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Bouncing balls. Research question: What is the relation between the height from which the ball falls and the time in which the ball bounces? How is the time dependent on the height?

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Introduction

Gracja Kowalska kl. 2 IB

BOUNCING BALLS

Research question:

What is the relation between the height from which the ball falls and the time in which the ball bounces? How is the time dependent on the height?

Variables:

INDEPENDENT

DEPENDENT

CONTROLLED

Height from which the balls are let freely

Time in which the balls make 6 bounces

Mass of each ball

Surface on which the experiment is carried

Amount of 6 bounces

Value of gravitation

Apparatus:

  • 2 table tennis balls of different mass
  • stopwatch [±0.05 s]
  • measuring tape [±0.05 cm]
  • 2 different surfaces

image00.png

Sketch: The way experiment was carried

Method:

  1. 7 different heights (45-130 cm) were established using measuring ruler
  2. 2 balls of different mass were picked
  3. starting with the lowest height. the ball was let freely
  4. the time during which ball bounced 6 times was measured and recorded using stopwatch
  5. the experiment was repeated 3 times for each height
  6. the same experiment was carried out with another ball

DCP:

I divided this experiment into 2 phases: the first one, original, was using floor as the surface on which the experiment was carried. The second phase was invented to reduce the uncertainties and make the experiment more reliable, precise and accurate.

For the first phase of the experiment.

...read more.

Middle

3.22

3.15

3.23

130.00

3.59

3.59

3.53

3.28

3.30

3.31

rounded to 2 decimal place

Again, the mean was calculated using given equation.

mean= image01.pngimage02.png

Table 4: Measurements of time it takes for a ball to bounce 6 times on the table

Height [±0.05 cm]

Time [±0.05 s]

Pioneer

Dante

40.00

2.35

2.20

55.00

2.60

2.53

70.00

2.91

2.72

85.00

3.12

2.90

100.00

3.27

3.01

115.00

3.46

3.20

130.00

3.57

3.30

rounded to 2 decimal place

Having all measurements done. I decided to put them in one table to discuss the observations more easily.

Table 5: Measurements for both phases of experiment.

Height [±0.05 cm]

Time [±0.05 s]

Pioneer

Dante

floor

table

floor

table

40.00

2.29

2.35

2.19

2.20

55.00

2.59

2.60

2.54

2.53

70.00

2.97

2.91

2.78

2.72

85.00

3.24

3.12

2.96

2.90

100.00

3.38

3.27

3.17

3.01

115.00

3.58

3.46

3.24

3.20

130.00

3.70

3.57

3.36

3.30

Rounded to 2 decimal place

Considering the values of measurements from the table above, I can say that there is a significant differences between Pioneer ball and Dante. As the Pioneer took more time to bounce 6 times, I can deduce that the ball blew higher and therefore was lighter than the Dante ball, which needed less time to bounce and therefore I can say that it had bigger weight. Also, considering the difference between the measurements of the same ball but on different surfaces, I assumed that since the ball needs less time to bounce on the floor, it means the floor is more stiff and therefore more adequate and suitable for experiment. What is more, I couldn't deduce it without the other surface to compare the measurements.

Also, I calculated the uncertainities for each measurement using the equation

Uncertainity=image03.png

Table 6: Uncertainities for both phases of experiment.

Height [±0.050 cm]

Time uncertainities

Pioneer

Dante

floor

table

floor

table

40.00 0

0.010

0.015

0.035

0.025

55.00 0

0.050

0.015

0.015

0.005

70.00 0

0.010

0.010

0.005

0.010

85.00 0

0.050

0.030

0.025

0.025

100.00 0

0.020

0.030

0.010

0.045

115.00 0

0.035

0.015

0.035

0.040

130.00 0

0.020

0.030

0.015

0.015

Rounded to 3 decimal place

...read more.

Conclusion

  • different types of balls, as each ball have different properties
  • different types of surface, as again, each have different properties
  • time of human reaction [about 0.15 s]
  • the uncertainty of measuring tape [±0.05 cm]
  • the uncertainty of a stopwatch [±0.05 s]
  • the initial velocity of ball could have been other than intentional 0 ms-1
  • the height from which the balls were let free could be imprecise
  • air friction and friction forces could also affect the time of the measurement
  • the uneven loss of energy of the balls during bounces also affected the experiment
  • the bounces were uneven, depending mostly on the surface on which the experiment was taken

Some improvements could be made to make the experiment more reliable and to limit the influence of the uncertainities on the measurements:

  • dropped the balls from higher level, so that the uncertainties of time are less significant and the measurements were easier to take
  • made more measurements - this would lead to more accurate graphs
  • use better stopwatch, reducing the uncertainty of time
  • make sure the intitial velocity of balls are equal to zero, f.e. using starting block
  • measure the time for one bounce and calculate from the equation of free fall
  • use more balls of different type, to get more reliable results
  • use more precise equipment like Vernier to have the measurements of velocity

...read more.

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