A balloon system of mass m moves upward with acceleration a. What mass x must be removed so that its upward acceleration becomes 3a? Neglect the volume of the removed mass.

Question

G1 Physics · Accepted Answer

Initially F B − m g = m a . F_B-mg=ma. F B ​ − m g = ma . After removing mass x, F B − ( m − x ) g = 3 a ( m − x ) . F_B-(m-x)g=3a(m-x). F B ​ − ( m − x ) g = 3 a ( m − x ) . Eliminating F B F_B F B ​ gives ma+xg=3am-3ax, so x(g+3a)=2ma and x=2ma/(3a+g).