Calculating Force on a Man from Variable Mass Water Jet

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Homework Help Overview

The problem involves calculating the force acting on a man from a variable mass water jet, considering different scenarios: one where the man is at rest and another where he is moving away from the jet. The context includes concepts of momentum and mass flow rate.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to derive an expression for force using momentum conservation principles but struggles with the variables involved, particularly with the mass flow rate and velocity changes. Some participants question the use of certain variables and suggest alternative formulations based on mass density and cross-sectional area.

Discussion Status

The discussion is ongoing, with participants providing insights and alternative approaches. There is a recognition of the complexity in relating mass flow rate to changes in velocity, and some guidance has been offered regarding the calculation of momentum. The original poster indicates a potential breakthrough in understanding.

Contextual Notes

Participants are navigating the constraints of the problem, including the assumptions about water absorption and the dynamics of the water jet. There is an acknowledgment of the need for clarity on the relationship between mass flow and velocity changes.

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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hi itay2424! welcome to pf! :smile:

(try using the X2 button just above the Reply box :wink:)
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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