In need of help with a physics problem, anything is appreciated.

Question

Answer 1

Let

g be the gravitation acceleration (known),

M be the mass of the bucket (assumed given),

m be the mass of the reel (assumed given),

r be the radius of the reel (assumed given),

a be the acceleration of the bucket (to be calculated),

T be the tension in the string (to be calculated),

I = mr²/2 be the moment of inertia of the reel.

a.

There is one force acting on the reel -- the downward tension T.

There are two forces acting on the bucket --

downward weight Mg, and

upward tension T.

b.

Reel:

Ia/r = Tr (Moment of inertial x angular acceleration = torque)

amr/2 = Tr (After substituting I into the above)

Bucket:

Ma = Mg - T (Mass x acceleration = force)

c. and d.

T = am/2 (From the equation for the reel)

Ma = Mg - am/2 (After substituting T into the equation for the bucket)

a = gM/(M+m/2) (Solving for a)

T = gMm/(2M+m) (Substituting a into solution for T)

e.

Let t = 3s be the time the bucket falls.

From definition of acceleration the distance is

at²/2 = 9gM/(2M+m)