A hot air balloon loaded with sandbags has a total mass of M. It is descending with a downward acceleration of g/2, where g is the acceleration of free fall. How much sand must be released from the sandbags in order that hot air balloon ascends with the same acceleration?
Answers
During downfall,
let the force exerted by the hot air = F
So upward force = F
Downward force = weight = Mg
Hence
F -Mg = -Mg/2
=> F = Mg/2
This force of hot air will remain constant during the upward motion also.
Let during upward motion the net mass will be m after releasing the sandbags.
Hence ,
F - mg = mg/2
=> F = 3m/2g
=> Mg/2 = 3m/2g
=> M = 3m
=> m = M/3
Hence the amount of sandbags to be thrown,
= M-m = M - M/3 = 2M/3
Hence 2/3rd of the total weight must be thrown away in order to give the system an upward acceleration of g/2 .
Answer:
The answer is 2 M/3.
Regards,
Nishanth V
Explanation:
Here,
B = buoyant force of air
M = mass of hot air ballon
m = mass of sandbags
g = acceleration due to gravity
a = the upward/downward acceleration of ballon(net acceleration)
