Bucket being lowered vertically by a rope

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In summary, the acceleration of a bucket is 3.78 m/s^2 when it is being lowered by a rope with a 163N of tension.
  • #1
e-zero
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Homework Statement



A 12.0kg bucket is lowered vertically by a rope in which there is 163N of tension at a given instant. What is the acceleration of the bucket? Is it up or down?

Homework Equations



Ft - mg = ma

The Attempt at a Solution



I solved for 'a' and got a = 3.78 m/s^2, but how do I figure out which direction?
 
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  • #2
With respect to the bucket, can the force of tension be upward? Downward?
 
  • #3
upward
 
  • #4
What is upward in terms of signs? Positive or negative?
 
  • #5
If the bucket is being lowered carefully would you say that it is accelerating upwards?
 
  • #6
I would say that if its lowering at a constant speed then there is no acceleration.

Also, I would say that, if anything, since its moving downwards it would be decelerating. Which I guess is the same as accelerating upwards??
 
  • #7
e-zero said:
I would say that if its lowering at a constant speed then there is no acceleration.

Also, I would say that, if anything, since its moving downwards it would be decelerating. Which I guess is the same as accelerating upwards??

Well you are right but there was no mentioning the fact that the bucket was being lowered at a constant speed. If that were the case then that means that mg = Ft which is not true in this case because it is not being lowered at a constant speed.

As for direction the answer to the question implies that the bucket is being pulled up and yet the question states that it is being lowered, so either I got confused or the question is misleading.
 
  • #8
How could mg = Ft if it were lowered at a constant speed?? That would indicate that the bucket is at rest.
 
  • #9
e-zero said:
How could mg = Ft if it were lowered at a constant speed?? That would indicate that the bucket is at rest.
No, it would just mean that the net force is zero and thus the acceleration, not the speed, is zero. The speed could be anything, as long as it remained constant.
 
  • #10
Damn, I missed again :/
 

FAQ: Bucket being lowered vertically by a rope

What is the force acting on the bucket when it is lowered vertically by a rope?

The force acting on the bucket is the weight of the bucket itself, which is equal to the force of gravity on the bucket's mass.

How does the length of the rope affect the speed of the bucket as it is being lowered?

The length of the rope does not affect the speed of the bucket as it is being lowered. The speed is determined by the force of gravity and the weight of the bucket.

What is the relationship between the acceleration of the bucket and the mass of the bucket?

The acceleration of the bucket is directly proportional to the mass of the bucket. This means that as the mass of the bucket increases, the acceleration also increases.

What happens to the potential energy of the bucket as it is being lowered?

The potential energy of the bucket decreases as it is being lowered, since potential energy is dependent on the height of an object and the bucket is moving closer to the ground as it is being lowered.

Why does the bucket not accelerate at a constant rate as it is being lowered?

The bucket does not accelerate at a constant rate because the force of gravity remains constant, but the weight of the bucket decreases as it is being lowered due to the work being done by the rope. This results in a decrease in the net force on the bucket, causing a decrease in acceleration over time.

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