Calculating Force and Acceleration in a Bucket Pulley System

[Fused]

I found this question to be answered twice on this site, both by hallsofivy. However, I still don't quite get it. Please help.

A window washer pulls herself upward using the bucket pulley appartus. a. how hard must she pull downward to raise herself slowly at constant speed? b. if she increase this force by 15% what will her acceleration be? The mass of the person plus the bucket is 65 kg.

It was posted that I need to use the formula F=ma, i understand this part and I understand that there is no acceleration because there is constant speed. But how do I use what I know? The bucket and HEr is equal to 65. I multiplied this by 9.8 to find the weight which equals 637 kg. But this isn't the correct force. The answer should be 320, or as I found about half of the answer I obtained. What am I doing wrong?

 

[quantumworld]

are u doing part a?
are u sure they are asking for the force, or for the work done...?

 

[Fused]

Because the problem was in a chapter dealing with forces, I'm assuming that's what they're asking for. Also by asking how hard must she pull downwards, doeson't that ask for the force she has must exert onto the rope to pull herself down?

 

[Doc Al]

It was posted that I need to use the formula F=ma, i understand this part and I understand that there is no acceleration because there is constant speed. But how do I use what I know? The bucket and HEr is equal to 65. I multiplied this by 9.8 to find the weight which equals 637 kg. But this isn't the correct force. The answer should be 320, or as I found about half of the answer I obtained. What am I doing wrong?

Draw yourself a picture of what's going on. Let the "object" be the "bucket + woman". Draw all the forces acting on that object. Hint: How many ropes are pulling on the object? What must be the tension in the ropes? How hard must she pull on her rope?

 

[Fused]

Oh I see.. So because we are using a pulley system, there is tension on each side of the pulley . So would I solve 2T-mg = ma
2T-637 = 0
=318.5 or about 320.
So is it okay to assume that 1 pulley will always divide the force needed in half?

 

[quantumworld]

exactly...

 

[Fused]

Got part a. Thanks -

For part b. I take .15 x 320 = 48
320+48=368.
F= ma
368/65 = a
a= 5.66? What am I doing wrong here?
It should be 1.5 ...

 

[Doc Al]

Got part a. Thanks -

For part b. I take .15 x 320 = 48
320+48=368.

That's the force she exerts. So what's the new force on "bucket + woman"? Don't forget to consider all the forces: the ropes pulling up, gravity pulling down. Then apply F = ma using the net force.

 

[NateTG]

Also, remember that the tension is equal on both sides of the pulley, so if the woman pulling harder increases the tension on one side...

 

[Fused]

will I use Newton's formula to figure out this change in tension?

 

[Doc Al]

will I use Newton's formula to figure out this change in tension?

Hint1: You already figured out the change in tension in the rope. It was given.

Hint2: Before the increase in tension, the forces on the "bucket + woman" added to zero since she was not accelerating. So what additional force has been added? So the net force is now what?

Once you realize what the net force is, then use Newton's F = ma to find the acceleration.

 

[Fused]

T= 320 x .15 = 48 + 320 = 368 N
F=ma
368= 320a
a= 1.15 m/s^2 . This is correct! However, I have another quick question. For part a and for the first part of part b, I solved for the tension when they asked for her force. How is her force equal to the tension of the rope? Shouldn't it be different... ?

 

[Doc Al]

not so fast...

T= 320 x .15 = 48 + 320 = 368 N
F=ma
368= 320a
a= 1.15 m/s^2 . This is correct!

No it isn't! First, 368 N is just the tension in the rope, not the net force on the "object". Second, why did you put 320 as the mass? You know the mass of the "bucket + woman" is 65 kg.

Answer these questions, in order: (1) what is the tension in the rope? (2) what force do the ropes exert on the bucket + woman? (3) what is the weight of the bucket + woman? (4) what is the net force on the bucket + woman? (5) what is the acceleration?

However, I have another quick question. For part a and for the first part of part b, I solved for the tension when they asked for her force. How is her force equal to the tension of the rope? Shouldn't it be different... ?

The woman pulls on the rope and the rope pulls back on the woman. (Recall Newton's 3rd law.) What allows a rope to pull is the tension in the rope. If the woman pulls the rope with 10 N of force, then the tension in the rope pulls back on her with 10 N of force.

 

[Fused]

OHh I see. Though I did it incorrectly I got the same answer. Everything makes sense now. Thanks for the help!

 

[Doc Al]

Though I did it incorrectly I got the same answer.

Not sure what you mean, since a= 1.15 m/s^2 is not the correct answer.

 

[Fused]

Yes, sorry about that... I actually got 1.5 m/s^2.