Mapdd Sapling Learning macmillan learning 481 kg metal cylinder is placed inside

Question

Mapdd Sapling Learning macmillan learning 481 kg metal cylinder is placed inside the top of a plastic tube, ne 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. v-0 a-0 Number 11.01 m/s

Explanation / Answer

Since initially the cylinder is at rest,

so pressure = weight of cylinder / area + atmospheric pressure

= 0.481 * 9.81 / ( pi * 0.00707^2 ) + 101325 = 131373.68 Pa

after the plunger suddenly moves

new pressure = 2.79 * inital pressure = 2.79 *131373.68 = 366532.56 Pa

so, for the cylinder

( new pressure - atmospheric presure ) * area -   weight = mass * acceleration

( 366532.56 - 101325 ) * ( pi * 0.00707^2 )    -   0.481 * 9.81 = 0.481 * a

Therefore, acceleration, a = 76.77 m/sec2

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