A stack of books (conflicting answers)

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In summary, the minimum horizontal force needed to start sliding the top five books off the bottom one is 5N, which is equal to the coefficient of friction (0.2) multiplied by the weight of the books (5N). This is because the force applied must be equal to the resisting force in order for there to be no acceleration and for the books to just barely start moving.
  • #1
ashum
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There are six books in a stack, and each book weighs 5N. The coefficient of friction between the books is 0.2. With what horizontal force must one push to start sliding the top five books off the bottom one?

For the five books:
m * a_max = u_s * m * g
a_max = u_s * g
a_max = 0.2 * 10 m/s^2 = 2 m/s^2

For the system:
F_max = M * a_max
F_max = 3 kg * 2 m/s^2 = 6N

Was there a mistake in the approach I took? Apparently, the correct answer is 5N, since you only need to find F_s between the five books and the sixth book which is u_s * m * g. However, this would mean each book gets an applied force of 5/6 N. With a mass of 0.5 kg each, each book would only accelerate at 1.67 m/s^2, which is not equal to a_max (2 m/s^2). Any thoughts?
 
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  • #2
Ahh, the equation F=ma should be written as F_net=ma. So in this case, the force you are applying is not F_net, F_net also needs to take into account the friction that is resisting the motion.

You should assume that there will be no acceleration, and you want to find the minimum force that will just barely start the books to move. For this to occur, the force applied has to be equal to the resisting force.

F = u_s * m * g

Note here that since we are letting the applied force equal the resisting force, F_net = 0, hence there is no acceleration.
 
  • #3


It appears that there may be a mistake in the given information. If each book weighs 5N and there are six books in the stack, the total weight of the stack would be 30N. This means that the maximum force required to start sliding the top five books off the bottom one would be 30N, not 5N as stated in the conflicting answer. This can be calculated using the formula F_max = u_s * m * g, where u_s is the coefficient of friction, m is the mass of the top five books (2.5 kg), and g is the acceleration due to gravity (10 m/s^2). This would result in a maximum force of 5N for each book, which is consistent with the given information. Therefore, the correct approach would be to find the maximum force required for the entire stack, not just for the top five books.
 

1. What causes books to have conflicting answers?

Books can have conflicting answers due to a variety of reasons. One possible reason is that the information in the book is outdated or has been disproven by newer research. Another reason could be that the authors of the books have different perspectives or interpretations of the same information.

2. How can I determine which answer is correct?

It is important to critically evaluate the information presented in the books and consider the credibility of the sources. Look for supporting evidence and consider the qualifications of the authors. It may also be helpful to consult other sources or experts in the field.

3. Are there any strategies for dealing with conflicting answers?

One strategy is to look for common themes or ideas among the conflicting answers and try to understand the different perspectives. It can also be helpful to seek out additional sources and compare the information presented. Ultimately, it is important to carefully consider the evidence and make an informed decision.

4. Can conflicting answers be a good thing?

Conflicting answers can be beneficial in that they encourage critical thinking and allow for different perspectives to be considered. It also highlights the importance of evaluating information and not blindly accepting everything we read.

5. How can conflicting answers impact scientific research?

Conflicting answers can lead to further research and investigation to determine the most accurate answer. It can also spark debate and discussion among scientists, leading to new insights and advancements in the field. However, it is important for scientists to carefully consider conflicting answers and thoroughly evaluate the evidence before drawing conclusions.

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