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 0.175 m that is used to draw water from a well. a bucket of mass 1.5 kg is attached to a cord wrapped around the cylinder. the bucket starts from rest at the top of the well and falls for 2.5 s before hitting the water at a distance of 6 m below the top of the well. neglect the mass of the cord.-what is the linear acceleration of the falling bucket? hint: remember that h=(1/2)at^2 ? a=2h/t^2 -what is the angular acceleration of the rotating pulley? -what is the tension in the cord? -what is the value of the torque that is applied to the pulley by the bucket hanging on the cord? use the tension from the previous question. -find the moment of inertia of the rotating pulley using the torque and the angular acceleration. -calculate the mass of the pulley using the moment of inertia. -what is the change in the potential energy of the bucket from the top of the well to the water level? -what is the linear velocity of the falling bucket just as it hits the water? -what is the angular velocity of the rotating pulley just as the falling bucket hits the water? use the relation between the angular velocity and the linear velocity. -what is the angular momentum of the rotating pulley just as the falling bucket hits the water? use the moment of inertia and the angular velocity of the pulley. -what is the kinetic energy of the falling bucket just as it hits the water? -what is the kinetic energy of the rotating pulley just as the falling bucket hits the water? -what is the total kinetic energy of the falling bucket and the rotating pulley just as the falling bucket hits the water? give your answer to 3 sig figs. -is the total kinetic energy smaller than, equal to, or larger than the magnitude of the potential energy change? ignore small differences in the least significant digit. ke is smaller than ? pe ke is equal to ? pe ke is larger than ? pe -if the pulley were not frictionless, would the total kinetic energy be smaller than, equal to, or larger than the magnitude of the potential energy change? ke would be smaller than ? pe ke would be equal to ? pe ke would be larger than ? pe