What Torque Is Required to Raise a Water Bucket from a Well?

[OierL]

Homework Statement

Water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a cylinder of mass 50 kg and diameter 25 cm. As you turn this cylinder with a crank, the rope raises the bucket. If the mass of a bucket of water is 20 kg, what torque must you apply to the crank to raise the bucket of water at a constant speed?

Solution:
a. 2.5 N.m
b. 24 N.m
c. 80 N.m
d. 2400 N.m
e. 49 N.m
I don't know which one is the correct solution and why they give me the data of the weight of the cylinder.

Homework Equations

∑F=m*a
∑M=F*r and ∑M=I*α

The Attempt at a Solution

If we raise the bucket at a constant speed, ∑M=0
-m(bucket)*g + T=m*α*r=0 (constant speed) ⇒ T=m*g
∑M= (-T*R) + (τ)=0 (Being τ the torque I apply) ⇒ -(m*g*R) + τ=0 ⇒ τ= 20 * 9,8 * (0,25/2)
τ=24,5N*m

 

[kuruman]

Your answer looks fine. The mass of the cylinder will be needed if the bucket has a given acceleration different from zero.

 

[Doc Al]

Your solution looks good to me. The mass of the cylinder was just to throw you off.

 

[OierL]

Ok thank you! Now I'll have to think which of the solutions choose, since my result is different from the others hahaha.

 

[Doc Al]

Now I'll have to think which of the solutions choose, since my result is different from the others hahaha.

The choice should be clear.

 

[kuruman]

Ok thank you! Now I'll have to think which of the solutions choose, since my result is different from the others hahaha.

That should not be too hard. Note that the numbers are given to two significant figures.