Task 1 It is required to design a tennis ball for recreational use by settlers on Mars. The primary requirement is that the balls must pass the same 'bounce test' specified for tennis balls used on Earth. This requires that a ball dropped from a height of 254 cm onto concrete will bounce back to a height of 140 cm. The games will be played in a sealed gymnasium pressurised with standard air to 70 kPa. The balls are to have the same mass and diameter as those used on Earth, with modifications to account for the reduced gravity on Mars and the lower air pressure in the habitat. The height a ball recovers after a single bounce is believed to depend on the following parameters: Earth Drop height, L (m) Gravitational acceleration, g (m/s²) Internal pressure of ball above atmospheric (kPa) Diameter, D (m) Mass of ball, M (kg) Target bounce height, h (m) 2.54 9.8 83 0.067 0.057 0.14 Mars 2.54 3.71 ? 0.067 0.057 0.14 0 ms 2 ms 4 ms 3 ms a) Identify the dimensionless parameters which would control the bounce height under these assumptions. b) What pressure should the balls be filled to?

Task 1 It is required to design a tennis ball for recreational use by settlers on Mars. The primary requirement is that the balls must pass the same 'bounce test' specified for tennis balls used on Earth. This requires that a ball dropped from a height of 254 cm onto concrete will bounce back to a height of 140 cm. The games will be played in a sealed gymnasium pressurised with standard air to 70 kPa. The balls are to have the same mass and diameter as those used on Earth, with modifications to account for the reduced gravity on Mars and the lower air pressure in the habitat. The height a ball recovers after a single bounce is believed to depend on the following parameters: Earth Drop height, L (m) Gravitational acceleration, g (m/s²) Internal pressure of ball above atmospheric (kPa) Diameter, D (m) Mass of ball, M (kg) Target bounce height, h (m) 2.54 9.8 83 0.067 0.057 0.14 Mars 2.54 3.71 ? 0.067 0.057 0.14 0 ms 2 ms 4 ms 3 ms a) Identify the dimensionless parameters which would control the bounce height under these assumptions. b) What pressure should the balls be filled to?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

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Task 1
It is required to design a tennis ball for recreational use by settlers on Mars. The primary requirement
is that the balls must pass the same 'bounce test' specified for tennis balls used on Earth. This
requires that a ball dropped from a height of 254 cm onto concrete will bounce back to a height of
140 cm. The games will be played in a sealed gymnasium pressurised with standard air to 70 kPa.
The balls are to have the same mass and diameter as those used on Earth, with modifications to
account for the reduced gravity on Mars and the lower air pressure in the habitat.
The height a ball recovers after a single bounce is believed to depend on the following parameters:
Earth
Drop height, L (m)
Gravitational acceleration, g (m/s²)
Internal pressure of ball above atmospheric (kPa)
Diameter, D (m)
Mass of ball, M (kg)
Target bounce height, h (m)
2.54
9.8
83
0.067
0.057
0.14
b) What pressure should the balls be filled to?
Mars
2.54
3.71
?
0.067
0.057
0.14
0 ms
2 ms
4 ms
3 ms
a) Identify the dimensionless parameters which would control the bounce height under these
assumptions.

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