Tension in a Rope: Understanding Acceleration in Lifting a Bucket of Water

In summary, a person is lifting a 4.25-kg bucket of water from a well with an acceleration of 1.80 m/s². The question is what is the tension in the rope? The net force on an object determines its acceleration, and given the acceleration, the net force can be found. Newton's second law states that net force equals mass times acceleration. In this scenario, there is a force pulling up, the tension in the rope, and a force pulling down, the weight of the bucket and water. The net force is equal to the tension minus the weight. By setting this equal to the mass times acceleration, the tension can be calculated.
  • #1
izmeh
I have the following problem

Pulling up on a rope, you lift a 4.25-kg bucket of water from a well with an acceleration of 1.80 m/s². What is the tension in the rope?

What part exactly does the acceleration play in this scenario?
 
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  • #2
Originally posted by izmeh
What part exactly does the acceleration play in this scenario?
The net force on an object determines its acceleration. Given the acceleration, you can find the net force. Tell us what you know about Newton's second law.
 
  • #3
net force = ma
a = f/m
1.80 = f/4.25
f = 7.65
 
  • #4
First step: Describe all the forces acting on that bucket! Then add them up to find the net force.

Draw yourself a diagram.
 
  • #5
there is the force of me pull it up @ 1.80m/s²
the mass 4.25 pulling down...
 
  • #6
Originally posted by izmeh
there is the force of me pull it up @ 1.80m/s²
the mass 4.25 pulling down...
There is a force pulling up, that's the tension (T) in the rope. There's also a force pulling down, the weight (not mass!) of the bucket&water. (Note: gravity pulls on the mass, that pull is the weight. You can calculate the weight by multiplying the mass by g, the acceleration due to gravity. g = 9.8 [m/s2])

The net force is (choosing up as positive):

Fnet = T - mg

From Newton's second law:

Fnet = ma

Now it's your turn. You know a (it's 1.8 m/s2 upwards) and you know m . Find T. Give it a try.
 

1. What is tension in a rope?

Tension in a rope is the force exerted by the rope when it is pulled or stretched. In other words, it is the force that keeps the rope taut and prevents it from breaking.

2. How does tension affect the acceleration of lifting a bucket of water?

The amount of tension in the rope directly affects the acceleration of lifting a bucket of water. The greater the tension, the faster the bucket will accelerate. This is because tension is one of the forces acting on the bucket, along with gravity, and it contributes to the overall net force on the object.

3. What other factors besides tension can affect the acceleration of lifting a bucket of water?

Besides tension, the mass of the bucket and the strength of the person lifting it can also affect the acceleration. A heavier bucket will require more force to lift, and a stronger person will be able to exert more force, resulting in a greater acceleration.

4. How can understanding tension in a rope help in real-world situations?

Understanding tension in a rope can be useful in many real-world situations, such as construction, engineering, and sports. It can help determine the strength of ropes needed for different tasks, calculate the maximum weight that can be lifted, and ensure safety in activities like rock climbing or zip lining.

5. What is the difference between tension and weight when lifting a bucket of water?

Tension and weight are two different forces that act on an object when lifting a bucket of water. Tension is the force exerted by the rope, while weight is the downward force of gravity on the bucket. Both forces contribute to the acceleration of the bucket, but they are not the same.

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