# Newton laws and variable mass

1. May 5, 2012

### itay2424

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
dp/dt=ƩF

3. 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 couldnt get an expression of the force without dm or dt.
Thanks for the helpers!

2. May 5, 2012

### tiny-tim

welcome to pf!

hi itay2424! welcome to pf!

(try using the X2 button just above the Reply box )
why are you using dm ?

the rate of momentum hitting the man can be calulated from ρ A and vo

3. May 5, 2012

### itay2424

ok, so I replace dm with ρAv0dt. I still have the same problem.

4. May 5, 2012

### tiny-tim

force = rate of change of momentum …

what's the problem?

5. May 5, 2012

### itay2424

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: May 5, 2012