Answer: a=2.45m/s/s
Step-by-step explanation:
By newton's second law
The forces on the bucket are the tension in the string and the weight of the bucket; the bucket accelerates down, so we have
T - mg = -ma (eq. 1)(m is mass of bucket)
the tension exerts a torque on the reel of magnitude TR where R is the radius of the reel; this torque causes an angular acceleration A, such that
torque = I A
the moment of inertia of a cylindrical disk is 1/2 MR^2 where M is the mass of the reel, so we have
torque = T R = I A = 1/2 MR^2 A
or T=1/2 MR A
the angular acceleration is related to linear acceleration via
a = RA, so we get
T=1/2 MR(a/R)=1/2Ma
use this in equation (1) to get
T-mg=-ma
1/2Ma-mg=-ma
a(1/2M +m)=g
a=g/(1/2 M +m)
using relevant values, we get:
a=9.8m/s/s/(0.5x4 kg + 2.00kg)
a=2.45m/s/s
