Fluid dynamics+calculus: picking which vars to integrate

In summary: The rate of change of momentum is:What this tells you is that the momentum of the water being forced through the snorkel is being reduced by a certain amount each second. This amount is given by:This tells you that the water's momentum will be reduced by 9.8 kg each second. This is the force that slows the sled down.
  • #1
white 2.5rs
14
0

Homework Statement



This is extra credit, and the test has passed (no one got it), the prof said he'll still take efforts on it so here is my attempt.

A rocket sled is going down a test track at 180 km/hr (calculated to 50 m/s). It drops a snorkel into a trough of water. This diverts 30 kg/s of water vertically. The sled has mass of 500kg (including the snorkel and water in it).

The question is how far will the sled travel once it drops the snorkel.

I know I need to integrate from 50 to 0... but beyond that I don't know what vars to integrate in order to get something to plug into kinematic equations...

negate fluid+track+air friction.


Homework Equations





The Attempt at a Solution



I know to integrate from 50 to zero... but i don't know which vars to integrate
 
Physics news on Phys.org
  • #2
Ask yourself what is causing the sled to slow down (lose momentum:wink:)...What rate does that 'something' decrease the sled momentum at?

Also, are you told the angle that the sled makes with the vertical or anything about the shape of the snorkel?
 
  • #3
The sled slows due to the resultant force associated with shooting water 90 deg from the horizontal.

The shape/angle aren't important as far as the class knows. Only knowing flow @ 180km/hr is important.
 
  • #4
white 2.5rs said:
The sled slows due to the resultant force associated with shooting water 90 deg from the horizontal.

The shape/angle aren't important as far as the class knows. Only knowing flow @ 180km/hr is important.

The shape/angle are actually very important! However, since you are not told anything about them you will need to make some simplifying assumptions. I would assume that the track is horizontal if not told otherwise. And I would assume that the shape of the snorkel is such that all of the force of the water that is ejected is directed opposite to the sled's motion. (In general, only a fraction of that force will actually be directed opposite the sleds motion)

Anyways, what is the rate of change of the momentum of the water being forced through the snorkel at time [itex]t[/itex] (in the rest frame of the track/water) if the sled's speed at time [itex]t[/itex] is [itex]v(t)[/itex] (Remember, momentum is a vector!)? What acceleration [itex]a(t)[/itex] does that cause the sled?
 
  • #5
this is only a quick response but the angle is at 90 deg
the shape is to be neglected
the change in momentum does change as it is integrated from 50 to 0 but i am still unfamiliar w/ which vars to integrate
 
  • #6
white 2.5rs said:
the change in momentum does change as it is integrated from 50 to 0 but i am still unfamiliar w/ which vars to integrate

Start by finding a relationship between the speed of the boat at a given instant and the rate of change of its momentum at that instant:

gabbagabbahey said:
Anyways, what is the rate of change of the momentum of the water being forced through the snorkel at time [itex]t[/itex] (in the rest frame of the track/water) if the sled's speed at time [itex]t[/itex] is [itex]v(t)[/itex] (Remember, momentum is a vector!)? What acceleration [itex]a(t)[/itex] does that cause the sled?
 

FAQ: Fluid dynamics+calculus: picking which vars to integrate

What is fluid dynamics?

Fluid dynamics is a branch of physics that studies the movement of liquids and gases under the influence of external forces.

What is calculus in the context of fluid dynamics?

Calculus is a branch of mathematics that is used to describe and analyze the behavior of fluids using concepts such as derivatives and integrals.

How do you determine which variables to integrate in fluid dynamics?

The variables to be integrated in fluid dynamics depend on the specific problem being solved. Generally, one chooses to integrate variables that are easily measured and are relevant to the problem at hand.

What is the significance of integrating variables in fluid dynamics?

Integrating variables in fluid dynamics allows us to find the relationships between different physical quantities and understand the behavior of fluids in different situations. It also allows us to make predictions and solve complex problems.

Are there any specific techniques for choosing which variables to integrate in fluid dynamics?

Yes, there are several techniques for choosing which variables to integrate in fluid dynamics, such as using physical reasoning, dimensional analysis, and considering the boundary conditions of the problem. It is important to carefully consider all relevant variables and their relationships to accurately integrate and solve a problem.

Back
Top