A hot-air balloon has a total mass of 720 kg. It accelerates downwards (towards the ground) at 2.7m/s^2 even though an upwards lift force in acting on it.

Question

Find
a:Find the lift force acting on the balloon

B)What must be the total mass that needs to be thrown overboard if the operator on the hot-air balloon decides to accelerate upwards at 3.6 m/s^2 ?
Assume the upwards lift force remains the same.

Answer 1

net force=ma
lift-mg=ma but a=-2.7
solve for lift.

Answer 2

a. We'll call downward acceleration
(-), and upward (+).

a + g = -2.7 m/s^2,
a - 9.8 = -2.7,
a = -2.7 + 9.8 = 7.1 m/s^2.

F = ma = 720 kg * 7.1 m/s^2 = 5112 N.

b. a + g = 3.6 m/s^2,
a - 9.8 = 3.6,
a = 3.6 + 9.8 = 13.4 m/s^2.

F = ma = 5112 N,
m * 13.4 = 5112,
m = 5112 / 13.4 = 381.5 kg, max.

m = 720 - 381.5 = 338.5 kg to be thrown overboard.