average ± 0.5 cm T1 = 01.50 ±3.00 C̊ 45.2 cm | 32.0 cm T2 = 20.00 ±3.00 C̊ 53.2 cm | 41.4 cm T3 = 40.00 ±3.00 C̊ 54.0 cm | 43.8 cm T4 = 60.00 ±3.00 C̊ 56.4 cm | 44.4 cm T5= 80.00 ±3.00 C̊ 57.6 cm | 45.8 cm T6 = 97.50 ±3.00 C̊ 58.6 cm | 46.0 cm

We get the following percentages of the total drop height: Tx 1st Bounce ± 0.76 %

45.2 2nd Bounce ± 0.76 %

T1 100 . % .0

65.032

100 .  % 53.2 65.0 

100 . % 41.465.0

T2 100 .  % 54.0 65.0 

100 . % 43.865.0

T3 100 .  % 56.4 65.0 

100 . % 44.465.0

T4 100 .  %T5 57.6 

65.0 100 . %

45.865.0

100 .  %T6 58.6 

65.0 100 . %

46.065.0

100 .  %

ere see that the bouncing height increases as the temperature of the ball

y doing this we have also found the first bouncing heights in percentage from the

.  %

.  %

.  %

.  %

.  %

We can hincreases towards the boiling point. Bconstant drop height 65.0 cm: Tx 1 Bounce ± 0.76 % st

T1 .  % T2

T3 T4 T

5

T

6

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Physics experiment #15: Investigating a bouncing ball Nicolai Solheim 3IBG

Physics 3HL

B ing the average values of bouncing heights from the first bounces, we can calculate e percentages of the second bounces.

1 45.2 cm | 32.0 cm

1

y usth Tx Average ± 0.5 cm TT2 53.2 cm | 41.4 cm T3 54.0 cm | 43.8 cm T4 56.4 cm | 44.4 cm T5 57.6 cm | 45.8 cm T6 58.6 cm | 46.0 cm Tx 2nd Bounce ± 0.76 %

32.0 45.2 

100 .41.4 

T %

53.2 T2 100 . %

43.8 54.0 

T3 100 . % 44.4 56.4 

T4 100 . % T5 45.8 

57.6 100 . %

T6 46.0 58.6 

100 . %

now are to compare the two bouncing heights with respect to individual drop height, we get the following. Tx 1st Bounce ± 0.76 % 2nd Bounce ± 0.76 % Difference ± 0.76 %

. % + 4.03 %

.  % 7 . %

.  % . %

We can from this get an impression of the difference in the first and second bouncing height, and see that the bouncing height increases as the te armer.

e

ht. W

the bouncing height of the ball used in this experiment increases as the temperature

If we

T1 .  % . % − 1.26 % T2 .  % T3 .  %

.  %. % . %

+ 1.96 % T4

+ 8.05 %

T5 + 9.10 % T6 + 11.66 %

mperature becomes w

Conclusion: If we are to draw a conclusion from this experiment, we can definitely say that change in temperature affects the bouncing of the ball used in this experiment. When thball is cooled down to T1 the bouncing height is only 69.53 percent of the total drop heig e do however see that the bouncing height of the second bounce is increased by1.26 percent. We can assume that this is a result of the room temperature which was approximately 24 Celsius; the body was in other words heated as it was moving. If we look at the other bounces, from T2 and up, we may see that the bouncing heights have increased by approximately 7 percent and more. We may therefore say that

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Physics experiment #15: Investigating a bouncing ball Nicolai Solheim 3IBG

Physics 3HL

8 

eet a

tes,

is cooler. It

nce

,

erature (within the boundaries used in this experiment)

increases. It is, however, not unlikely that the elastics of the ball at some point will mlimit, and hence, the bouncing height will decrease – or the ball will melt.

We do at T6 see that the first bouncing height is 11.66 percent larger than the second bouncing height. An explanation for this may be that the high temperature is being cooled down as the body is moving. As the ball only was boiled for three minuwe may assume that the core and the outer areas have different temperatures. It’s likely that the outer areas have the same temperature as the water, and that the coreis therefore possible that the ball is cooled down as it moves. This may be supported as T4 and T5 experiences the same as in T6. The differealso decreases towards T3. For further investigation on this issue, one could increase the experimental trialsdifferent heights and include more temperatures. More precise digital observation tools would be adequate, as well as including different bodies.

We may from this conclude that the temperature will affect the bouncing height of the ball used. As the tempincreases the bouncing height will increase, and as the temperature decreases the bouncing height will decrease.