Question

A 0.389 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 6.22 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 2.07, what is the initial acceleration of the metal cylinder? Assume the pressure outside of the tube is 1.00 atm.

Answer 1

To calculate the initial acceleration of the metal cylinder, use the equation F = ma by subtracting the pressure inside the tube from the pressure outside the tube and multiplying it by the area of the cylinder.

Step-by-step explanation:

To calculate the initial acceleration of the metal cylinder, we can use the equation F = ma, where F is the net force acting on the cylinder and a is the acceleration.

The net force can be found by subtracting the pressure inside the tube from the pressure outside the tube and multiplying it by the area of the cylinder.

The pressure difference can be determined by multiplying the atmospheric pressure by the factor of 2.07. The area of the cylinder can be calculated using the formula A = πr^2, where r is the radius of the cylinder.

Substituting these values into the equation F = ma, we can solve for the acceleration.