Cody's Awesome Balloons- 1

Cody (colored Yellow head) wants to fly up in the sky, so he has tied infinite hot air balloons to each other as shown in the right part of the image (Yeah, he can do that, infinite balloons ) .

The largest balloon is providing him an upward force of 100 100 N. The balloon just above that largest balloon is providing an additional force of 10 10 N. The third provides 1 1 N, and so on.

If Cody weighs 54.4 54.4 kg, find with how much acceleration he is going up in the sky.

Details and assumptions :-

\bullet 54.4 54.4 kg is Cody's mass.

\bullet Acceleration due to gravity g = 10 m / s 2 g=10 m/s^2

\bullet Cody is so awesome that he made balloons of really negligible mass.


This problem is a part of the set Cody Mechanics


The answer is 0.

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2 solutions

Lets claculate total upward force .....its like 111.1111...... till infinity . So lets say x =111.11...
Now 10x = 1111.11....... On subtracting 9x = 1000 X = 1000÷9 Total downward force is mg = 544 which is more than upward force so he wont accelerate up So his upward acceleration is 0

True ! That was just a tricky troll problem, try it's part 2 too ;)

Aditya Raut - 6 years, 9 months ago

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Ya, I got stumped when -7.957 was marked rong.

Satvik Golechha - 6 years, 9 months ago

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Tricky trickster.... I asked upward acceleration, and here Cody won't fly only ! LOL

Aditya Raut - 6 years, 9 months ago

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@Aditya Raut @aditya raut !!!!your series of cody mechanics is awesome please keep on sharing more problems

sanshodhan shende - 6 years, 6 months ago
Sanshodhan Shende
Nov 23, 2014

The total force upwards can be calculated by a formula for sum of a decreasing infinite GP which is a/1-r(a whole upon 1-r) where a- is first term of a GP ,r is the common ratio .Here GP is 100,10,1,0.1------------with r=0.1 thus by using formula we get total upward force as 1000/9 and weight mg=544 N(newton) which is greater than upward force and hence acceleration with which he is going up is equal to 0.

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