Solve Pressure Problem: Find Plug Position

[bfr]

[SOLVED] Pressure Problem

SOLVED

Homework Statement

A vertical cylindrical tank is 42 cm tall, 2.00 cm in radius, and is open at the top. Atmospheric pressure is 1.013 x 10^5 N / m^2. A close-fitting cylindrical plug of mass 5 kg is inserted at the top, and is let fall inside. If the temperature of the trapped air does not change, how far from the top of the cylinder is the base of the plug when it comes to rest?

(This is the exact problem, word for word)

Homework Equations

(p1*v1)/t1=(p2*v2)/t2

The Attempt at a Solution

Should I compare the pressure caused by the plug to the atmospheric pressure? ((5*9.8*x)/((.02)^2 * pi))((.02)^2 * pi * x)=1.013 * 10^5 * (.02)^2 * pi * .42 ...or, in terms of variables... m*g*h/(pi*r^2) * (pi*r^2*h)=atmospheric pressure * (pi*r^2*height_of_cylinder)

(pi*r^2*height_of_cylinder) is the volume of the cylinder, (pi*r^2*h) is the volume under the plug.

EDIT: I think this is right. Thanks!

 

[Andrew Mason]

Should I compare the pressure caused by the plug to the atmospheric pressure? ((5*9.8*x)/((.02)^2 * pi))((.02)^2 * pi * x)=1.013 * 10^5 * (.02)^2 * pi * .42 ...or, in terms of variables... m*g*h/(pi*r^2) * (pi*r^2*h)=atmospheric pressure * (pi*r^2*height_of_cylinder)

(pi*r^2*height_of_cylinder) is the volume of the cylinder, (pi*r^2*h) is the volume under the plug.

What is the downward force on the plug? What is the upward force on the plug? How are the two related? (ie. does the plug move?). Translate the downward force into pressure and apply the ideal gas law: P1V1 = nRT1 = nRT2 = P2V2

AM