A 0.504 kg metal cyclinder is placed inside the top of a plastic tube, the lower

Question

A 0.504 kg metal cyclinder is placed inside the top of a plastic tube, the lower end of which is sealed off by an adjustable plunger, and comes to rest some distance above the plunger. The plastic tube has an inncer radius of 6.39 mm and it's frictionless. Neither the plunger nor the metal cyclinder allow any air to flow around them.

If the plunger is suddenly pushed upwards, increasing the pressure between the plunger and the metal cyclinder by a factor of 1.59, what is the initial acceleration of the metal cyclinder? Assume the pressure outside of the tube is 1.00 atm.

Number: m/s^2

Explanation / Answer

here
The cylinder has cross-sectional area A.

initially, pressure p = mg / A, since p*A = mg

Later, p = mg/A + 0.59mg/A = weight/A + acceleratingforce/A

Ergo, the acceleratingforce = 0.59mg

and therefore the acceleration = 0.59g = 0.59 * 9.8m/s^2 = 5.78 m/s^2

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