Solving Part A & B of a Frictionless Piston Problem

AI Thread Summary
To solve Part A of the frictionless piston problem, the flow speed of water exiting the small tube can be determined using the principle of conservation of mass, specifically the equation of continuity, which states that the product of cross-sectional area and flow speed must remain constant. Given the cross-sectional areas of the large and small tubes, the flow speed at the small tube's exit can be calculated based on the piston’s downward speed. For Part B, once the flow speed is known, it can be substituted into the energy conservation equation 1/2mv^2 = mgh to find the height of the piston. The discussion highlights the need for guidance on the appropriate equations to apply in these calculations. Understanding these principles is crucial for solving the problem effectively.
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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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