A 0.481 kg metal cylinder is placed inside the top of a plastic tube, the lower
ID: 1301847 • Letter: A
Question
A 0.481 kg metal cylinder 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 inner radius of 7.07 mm, and is frictionless. Neither the plunger nor the metal cylinder allow any air to flow around them. If the plunger is suddenly pushed upwards, increasing the pressure between the plunger and the metal cylinder by a factor of 2.79, what is the initial acceleration of the metal cylinder? Assume the pressure outside of the tube is 1.00 atm.
Explanation / Answer
If P is the initial pressure and A the area of the cylinder, we know that initially PA = mg because the force holding the cylinder up (pressure times area) is equal to the weight.
If the pressure is increased by 2.79 then the net upwards force is 2.79mg - mg = 1.79mg. The acceleration therefore is 1.79g or 17.56 m/s2.
The other data in the problem is just noise.
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