Solving Part A & B of a Frictionless Piston Problem

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Homework Help Overview

The problem involves a frictionless piston within a tube, where a mass is placed on top of the piston. The setup includes two tubes with different cross-sectional areas, and the task is to determine the flow speed of water exiting the smaller tube and the height of the piston relative to the center of the small tube. The context is fluid dynamics, specifically relating to the principles of flow and pressure in connected systems.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to relate the problem to a previously discussed example involving energy conservation, but expresses uncertainty due to missing height information. Participants question how to proceed without this data and seek guidance on relevant equations.

Discussion Status

The discussion appears to be in an early stage, with participants seeking clarification and assistance. Some guidance has been implied, but no explicit solutions or consensus have emerged regarding the approach to the problem.

Contextual Notes

The original poster notes the absence of height information, which is crucial for applying the energy conservation equation. There is also an indication of imposed homework rules that may limit the type of help that can be provided.

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Homework Statement



A piston can move without friction inside a large tube of .002m^2 of cross sectional area. The weight of the piston is negligible. A mass of kg sits on top of the piston as shown in the figure below. The large tube is connected to a horizontal smaller tube which has 4 x 10^-6 m^2 of cross sectional area. the end of the small tube is open to atmosphere. the piston is moving down at a speed of v = .02 m/s. both of the tubes are filled by water and the density of water is 1000 kg/m^3. Assume frictions and the viscosity of water to be negligible.

A) Find the flow speed of water at the end of the small tube as the water exits to the atmosphere.

We went through a very similar example in class, where the professor used the formula 1/2mv^2=mgh to solve the problem.

However, on this problem the height is not given and I was unsure how to continue to solve the problem.

B) Find the height of the piston from the center of the small tube.

Well if I could figure out part A, I could put velocity into the equation 1/2mv^2=mgh and solve for h.If anyone could guide me towards what equations to use, that would be awesome.

Thanks.
 
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