Ask FunTrivia: Questions and Answers

**Answers to 100,000 Fascinating Questions**

Question #121316. Asked by **armindasantana**.

Last updated **May 04 2011**.

Originally posted May 04 2011 3:02 PM.

Answer has

16 year member

412 replies

Answer has

It was Galileo Galilei who showed that objects fall at the same rate regardless of their masses. The short answer, therefore, is that all 3 hit the deck at the same time.

Proof:

From Newton's Laws of Motion, F = m.a (force equals mass of the object times its acceleration).

From Newton's Law of Gravity, F = G.M.m/d%B2 (force equals the Universal Gravitational Constant times mass of the Earth times the mass of the object all divided by the square of the distance from the centre of the Earth to the object). Rearranging this equation we have:

F = m.(G.M/d ² )

So the acceleration a in the first equation is actually equal to G.M/d%B2 i.e. acceleration does not depend on the mass of the object, QED.

But (there's always a but) the three spheres will have different sizes. Obviously the 1kg sphere will be the smallest and the 3kg sphere will be the largest. That means the smallest sphere will have less air resistance than the larger and largest. Therefore they will hit the deck in the order 1kg, 2kg and 3kg.

Further, each sphere will suffer an upthrust according to Archimedes' Principle - "when a body is wholly or partially immersed in a fluid (in this case air) it will suffer an upthrust or loss in weight equal to the weight of the fluid displaced". Thus the 3kg sphere, displacing the most air, will suffer the greatest upthrust and thereby be retarded most. Therefore the spheres will hit the deck again in the order 1kg, 2kg and 3kg.

The long answer is to calculate these two effects and give a precise time for each sphere, and I leave it to the reader to do so. :-)

I suggest there will be no appreciable, practical effect and the spheres fall at the same rate over the 10 metres mentioned.

Proof:

From Newton's Laws of Motion, F = m.a (force equals mass of the object times its acceleration).

From Newton's Law of Gravity, F = G.M.m/d%B2 (force equals the Universal Gravitational Constant times mass of the Earth times the mass of the object all divided by the square of the distance from the centre of the Earth to the object). Rearranging this equation we have:

F = m.(G.M/d ² )

So the acceleration a in the first equation is actually equal to G.M/d%B2 i.e. acceleration does not depend on the mass of the object, QED.

But (there's always a but) the three spheres will have different sizes. Obviously the 1kg sphere will be the smallest and the 3kg sphere will be the largest. That means the smallest sphere will have less air resistance than the larger and largest. Therefore they will hit the deck in the order 1kg, 2kg and 3kg.

Further, each sphere will suffer an upthrust according to Archimedes' Principle - "when a body is wholly or partially immersed in a fluid (in this case air) it will suffer an upthrust or loss in weight equal to the weight of the fluid displaced". Thus the 3kg sphere, displacing the most air, will suffer the greatest upthrust and thereby be retarded most. Therefore the spheres will hit the deck again in the order 1kg, 2kg and 3kg.

The long answer is to calculate these two effects and give a precise time for each sphere, and I leave it to the reader to do so. :-)

I suggest there will be no appreciable, practical effect and the spheres fall at the same rate over the 10 metres mentioned.

May 04 2011, 4:15 PM

Answer has

17 year member

2344 replies

Answer has

An accepted way to show a superscript is with the carat.

2^4 means "two to the fourth power."

http://www.or.nrcs.usda.gov/technical/engineering/eng-data/tips/mtext_special%285-23-07%29.pdf

2^4 means "two to the fourth power."

http://www.or.nrcs.usda.gov/technical/engineering/eng-data/tips/mtext_special%285-23-07%29.pdf

May 04 2011, 5:30 PM

Answer has

18 year member

452 replies

Answer has

Great answer by watchkeeper. If you take air out of the equation, then all three travel at the same rate and will hit at the same time. This was elegantly demonstrated by astronaut Dave Scott on the Apollo 15 moon mission whereby he dropped a bird feather and a hammer and they clearly fell at the same rate. What sort of bird feather it was could be the subject of another question....

May 04 2011, 7:07 PM