Calculating Force on a Man from Variable Mass Water Jet

AI Thread Summary
The discussion focuses on calculating the force exerted on a man by a variable mass water jet. The initial calculations involve determining momentum changes and the relationship between mass flow rate and velocity. Participants suggest substituting the mass element with the product of water density, cross-sectional area, and velocity to simplify the equations. A key challenge remains in expressing the force without directly knowing the rate of change of velocity. Ultimately, the original poster appears to have resolved their confusion regarding the calculations.
itay2424
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Homework Statement


Water with mass density ρ are being shoot from a jet with cross sectional area A and velocity v0 at a man with mass m0.
1. Find the force acting on a man at rest (assume all the water are absorbed in the clothes)
2. Find the force acting on a man escaping at velocity v<v0.


Homework Equations


dp/dt=ƩF


The Attempt at a Solution


I calculated the momentum of a small water element dm = dmv0.
this is the same as the momentum of the water and the man after the water hits him(no external forces):
dmv0=(m0+dm)v
v=(dmv0)/(m0+dm)

The momentum of the man only after the water hit him is: dp=m0dmv0/(m0+dm).
dp/dt=m0*(dm/dt)*v0/(mo+dm)=ƩF

But i couldn't get an expression of the force without dm or dt.
Thanks for the helpers!
 
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itay2424 said:
Water with mass density ρ are being shoot from a jet with cross sectional area A and velocity v0 …

why are you using dm ? :confused:

the rate of momentum hitting the man can be calulated from ρ A and vo
 
ok, so I replace dm with ρAv0dt. I still have the same problem.
 
force = rate of change of momentum …

what's the problem? :confused:​
 
The problem is that I know the rate of change of mass but not the rate of change of velocity.
Edit: nevermind I think I got it.
 
Last edited:
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