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• Level: GCSE
• Subject: Maths
• Word count: 1838

# What relationship is there between the height a table tennis ball is dropped from and the height it bounces back up to

Extracts from this document...

Introduction

What relationship is there between the height a table tennis ball is dropped from and the height it bounces back up to?

Outline

If a table tennis ball (or any ball for that matter) is dropped onto a surface, it will bounce.  There are many factors that affect the way the ball bounces; air pressure inside the ball, the material it is made from, the surface it is dropped onto, the temperature of the air, the air pressure of the environment, the temperature of the ball and the height it is dropped from.  I am going to investigate how the height that a table tennis ball is dropped from affects the height it will bounce back up to.

Prediction

The only elastic collision that we know of is when particles collide, this is because the total kinetic energy of the particles is conserved and no energy is converted into heat, sound or any other type of energy. This leads me to believe that the table tennis ball or any other ball will never produce a totally elastic collision.  I also think that when the ball is dropped above a certain height, the ball will bounce up to around the same height because the ball will be reaching its terminal velocity and hitting the ground at surface at the same velocity.

Middle

Drop 1/cm

Drop 2/cm

Drop 3/cm

Average/cm

100

65

65

63

63.7

80

51

51

51

51

60

42

42

42

42

40

34

35

36

22

20

15

16

15

15.3

 Height dropped from/cm % of drop height reached by bounce 100 64.0 80 63.8 60 70.0 40 75.0 20 75.0 Average bounce height 69.6%

From the preliminary experiment I found that the lowest accurate height I could read the bounce height from was 20cm otherwise, any lower than that, and the results would not be very accurate. Because of the physical constraints of the physics lab I was working in it was not feasible to carry out any drops higher than 100cm because it was unsafe.

To ensure accuracy will be maintained throughout the experiment I will use the same table tennis ball for the actual experiment and I will make sure that the ball is not damaged by checking it regularly.

All the equipment I used was fairly accurate but could be made better by a number of instruments or methods.  The possibility of human error is quite large because the ball is traveling at quite a high speed. This error could virtually eliminated by using a high speed camera or possibly just a high quality home video camera. A preliminary drop could be done and the camera could be positioned so that it read vertically off the metre rule. The video could then be played back and the frame could be found where the ball ceases to be in motion.

Conclusion

-2 until it hits the ground.

The scatter graph illustrates the results from 20-100cm comparing the drop height with the bounce height.

The bounce height was never greater than the drop height at any point.

As well as proving this prediction I also said that after a certain drop height the bounce height would be the same because the ball would reach its terminal velocity. In the experiment I did not reach this height but it could be predicted by extrapolated from the data using a trend line (or a curve in this case). The drop height that the terminal velocity would be reached at would be around 270cm. I found this by extending the curve of the graph until it leveled out. Any height greater than 270cm should have the same (or nearly the same due to air resistance) bounce height because the terminal velocity would be reached each time.

In the experiment there were any sources of error. The main source of error would be the human eye and hand. This is because the ball is traveling at quite a high speed and it is sometimes hard to determine exact distances, hence the accuracy to +/- 1cm.

I started off with the smallest measurement (of 20cm) and worked my way up in 10cm increments until I reached 100cm.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

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