You sprint off down the track, quickly reaching a 10 meter height tower of water

Question

You sprint off down the track, quickly reaching a 10 meter height tower of water. At its base is a strange airlock mechanism and a large 60-cm-diameter airinflated balloon. There is also a collection of weights marked in 25, 10, 5, and 1 kg increments. Immediately you turn to the task: you need to enter the airlock and use the balloon to float to the surface. However, a small copper plate next to the airlock says “you must rise to the top in exactly 10 seconds or you lose the round!” What should your total weight be in order to rise to the top of the column of water in exactly 10 seconds?

Solve using Archimedes' principle if possible...

Explanation / Answer

radius of balloon r = 60/2 cm = 0.3 m

Net buoyancy force is equal to the weight of the water displaced

which is equal to Wwater = volume of water displaced x density of water x gravity

Wwater = (4/3)r3 x 1000 x 9.81 =  (4/3)0.33 x 1000 x 9.81 = 1109.484862 N

This is the total upward force. The total downward force, i.e your weight be w = mg where m is the total mass

So, net upward acceleration a = ( 1109.484862 - mg ) /m

To cover 10 m in 10 seconds, the acceleration required be a.

s = 0.5 at2

so, 10 = 0.5 x a x 102

a = 0.2 m/s2

a = 0.2 = ( 1109.484862 - mg ) /m

0.2 m = 1109.484862 - 9.81 m

10.01 m = 1109.484862

m = 110.8376486 kg

So, this should be the tota mass. Total weight will be mg = 110.8376486 x9.81 = 1087.317332 N

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