Question

An aerostat of mass m starts coming down with a constant acceleration ω. Determine the ballast mass to be dumped for the aerostat to reach

Answer 1

Let R be the constant upward thurst on the aerostat of mass m, coming down with a constant acceleration w. Applying Newton's second law of motion for the aerostat in projection form

Now, if Δm be the mass, to be dumped, then using the Eq. Fy=mwy  

Answer 2

Answer:

X = 2mw/g+w

Explanation:

Let R be the upthrust acting on the aerostat,

Let X be the ballast mass to be dumped,

Since the acceleration is acting downwards,

=>mg - R = mw

=> R = mg - mw ••• (1)

After removing the ballast mass, acceleration acts upwards,

=>R - (m - X)g = (m - X)w

=>R - mg + Xg = mw - Xw

=>R + Xg + Xw = mw + mg

=>mg - mw + X(g+w) = mw + mg

=>X(g+w) = 2mw

=>X = 2mw/g+w ••• (ans)