For your birthday, you decide to go on a hot-air balloon ride with a bunch of yo

Question

For your birthday, you decide to go on a hot-air balloon ride with a bunch of your friends. The total mass of the balloon, all the people aboard, and your party supplies is 268 kg. At one point, the balloon is motionless in the air, because the downward-acting weight of the people, balloon and supplies is balanced by an upward-acting "buoyant" force exerted by the air. If this upward force remains constant, what is the mass of the supplies that you should drop overboard so that the balloon acquires an upward acceleration of 0.223 m/s^2?

Explanation / Answer

let the mass remaining after dropping the supplies be 'm''

upward force = Fb= weight of 268 kg = 268 x 9.8 = 2626.4 N

downward force = Fg= weight of mass remaining = mg

upward acceleration = a = 0.223 m/s2

the force equation is given as ::

Fb - Fg = ma

2626.4 - mg = ma

2626.4 = m (g + a)

m = 2626.4 / (9.8 + 0.223)

m = 262.04 kg

so mass dropped = 268 kg - 262.04

mass dropped = 5.96 kg

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