One-dimensional dynamics question

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In summary, the student lowers herself down 40m at a constant speed of 1.0 m/s. The chair has a mass of 35kg and the rope has a force of 343N. If the student lost 5kg in the time between editions of the book, then the force of the rope would be 490N.
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Ascendant78
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Homework Statement



A 60kg student lowers herself down 40m at a constant speed of 1.0 m/s. The chair has a mass of 35kg. Find the force of the rope. (See image)

aZxccET.jpg


Homework Equations



I was using force equations in attempts to solve for the problem.

The Attempt at a Solution



Fchair+Fstudent-Frope-Frope=m(a)
35(9.8)+60(9.8)-2Frope=95(0)
343+588-2Frope=0
2Frope=931
Frope=465.5N

Although the answer I got above was 465.5N, the answer listed in the back of the book was Frope=490N. I am at a complete loss as to what I am doing wrong here? I did a similar problem where the person was traveling upwards like this at a constant velocity and got it right. Not sure what changed here that I am not taking into consideration?

I am also curious after having done a similar problem, since the force is split into 2 parts, the force quantity for the rope would be the value for each rope individually, correct (one attached to chair and the one held by the student)? I just want to make sure I am understanding this correctly. Also, if that is the case, then if I were asked what the total force being applied to the rope was, it would be double the value to account for each side being pulled, correct?
 
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  • #2
Your solution looks fine to me. Could be the student in question lost 5kg in the time between editions of the book :smile:
 
  • #3
gneill said:
Your solution looks fine to me. Could be the student in question lost 5kg in the time between editions of the book :smile:

Lol, in this book, I would not be surprised. As you can tell from the image, this book is not exactly top of the line (Spiral Physics).

Anyway, thanks for letting me know because it was driving me absolutely crazy.
 

1. What is one-dimensional dynamics?

One-dimensional dynamics is a branch of mathematics that studies the behavior of systems that can be described using one variable. It involves the study of how a single variable changes over time under the influence of a given set of rules or equations.

2. What are some examples of one-dimensional dynamics?

Some examples of one-dimensional dynamics include the motion of a pendulum, the growth of a population, and the change in temperature over time. These systems can be described using a single variable, such as angle, population size, or temperature.

3. What are the key concepts in one-dimensional dynamics?

The key concepts in one-dimensional dynamics include equilibrium, stability, and bifurcation. Equilibrium refers to a state where the system remains unchanged over time. Stability describes whether a system returns to equilibrium after being disturbed. Bifurcation refers to a sudden change in the behavior of a system when a parameter is varied.

4. How is one-dimensional dynamics used in real-world applications?

One-dimensional dynamics has many applications in various fields, including physics, biology, and economics. It is used to understand the behavior of systems such as chemical reactions, population dynamics, and stock market fluctuations. It also helps in predicting and controlling the behavior of these systems.

5. What are the tools and techniques used in studying one-dimensional dynamics?

The tools and techniques used in studying one-dimensional dynamics include mathematical models, differential equations, and computer simulations. These tools help in analyzing the behavior of complex systems and predicting their future behavior. They also allow for the exploration of different scenarios and the identification of patterns and trends in the data.

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