Determine acceleration when lifting a bucket.

In summary: So when I put it together F=ma and the downward force is mg, I get a=F/m= (3F-mg)/m = 3F/m-g. In summary, the span's acceleration upwards is (3F/m)-g.
  • #1
zeralda21
119
1

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 [Broken]

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.
 
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  • #2
You are forgetting about the weight. Acceleration is determined by the net force in F=ma.
 
  • #3
LawrenceC said:
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.
 
  • #4
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.
 
Last edited:
  • #5
LawrenceC said:
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.
 
  • #6
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.
 
  • #7
LawrenceC said:
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.
 

What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction.

How is acceleration calculated?

Acceleration can be calculated by dividing the change in an object's velocity by the time it took to change. The formula for acceleration is a = (v2-v1)/t, where a is acceleration, v1 and v2 are the initial and final velocities, and t is the time elapsed.

What factors affect the acceleration of a lifted bucket?

The acceleration of a lifted bucket can be affected by the force applied to lift it, the mass of the bucket, and the force of gravity pulling it downwards. Friction and air resistance may also play a role in the acceleration.

How can the acceleration of a lifted bucket be measured?

The acceleration of a lifted bucket can be measured by using a stopwatch to record the time it takes to lift the bucket from one point to another, as well as by measuring the distance and calculating the change in velocity. Alternatively, specialized equipment such as accelerometers can be used to directly measure the acceleration.

Can the acceleration of a lifted bucket be negative?

Yes, the acceleration of a lifted bucket can be negative if the bucket is being lowered rather than lifted. In this case, the acceleration would be in the opposite direction of the force applied to lift the bucket.

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