Question

1.

A 0.550 kg metal cylinder is placed inside the top of a plastic tube, the lower end of which is sealed off by an adjustable plunger. The cylinder comes to rest some distance above the plunger. The plastic tube has an inner radius of 6.39 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 2.792.79, what is the initial acceleration ?a of the metal cylinder? Assume the pressure outside of the tube is 1.00 atm

a=

2.

A consumer upset with the latest trend of postal rate increases has decided to try to send letters by balloon even though they may not reach their intended destinations. A 79200 cm gas-filled balloon will provide enough lift for a 45.1  package to be accelerated upward at a rate of 3.10 m/s. For these circumstances, calculate the density of the gas the consumer fills the balloon with. The acceleration due to gravity is ?=9.81 m/s2 and the density of air is ?air=1.16 kg/m3. Neglect the mass of the balloon material and the volume of the package.

3.

A tall, open container is full of glycerine. At what depth ℎh below the surface of the glycerine is the pressure 2230 Pa greater than atmospheric pressure? The density of glycerine is 1.26×103 kg/m3

please help me out. running low on questions. will give best answer

Answer 1

1)

Initial pressure, P1 = (0.55 x 9.8)/(pi x 0.00639^2) + 101325 = 143343.17 Pa

Final pressure, P2 = 2.79 x 143343.17 = 399927.44 Pa

0.55 x a = (399927.44 - 143343.17) x pi x 0.00639^2 - 0.55 x 9.8

Acceleration, a = 50.04 m/s^2

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