Max Accel for Pressure in Heart to Reach Brain

[aopaop03]

A man is standing up in aircraft that has a constant accerelation upward. Find the maximum accerelation that heart can't pump blood to brain. Head is 50cm above the heart. Pheart=100mmHg
ΣF=ma
Fn-mg=ma
Fn=m(g+a)=ρ(blood)V(g+a)
Pfoot=ρ(blood)H(g+a)
Pheart=Pfoot-ρ(blood)(H-0.5)(g+a)
I don't know in this situation Pheart=100mmHg or not

 

[CWatters]

It's a lot simpler than you think.

Pfoot=ρ(blood)H(g+a).....(1)
Pheart=Pfoot-ρ(blood)(H-0.5)(g+a)......(2)

The hard way to solve this is to expand (2) and substitute (1) into (2) to eliminate Pfoot and H.

Try it and the answer might suggest an easier way.

 

[CWatters]

I don't know in this situation Pheart=100mmHg or not

Yes. That's the pressure the heart can create.