Determine acceleration when lifting a bucket.

[zeralda21]

Homework Statement

A bucket of water is raised up out of
a well with a device of the rope, and
pulleys as shown in figure. The bucket is hanging from the
the lower hook and the upper hook is
attached to a fixed cross bar of the well. If
the mass of the bucket and the water together
is m, and the man pulls the rope with
a force F, how large is the span's acceleration
up? The mass of ropes and pulleys
can be neglected, as well as frictional forces.

http://bayimg.com/daOdPAAde

Answer: (3F/m)-g

Homework Equations

F=mg and maybe F=ma

The Attempt at a Solution

Due to gravity there is a force downward. Since the mass of the bucket and the water together is m, the downward force is mg. From figure I see that the device is constructed so that the cable runs three times between the bucket and the hook before I pull it. Therefore the force required for the bucket to move upwards is F=mg/3≥.

From here I am stuck. I know that F=ma and therefore a=F/m. However, if I insert F=mg/3 and m=mg, I get the wrong answer.

 

[LawrenceC]

You are forgetting about the weight. Acceleration is determined by the net force in F=ma.

 

[zeralda21]

You are forgetting about the weight. Acceleration is determined by the net force in F=ma.

The weight as in F=mg. Please explain, I can´t really see what I am doing wrong.

 

[LawrenceC]

The force up is 3F. What is the force down? You are considering it as if the bucket full of water were sitting on a frictionless horizontal surface and you are pulling it horizontally.

 

[zeralda21]

The force up is 3F. What is the force down? You are considering it as if the bucket full of water were sitting on a frictionless horizontal surface and you are pulling it horizontally.

I understand that the force upwards is 3F. And the force down is F=mg, caused by gravity. Is that right? How is now acceleration related. Well, F=ma, so 3F=3ma. From "you are forgetting about the weight", I understand it as 3ma-mg. So far so right? Sorry about my incompetence of the subject.

 

[LawrenceC]

The force up is 3F. The force down is mg. The net force is 3F-mg. The net force is what Newton's Second Law equates to the product of mass and acceleration. The mass is m not 3m.

 

[zeralda21]

The force up is 3F. The force down is mg. The net force is 3F-mg. The net force is what Newton's Second Law equates to the product of mass and acceleration. The mass is m not 3m.

Thank you LawrenceC. It makes sense now.