Calculating Force on a Man from Variable Mass Water Jet

In summary, we can calculate the force acting on a man at rest and a man escaping at velocity v<v0 by using the formula dp/dt = ρAv0^2 and substituting in appropriate values for mass density and velocity.
  • #1
itay2424
3
0

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!
 
Physics news on Phys.org
  • #2
welcome to pf!

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
 
  • #3
ok, so I replace dm with ρAv0dt. I still have the same problem.
 
  • #4
force = rate of change of momentum …

what's the problem? :confused:​
 
  • #5
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:

1. What are Newton's laws of motion?

Newton's laws of motion are three fundamental principles that describe the behavior of objects in motion. The first law states that an object at rest will remain at rest, and an object in motion will continue in a straight line at a constant speed unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

2. How do Newton's laws apply to variable mass systems?

In variable mass systems, the mass of the object is not constant and can change over time. Newton's second law still applies, but the mass needs to be considered as a function of time. This law can be applied to situations such as rocket propulsion, where the mass of the rocket decreases as fuel is burnt, causing the acceleration to increase.

3. What is the equation for Newton's second law?

The equation for Newton's second law is F = ma, where F is the net force acting on an object, m is the mass of the object, and a is the acceleration. This equation can be rearranged to find any of the three variables as long as the other two are known.

4. How does Newton's third law apply to variable mass systems?

Newton's third law states that for every action, there is an equal and opposite reaction. In variable mass systems, the reaction force can be affected by the mass of the object. For example, in a rocket, the expulsion of exhaust gases creates a reaction force that propels the rocket forward, but this force decreases as the mass of the rocket decreases.

5. Can Newton's laws be applied to non-inertial reference frames?

No, Newton's laws can only be applied to inertial reference frames, which are frames of reference that are not accelerating. In non-inertial reference frames, such as a rotating frame, fictitious forces need to be taken into account, making the application of Newton's laws more complicated.

Similar threads

Rocket acceleration problem: confused about Newton's 2nd Law
    • Introductory Physics Homework Help
2
Replies
42
Views
3K
Weight of gold chain when dropped on a weighing scale
    • Introductory Physics Homework Help
Replies
12
Views
1K
Trouble with a Rocket Propulsion question (Variable Mass & Momentum)
    • Introductory Physics Homework Help
Replies
2
Views
1K
Atwood machine with variable mass
    • Introductory Physics Homework Help
Replies
7
Views
3K
Momentum in different referance frames
    • Introductory Physics Homework Help
Replies
6
Views
911
Solving Baseballs Colliding with a Car: Find Speed & Position
    • Introductory Physics Homework Help
Replies
5
Views
1K
I Newton's Second Law - variable mass case
    • Mechanics
Replies
14
Views
1K
How Is Velocity Calculated When a Rod Falls onto a Mass Connected by a Spring?
    • Introductory Physics Homework Help
Replies
23
Views
2K
Insights How to Apply Newton’s Second Law to Variable Mass Systems
    • Mechanics
Replies
0
Views
1K
I Doubt about variable mass systems
    • Mechanics
Replies
30
Views
815

Hot Threads

Recent Insights

Back
Top