What is the Mass of the Late Arrival in a Hot-Air Balloon Ride?

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Homework Statement

For a birthday gift, you and some friends take a hot-air balloon ride. One friend is late, so the balloon floats a couple of feet off the ground as you wait. Before this person arrives, the combined weight of the basket and people is 1200kg , and the balloon is neutrally buoyant. When the late arrival climbs up into the basket, the balloon begins to accelerate downward at 0.52m/s^2

What was the mass of the last person to climb aboard?

Homework Equations

F=ma

The Attempt at a Solution

Looked through my notes and I am struggling to find any formula without having a known mass. Any help is appreciated, thanks.

 

[Delphi51]

Welcome to PF, paste!
Try turning it around. If you did know the mass, could you calculate the acceleration?
But you do know the acceleration, so use the same formula to find the mass.

 

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Thanks, how is the mass found if the force with the extra mass unknown.

 

[Delphi51]

There is a downward force of gravity on the whole mass. And an upward buoyant force. These cancel out before the extra passenger gets on. The unbalanced force of the passenger's weight is the F in F = ma. Weight is a force, found using F or W = mg.

 

[paste]

The new force and mass are both unknowns, how does this help?

I've solved it now, thanks.

Spoiler

(1200+m)*0.52=mg
624+0.52m = mg
=9.81*m
624+0.52m-0.52m=9.81m-0.52m
624=9.29m
624/9.29=9.29m/9.29
m=67.17kg