Hanging bag by a vertical rope

In summary, the question discusses a mail bag hanging from a vertical rope and being displaced by a postal worker to a position 2.2m sideways from its original position. The question asks about the amount of work done by the rope during this displacement. The solution involves calculating the tension in the rope and finding that it is zero, which means that the work done by the rope is also zero. The justification for this is that the length of the rope does not change during the displacement. This is further supported by the fact that the tension is perpendicular to the displacement.
  • #1
Toranc3
189
0

Homework Statement



A 115kg mail bag hangs by a vertical rope 3.3m long. A postal worker then displaces the bag to a position 2.2m sideways from its original position, always keeping the rope taut.

As the bag is moved to this position, how much work is done by the rope?

Homework Equations



W=F*d

The Attempt at a Solution


Tx=-Tcos(theta)
Ty=Tsin(theta)

W=-Tcos(theta)*d

T/3.3m =mg/2.5m to get T

I wanted to know why this is zero. Doesn't the Tension have a negative component in the opposite direction of motion, so the work done will be negative. The answer is zero but I just wanted an explanation on this one. Thanks!
 
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  • #2
Wrope = Fropedrope.

If Wrope = 0 and Frope (tension) is nonzero, what must be true about drope?
 
  • #3
its zero
 
  • #4
ive got it! thanks!
 
  • #5
Which it is, due to the length of the rope not changing. All clear?
 
  • #6
lewando said:
Which it is, due to the length of the rope not changing. All clear?

Wouldn't it also be correct to say that T is perpendicular to the displacement?
 
  • #7
No, it is at some angle, but not 90°.
 

1. How does the vertical rope support the weight of the hanging bag?

The vertical rope supports the weight of the hanging bag through tension. When an object is suspended from a rope, the rope experiences tension, which is a pulling force that acts in all directions along the length of the rope. As long as the tension force in the rope is greater than the weight of the bag, the bag will be supported.

2. What factors affect the tension in the vertical rope?

The tension in the vertical rope is affected by the weight of the hanging bag, the length of the rope, and the angle at which the rope is attached to the bag. The greater the weight of the bag, the more tension is required in the rope to support it. Similarly, a longer rope or a steeper angle will require more tension to support the bag.

3. How does the angle of the rope affect the tension?

The angle at which the rope is attached to the hanging bag affects the tension in the rope. The smaller the angle, the greater the tension needed in the rope to support the weight of the bag. This is because a smaller angle increases the horizontal component of the tension force, making it more difficult for the rope to support the weight of the bag.

4. Can the hanging bag swing back and forth without breaking the vertical rope?

Yes, the hanging bag can swing back and forth without breaking the vertical rope as long as the tension in the rope remains greater than the weight of the bag. The tension in the rope will change as the bag swings, but it will not exceed the maximum tension that the rope can handle without breaking.

5. How does the length of the rope affect the swinging motion of the bag?

The length of the rope affects the swinging motion of the bag by determining the period, or time it takes for one complete swing, of the bag. A longer rope will have a longer period, meaning the bag will take longer to swing back and forth. A shorter rope will have a shorter period, resulting in a faster swinging motion for the bag.

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