How much work was done by the tension in the cable?

In summary, the question is asking for the work done by the tension in the cable as a 1500-kg elevator moves upward with a constant speed through a vertical distance of 25m. The tension in the cable must balance the force of gravity, so the total force on the object is 0. Therefore, the tension can be calculated as T=mg.
  • #1
brncsfns5621
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I think I have been staring at this question too long as I can not figure it out. I am sure the answer is simple:

A 1500-kg elevator moves upward with a constant speed through a vertical distance of 25m. How much work was done by the tension in the cable?

I know that W= (F cos 0)s, and that F= ma. What I can't figure out is the acceleration. It doesn't have one as it is moving with a constant speed. Any info on where to start?
 
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  • #2
F=ma when F is the total force on the object. Here, the total force is 0, since the object isn't accelerating, and so the tension in the cable must exactly balance the force of gravity.
 
  • #3
So F= 0 and T= mg?
 
  • #4
Yea, if F is the total force on the object (you can always use F to stand for only one contribution to the force, it's just then F=ma won't hold).
 

1. How do you calculate the work done by tension in a cable?

The work done by tension in a cable can be calculated by multiplying the force of tension by the displacement in the direction of the force. The formula for work is W = F * d * cos(theta), where F is the force of tension, d is the displacement, and theta is the angle between the force and displacement vectors.

2. What factors affect the work done by tension in a cable?

The amount of work done by tension in a cable can be affected by several factors, including the magnitude of the tension force, the distance over which the force is applied, and the angle between the force and displacement vectors. Additionally, the weight of the object being lifted by the cable can also impact the work done.

3. How does the work done by tension in a cable relate to the energy of the system?

The work done by tension in a cable is directly related to the change in energy of the system. If the cable is lifting an object, the work done by tension will increase the potential energy of the object. On the other hand, if the cable is lowering an object, the work done by tension will decrease the potential energy of the object.

4. Can the work done by tension in a cable ever be negative?

Yes, the work done by tension in a cable can be negative. This occurs when the displacement is in the opposite direction of the force of tension, resulting in a negative value for work. For example, if the cable is lowering an object, the displacement vector will be downward while the tension force is upward, resulting in a negative value for work.

5. How can the work done by tension in a cable be used in real-world applications?

The work done by tension in a cable is used in many real-world applications, such as elevators, cranes, and suspension bridges. It is also relevant in activities like rock climbing and bungee jumping, where the tension in a cable is used to lift or support a person. Understanding the work done by tension in a cable is crucial for designing and optimizing these types of systems.

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