Question

A solid, frictionless cylindrical reel of mass M=3.00 kg and radius R=0.400m is used to draw water from a well, A bucket of mass m=2.00kg is attached to a cord that is wrapped around the cylinder. If the bucket starts from rest at the top of the well and falls for 3.00s before hitting the water, how deep is the well.

Answer 1

so sum forces for bucket

mg - T = ma

sum torque for reel

r T = I alpha

but I = 1/2 M R^2 and alpha = a/R

so T = 1/2 M a

mg - 1/2 M a = ma

2*9.81 - 0.5*3*a = 2*a

a=5.606 m/s^2

use kinematics for fall

y = y0 + v0t + 1/2 a t^2

0 = h + 0.5*a*t^2

h = 0.5*5.606*3^2=25.23 m