What is the linear acceleration of the falling bucket?The principles that you will examine in this lab can be illustrated by studying a falling bucket. Imagine a frictionless pulley in the shape of a solid cylinder of unknown mass M

and radius $0\mathrm{.}235$ m that is used to draw water from a well. A bucket of mass $1\mathrm{.}5$ kg is attached to a cord wrapped around the cylinder. The bucket starts from rest at the top of the well and falls for $2\mathrm{.}5$ s before hitting the water at a distance of $6$ m below the top of the well. Neglect the mass of the cord. $1)$ What is the linear acceleration of the falling bucket? $2)$ What is the angular acceleration of the rotating pulley? $3)$ What is the tension in the cord? $4)$ What is the value of the torque that is applied to the pulley by the bucket hanging on the cord? $5)$ Find the moment of inertia of the rotating pulley using the torque and the angular acceleration. $6)$ Calculate the mass of the pulley using the moment of inertia. $7)$ What is the change in the potential energy of the bucket from the top of the well to the water level? $8)$ What is the linear velocity of the falling bucket just as it hits the water? $9)$ What is the angular velocity of the rotating pulley just as the falling bucket hits the water? $10)$ What is the angular momentum of the rotating pulley just as the falling bucket hits the water? $11)$ What is the kinetic energy of the falling bucket just as it hits the water? $12)$ What is the kinetic energy of the rotating pulley just as the falling bucket hits the water? $13)$ What is the total kinetic energy of the falling bucket and the rotating pulley just as the falling bucket hits the water? $3$ sig figs $14)$ Is the total kinetic energy smaller than, equal to$,$ or larger than the magnitude of the potential energy change?